Coming from someone who did card magic years ago, getting a perfect shuffle isn't actually too hard with a good deck of cards and the right shuffling technique. In fact, I was even able to do enough perfect shuffles in a row that it would bring the deck back to the original order. That being said, I agree that it should be random for a random person shuffling a random deck. Great video
yea I used to carry a deck of cards in school and would be permananly shuffling between classes. After a year of that I got pretty consistant at getting them.
If you do 8 “out” Faro shuffles the deck gets back to the initial state. The “out” faro keeps the top and bottom card the same every time. If you do an “in” faro where the top and bottom cards are interleaved, it takes 52 perfect shuffles to get back to where you started!
Yeah agree , Faro shuffle is not that hard as ppl may think, with a bit of practice (like 10-20h , don't actually remember how much time it took me but somewhere around that time) , you can get pretty consistent with it to the point where you can use it in magic tricks. Had to learn it for a trick , but it was more useful for some cardistry (double fans , waterfalls etc).
This is true. As someone who also dabbled in card magic as a child and is now a professional dealer, I can do a perfect shuffle almost every time just by making sure my thumbs are moving at the same rate. In my job, though, I purposefully make sure not to do this so cards are shuffled fairly.
I'd say that most channels have videos with titles and thumbnails that _sound_ interesting, but you get bored five minutes into the video. This channel is the inverse lol.
@@AlphaPhoenixChannel Card shuffling is deeply related to mixing of Markov chains. In addition, there is a rather simple way to model faro shuffling. Here is the most famous reference on the subject (proving a theorem which applies to many other Markov mixing problems: there is a critical number of shuffling below which you only explore "a few" configurations; no need to shuffle more than that number since the shuffling is already perfect) projecteuclid.org/journals/annals-of-applied-probability/volume-2/issue-2/Trailing-the-Dovetail-Shuffle-to-its-Lair/10.1214/aoap/1177005705.full statweb.stanford.edu/~cgates/PERSI/papers/aldous86.pdf en.wikipedia.org/wiki/Markov_chain_mixing_time www.ams.org/publicoutreach/feature-column/fcarc-shuffle
I got a royal flush of hearts on the deal once when we were playing poker at school and absolutely no one believed me when I tried to tell them I didn't cheat. I was the dealer so it made it harder lol.
There is something incredibly interesting (and somewhat bizarre) about random distributions. You measured atomic decay (which are supposed to be "truly" random, at least from a quantum physics point of view) and card shuffling (which are supposed to be NOT random at all, at least from a quantum physics point of view). What I think is very fascinating is that there the same Mathematics that can be used to study "true" randomness also works for uncertain events. Even something fully predictable (like a pseudo-random generator) becomes more and more indistinguishable from "true" randomness the less and less you know how it works.
@@treyt6474 That is exactly what quantum mechanics means. A system can be both deterministic and also unpredictable if the state of that system cannot be measured without altering it in a predictable way. To be more precise, by "predictable" I mean an experimenter could correctly call out in advance an arbitrary series of future states with better accuracy than random chance. Flipping a coin and calling out "it will come up heads about half the time" doesn't count any more than saying "it will definitely be either heads or tails": those are facts about the system as a whole and do not demonstrate an ability to predict the behavior of the system. To be predictable, one would have to be able to beat random chance. In the case of a coin flip, one would have to be right more than half the time. How much more would indicate how predictable the system is. QM says you can't predict the decay of a nucleus any better than random chance. You can predict that it will decay and you can even calculate an element's half-life, but if you try to call out the numbers coming from Brian's box, you won't get the answer right any more often than someone else just calling out the numbers from another similar box or another person just calling out the same number over and over.
Somewhere in the multiverse, 10,000 monkeys are taking a break from randomly writing Shakespeare, and playing a perfect game of bridge after shuffling way too many times. 😅
I love how you edit over parts with editing Brian. Takes a lot of self reflection to be like "that was ass, I'm gonna dub over it" and then tell the viewers that. 😂 Chad move
I haven't watched the video yet, but I am aching to share my story. Basically in 2015ish I was adjudicating a debate competition. While we were waiting for the next round me and a few judges started playing a board game called "Ne se surdi, choveche", which is the german Mensch ärgere Dich nicht, or as Wikipedia claims also known as Parcheesi, Ludo, Trouble etc. We were just killing time and this was just a game that happened to be laying around in the resting room we were provided with at the school, the venue where the competition was hosted. It's a basic and heavily luck dependent game with the players moving their pieces by rolling a six sided die and eliminating opponent figures. If you roll a six, you can move six spots and roll again. That's basically 90% of the rules. I don't really know how to best tell this story and explain everything that happened. All I can tell you is that it was extraordinary, there was laughter, maniacall laughter, there was sadness, there were offended friends and there were astronomical probabilities, which led to personal confusion and disappointment. One thing to note: we decided to roll two dice instead of one so as to at least be able to finish the game in time. I'm not convinced now that this was the best option to finish the game early as, as we soon found out it meant that doubling or tripling of your turn happened way less frequently. And that chance to do things twice or to use special features is the only "strategic" moment of the entire game. Now on to the story proper. A few rounds in the game and on my turn I rolled two sixes. This wasn't the first time it happened in the game, I think, but it was amongst the first ones and definitely many rounds in. I moved my pieces and rolled again: 12. We laughed and my friends told me I was very lucky. I played, I rolled again. Guess what: another 12. Everyone was amazed. We were beside ourselves laughing our asses off. I rolled yet again. 12. Now I was laughing pretty maniacally, but my friends were in disbelief. One of them, especially. I played my turn and rolled again. 12 as expected. Now the guy that was pissed last time, asked me directly: "how are you doing this?" His tone revealed curiosity, little anger. People were confused, but not yet agitated. I told him I haven't done anything, but I was still laughing and pretty much shaking. I was more confused than amused tbh. I didn't want to anger anybody while also being a bit annoyed at being suspected of something. On retrospect if I was somehow cheating and confessed about it AND showed them how I did it, I am certain that people would have even taken it in jest and be entertained by my skill. The reality, however, was that I was in fact not faking it and was just being lucky. I guess thinking that it would ease the tension or at the very least move the game along when the time came to roll, I just dropped my dice on the table without rolling them, from about 30~40cm. Well... it did not help. They spun and settled on 12. Sixth time in a row. I was still chuckling, but inside I did not know what to do. People were reeeally annoyed. I said that this was my final roll and will pass on to the next person. Now that I think about it this might have made me even more sus, but oh well hindsight is 20/20. Next time my round came people were convinced I couldn't possibly roll 2 sixes again. We were joking about my incr. luck and being friendly again. Things were getting back to normal. That is until I rolled 12. One of my friends said: "Here we go again", in a friendly manner, but some undeclared threat or tension was present. After I played my turn and was ready to roll again, people were on the edge of their seats. The tension was very palpable. 12. Again. "Bullshit" I heard. ("Gluposti") ''Impossible" someone said, "Nee, ti se ebawash", ( "You are messing with us") another one exclaimed. They politely, but firmly on the edge of ordering told me to roll with another set of dice. I did willingly, almost eagerly. One of dice was green and very small like for backgammon and the other was regular size. (The new ones) I rolled with them. The green bounced and shoot up from the wall of the cardboard lid we were throwing them in. I immediately regretted changing dice as I felt as if I was admitting smtg. The dice spun wildly, but when they settled both were sixes. The guy that originally was quick to get annoyed said "You must be spinning them somehow? Tell us how you are doing this? Come on..." I again, declined of having done anything illegal or mischievous. He told me next time I want you to roll with my phone. Now that really pissed me off, both the demand, which I found demeaning and also bcs of my rolls, bcs I just wanted a casual game with just jokes and having a good time and not having this "cross-examination" and seriousness. Ultimately I did "roll" with his phone. It was an app of some sort or just a random number generator. Well I got 12 regardless. For the tenth time. Another friend accused the person who handed me the phone, the one who has been so far the most vocal, and myself of staging the whole thing. Saying it "wasn't funny" and that it was all quite "boring", while being visibly upset. We were all vaguely aware of how miraculously improbable was for the rolls to happen naturally. I told him earnestly and trying to calm things down that I was not cheating and that our first friend has nothing to do with it. Inside I was bitter and perhaps some of that showed. I told him if he wanted me to I can use his phone and whatever app he wanted me to next time I roll. I again said that I am passing my turn to the next player to ease the tension. This time it was less effective as no one really wanted to keep playing. He said I should just stick to the original dice and not to do stupid stuff. He clearly meant that I was so far HAVE BEEN doing stupid stuff. Words were heated now. People were not having a good time. We agreed that henceforth if you roll two sixes you get one extra roll PER TURN and not as originally each time you roll a set of sixes. Play continued. People really did not want to play, or talk, or interact. The vibe was dead. Next time it came my turn, I rolled and I rolled 12. People now just accepted it with quiet judgement. I felt miserable. I felt like I was just purposefully hurting my friends. I did not enjoy it one bit. Now thinking back I was a bit like an automaton. I didn't really have a say in what was happening, yet I was causing this distress. I had no control over the rolls, I could only try and deal with the outcome of each one. I felt powerless in a moment in which I should be feeling powerful. I am in the context of the game winning after all. And AND we are all witnessing smtg. Incredible. I rolled for the 12th time and for the 12 time two sixes stared at me from the bottom of the cardboard. Sharply the second friend said: "Go on, roll a third time." I told him it wasn't my turn anymore, but I ultimately agreed. Finally it was 5 and 3. Next turn it wasn't double sixes. The magic was gone. We carried on for a few more rounds, but we never finished the game. We ended it early and just did other stuff for the remainder of the time. For the rest of the day people were bitter with me. Later when I came back home I reflected on the day and I thought about how astronomical were the odds of this happening. To me it became abundantly clear that I would never witness another event of such a rarity. Or to put it less fatally the chances of me seeing or participating in two events of such rarity are infinitecimally significant. I felt and still feel like I have "wasted" my luck, which is bull, but it still feels like it. Of course from the POV of the dice there is one six in a row 12 roll, a 4 of sorts in a row and a 2 in a row, bifurcated by the turns of other players, (provided you count the changing of the dice and the phone as a valid rolls). But from my POV you have 12 times I have rolled consecutively, one after the other the same set of two, the chances of which optimistically is 1 to 4.73838134e18. This might be the first and only time this will happen in the history and the future of the universe and for all it's worth it was "wasted" on a stupid board game, observed by no one but the participants, which were largely pissed for unwillingly taking a part in the event. Ultimately I rolled 12 times two sixes and felt bad about it.
Wow. Just wow. "Čovječe ne ljuti se" is called around here. Lots of fond memories with that game. Yeah, randomness sometimes laughs you in the face with a strange grin. Devil's business.
One thing I think is extremely important that you didn't mention when talking about physically doing the tests instead of simulation, is the cards you used. The cards you used are pretty thin cards with a glossy looking top. They will bend more easily, stick to each other slightly more, and most importantly stick to your thumb more. I think it might surprise you how drastically the probability would increase if you used newer decks of slightly higher quality cards like bicycle cards. I would guess with your level of shuffling after this project that it would already by down by nearly 2 orders of magnitude from your 1 in 119k number. This is assuming you use the same method of course, as a better method for perfect shuffling where you count out 26 and sort of just shove them into each other can get a perfect shuffle every time with practice, but I'm sure you know this.
@@AlphaPhoenixChannel I feel like you need to make a Shuffling machine to check the results against human error as issues like surface finish would be far less important. Obviously if someone wanted to go balls to the wall it could get a perfect every time but if one simply simulates the motion of it in machinery and compares the statistics of that against your current batch it could take any error bars to virtually zero.
It's really sobering to realise someone probably ended up with a perfectly shuffled deck at some point but they never knew about it because they continued shuffling before dealing.
I used to do magic as a kid for about 6 years and was shuffling cards constantly, and as I was watching this video I tried to shuffle a deck and I noticed that my shuffles almost never had a run more that 4 and rarely had one that was 3, so I agree that more shuffling makes you better at ferro shuffling. And great video love it as usual!
Speaking of underlying threads of mathematics, I just happened to randomly spend my entire day fiddling with card shuffling in the context of random number generation, within 24 hours of you posting this video, having not known about it prior to now. What an excellent and informative end to a perfect day of post-holiday putzing this video was, and a fun coincidence too.
The outro reminded me of a story: Back in high school, I was really into Dungeons and Dragons. I had an idea for a certain campaign that involved giving the players actual, genuine loaded dice as a puzzle mechanic. This had me looking into internet articles on loaded dice, and how to get them to a certain degree of “unfair,” and how to analyze… But most of what I found was how to tell if a die IS fair - the chi squared test, where getting a really low value means the die is fair. I thought “Huh, neat!” and then moved on. Years later, in college, I was talking with a friend about their research. They mentioned trying to raise their chi squared value, and I said, “Wait, don’t you want that to go DOWN?” And they said, “No? You always want it to go up, for more precision!” It turns out they’re both two sides of the same (fair) coin - you can use chi squared to prove a set of data is remarkably precise, but you can use it for the opposite purpose, to prove a set of data is remarkably IMPRECISE. We just came at it from opposite ends of the same problem. Also, just found you from your Algorithmic Gerrymandering video, and I really love what I’ve seen so far. Definitely sticking around!
(I am at 16:16) I mean, yeah! I do card magic as a hobby, and I am actually very good in faro shuffle. I can pull perfect faro shuffle almost any time I want, and even when I don't want. I can do that 8 times in a row, and then the deck just unshuffles itself. Idk, shuffling the deck of cards stopped to be some kind of random process for me at one point.
Wooo, Math! Love the conclusion. How many times have people asked me, "why is that important" or "why are you learning that?" when it is completely unrelated to my specialties. Well, because the more you know about the nature of the universe, the more connections you can make. It's the opposite of the saying "when all you have is a hammer".
So glad I found this channel. I had a realization while watching through your videos that I wasn't as smart as I thought I was. It's given me great motivation to see the things you can accomplish with an extensive understanding of science. I put this channel right next to Ben at Applied Science in terms of helping me push my understanding of the universe forward. I sometimes spend an hour on Wikipedia afterwards. Great stuff.
There's another factor you weren't considering: the split of the deck. The Farro shuffle is possible if and only if you split the deck perfectly in half, i.e. 26 and 26. The likelihood of that in a typical shuffler's hands isn't tiny, but it'd probably still add another order of magnitude or so.
This is exactly what I was wondering from your geiger meter random number generator video. That is awesome, such a cool concept! I just ordered all the stuff to make something like this!
for an example in a given playing card game, you don't need to perfectly Faro shuffle all 52 cards. If 4 players are only dealt 4 cards each, you only need to have perfectly shuffled the top 16 cards. This should make the likelyhood significantly higher, as possibly a majority of the time, your "error" in a non-perfect shuffle comes from the lower majority of the deck, which can be disregarded.
Your excitement for math and how it describes our physical world is great. I have the same excitement. Unfortunately, I struggled with it in school and never pursued it after.
Here's an idea for a convenient and money saving way to use quantum mechanics to generate random number. Get one of the older smoke detectors, most of the circuitry is done, and mod the board, so that the Americium decay detection timing is conditioned and shown on one of those 7-segment blocks
It can also be done solely with monolithic clock generators and flip-flops. Feed 32 clock generator outputs into D-inputs of 32 flops which are all clocked by the same clock at some fairly high rate. The first stage flops will go metastable with a fairly high frequency. Clock the output of each first flop stage into a one or more flops in series to capture a 32-bit value, some bits of which may be random as the metastabilities are resolved. It isn't necessary to feed different frequencies into the first stage flops as the clock generators will come up in completely unrelated phases to each other.
@@garymartin9777 you know, you could probably do a sample and hold of RF tuned to the cosmic background microwave, whether or not that truly is random is something well outside my knowledge!
Fun video. My own tendency is to consider almost anything with mathematical precision, and it is brilliant, entertaining, and very educational to instead have this fast-paced hands-on approach that adds in bits of mathematical modeling later. There's a simple model of a riffle shuffle that I have used in teaching where a card is equally likely to fall from the left hand or the right hand at each instance of a card falling. Of course it is a simplification, but I never thought of the physical reason for why it is wrong. As explained in the video, the relative motion between fingers and deck on the side where a card has not fallen is continuing, creating a negative correlation. The discussion of edge effects is a great lesson for trying to learn from empirical data. Very nice.
Magicians use a type of shuffle called a Faro shuffle which is performed by splitting the deck in half, holding each half in separate hands, then carefully interleaving the two halves so that you alternate a card from the top half, then a card from the bottom half, and so on. It is exactly the same as a perfect riffle shuffle where the cards alternate, card from left hand, card from right hand and so on. Magicians like doing the Faro shuffle because it takes skill and is showy. So, here is where this is leading. An out shuffle is a shuffle where the top card stays on top, and the bottom card stays on the bottom (they stay on the OUTside). An in shuffle is where the top card goes to the second position, i.e., it moves down one position, and the bottom card moves up one position. It only takes 8 perfect out shuffles to restore the deck to its original order. It does not matter if it is a Faro shuffle or a riffle shuffle as long as the cards are interleaved in alternating order and the top card remains on top. Here is the math. Let n = number of cards in deck, in this case n = 52, but any number can be used. Let k = position a card in the deck. k = 1 for the top card, k = 52 for the bottom card. The top half of the deck has a different rule for the movement of the cards than the bottom half of the deck. 1) Top half, k 26, the card moves to 2k - 52 The card in position 1 remains in position 1. 2 x 1 - 1 = 1 The card in position 52 also remains in position 52, 2 x 52 - 52 = 52 What about the rest? let's look at the cycles. 2 -> 3 -> 5 -> 9 -> 17 -> 33 -> 14 -> 27 -> 2 It should be obvious that that a card in any of the positions this sequence will end up back in its starting position in 8 shuffles. If we do this for the remaining positions, we find it takes 8 shuffles for any card to return to its starting position. Ther is one odd exception, 18 -> 35 -> 18. This cycle has two steps, but that is okay because the cards will be back in the original positions in 8 shuffles.
He gets longer runs in the middle because of the sound/feeling that gets easier to identify with a rhythm (getting “in the groove”) and with a musical pitch (440 cycles per second = A). I’m sure that given an infinitely tall deck mechanically fed to his hand that he could eventually and intuitively “hear” and “feel” the perfect rhythm… like learning to bounce a basketball without looking and even with your eyes closed by hearing the bounce and contact slap steady rhythm. Human hearing is amazing.
Regarding a unifying thread of physics that belies disparate things, it seems that if you take any set of things and look hard enough you will find some mysterious connection. Not that one creates their own correlation, but rather that ultimately there is really only one 'thread' that ties every perceivable thing together no matter how disparate. "What is it that breathes fire into the equations and makes a universe for them to describe?" I love your insight and passion for exploration of both the fantastic and (seemingly) mundane. Keep manning the bellows. 😉
apologies if i'm doing a cunningham's law here, but shouldn't the geiger tube setup be a textbook poisson distribution? the probability mass function does have an exponential in it. but that low part toward the start isn't a glitch, it's a natural part of the distribution
It _should_ be a textbook Poisson distribution, since arrivals at the Geiger tube are uniformly distributed in time, given an average rate. I think wait times in that case would then be exponentially distributed, so the glitch at the start is indeed a glitch. If you looked at the number of arrivals within time periods then that would indeed be the way you describe it iirc.
At 7:58 he shows the results of the actual Geiger tube and it IS a Poisson distribution. Only now he calls the low part a glitch because he expects an exponential instead of a Poisson distribution.
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Isn't it a textbook Poisson *process*, which would result in an exponential distribution? The definition of an exponential distribution is that it represents the time between events of a Poisson process. The Poisson distribution represents the number of events within a fixed period of time, which is not what he was measuring.
Yes, you are right, I was wrong. It is a Poisson process and the distribution of wait times between events should have been an exponential distribution, not a Poisson distribution. So the glitch must be caused by his setup, just like he said.
It is important for viewers to know that any random numbers generated by a computer are not at all really random. Rather they are a predictable sequence of numbers, which taken over their entire range (usually 32-bits), are random or close to it. But number-to-number there is little to no randomness. This is called pseudo-random. Depending on the quality of sequence seed, the sequence may repeat with far fewer than the maximum possible number of entries. A good seed is a large prime number of equal or close to equal the number of bits of the sequence generator (e.g. 32). If you have the option to select the seed, lists of primes can be found online. Two calls to the sequence generator starting with the same seed gets exactly the same sequence. This is handy when testing because the pseudo-random sequence used by an application will probably cause the same output, time after time, given that nothing else changes. It is possible to generate truly random numbers for use with an application but this requires extra hardware not found on a p.c.
As I watched I realized that you display an incredible scientific honesty about your own work; self evaluation leading to low marks for performance displayed is, sadly, increasingly rare in public performance. I suspect you are your very harshest critic.
Once I heard about perfect shuffles leading back to the same deck and how it could be used for some of the most ultimate card tricks I started trying to perfect doing a casual perfect shuffle. It was super hard and really boring so I eventually stopped focusing on it but I continued having a deck of cards at my desk. I have ADHD so when I am thinking about something at my desk, I like to keep my hands busy with something so I have a lot of things on my desk to mess with and even though I stopped trying to do a perfect shuffle, I did start just casually shuffling to keep my hands busy as it is immensely satisfying to shuffle cards well. Over time I got to a point where I could perfect shuffle about half the deck and do about a dozen shuffles in a minute. I haven't done any statistical analysis but I could probably get a perfect shuffle in less then a hundred attempts, but I am still far from being able to do it to the level required for insane magic tricks.
Dear Brian, I think the histogram at 08:00 is actually perfect as is. Yes, gas detectors have a bit of dead time, which might cause this attribute, but I think it is a necessary feature of this compound probability density function. Since the particles are coming from random directions and sources, the pulses should follow a Poisson distribution that has a root at t=0. After the peak it will indeed resemble the exponential distribution, but it should be 0 at t=0. Don't take this to heart, though, I'm not a statistician, but I remember doing an experiment resulting in pretty much the same histogram as yours.
I "liked" this video pretty immediately which means about 2/3 times thoughout the video I wanted to "like" it again and got disappointed because I saw I already "liked" it lmao. It's just a good video and I love your hilarious attitude
So we're really predicting random number generator that's powered by universe feelings huh Next what brian? A computer using 0,1,2 instead of just 0,1? Wait no....
Ternary computers were a thing! They could count either -1, 0, 1, or 0, 1, 2 depending on how it was implemented. The soviets built some in the early days of computing, the US and Canada both built one, and Samsung recently funded research on a silicon ternary computer.
15:23 the thing about clumps at the end of the deck (as I am sure has been pointed out by now) is that it (in part) happens because one side has to run out before the other. This can be by one card, but often more. This leads a whole stack to be deposited on top. This actually had a very interesting effect when I simulated shuffling. Because about half the time the card that was on the very top, remains on the top (as well as the cards close to the top) it is very likely for it to just not move. This can be fixed simply by moving a portion to the bottom between every riffle (which is what I now do)
I'd be intrigued to get my hand on that data and try to linearize the exponential. Would be intriguing to see how close to perfect the linearization actually is as to predicting the probabilities.
Nice Video Just a comment on randomness. The exponential shape has nothing to do with random behavior, You can create an exponential distribution from non random processes. Randomness means that within the distribution, the last number does not affect the result of the next number.
I think the claim in this case is that, of the plausible/likely physical explanations for what is causing the clicks for the device, that the “it is through this particular random process” is most supported by the gaps in the times being exponentially distributed. Of course, one could use the sha2 hash of an incrementing value to produce a sequence of pseudorandom bits, and use those to sample from an exponential distribution repeatedly, but that clearly isn’t what is happening with this particular device. The randomness test here is, I think, ruling out other explanations for the observations that would be compatible with his knowledge of how the device is made. I don’t think any physical + statistical test can ever confirm that something is truly random, because, if physics is computable, then one could imagine a modification of the laws of physics where everything which is random is replaced with a pseudorandom number generator with a cycle time much too long for us to notice. Of course, if one allows certain additional assumptions, such as strictly requiring locality (not just “local-as-far-as-we-can-tell”. Like, if the only possible form of faster than light communication was by influencing the internal state of a random number generator, but in a way that was so complicated that we could never figure out the correlation, then we wouldn’t be able to observe any non-locality, but it would technically still be there. So, by saying assuming locality, I mean assuming nothing like that is the case.), then with things like quantum entanglement and the EPR paradox, one might be able to rule out things like that, but that requires an additional assumption which we can’t truly test. That being said, it does feel somewhat implausible to me that all the randomness in the world is only nonlocal pseudorandomness? I suppose the assumption that randomness is actually only pseudorandom might make some theological questions easier? Like, in the area of “interpretations of quantum mechanics”+”how that fits in with theology” (the many worlds interpretation feels sorta weird theologically?) Some might say that true randomness would make the concept of free will easier to defend, but I think insofar as that is true, it is only because it makes it easier to defend it poorly. A good defense of free will should not rely on randomness per se. It should either be compatibilist, or be some third kind of thing, separate from both determinism and randomness. (I’m not an incompatibilist, though, I’m not sure whether free will is compatible with determinism, or is instead a concept so confused/broken/invalid of a concept that the question of whether it is compatible with determinism is a nonsense/ill-defined question . But I’m confident that *if* having free will is both a valid concept and such that whether or not we have free will is an important question, *then* we have it.)
@@satibel something can be effectively random if it is sufficiently hard to predict, but when people talk about something being truly random, they generally mean in an objective sense, not just in terms of it being subjectively unpredictable. Generally people will not say that something which uses its previous outputs as part of the process of generating its next output is more “truly random”. “Truly random” is usually meant as like, there isn’t anything that determines the value (only things which contribute to a probability distribution over the value). There is also a notion of algorithmic randomness, where a sequence of bits is algorithmically random when any (deterministic) program (in a given encoding scheme) that generates that sequence of bits, would be longer than the sequence of bits. So, for example, Chaitin's constant, which is the probability that a randomly selected Turing machine (from a particular distribution over Turing machines) will eventually halt, if run on a blank tape, expressed in binary (or whatever other base) is algorithmically random.
This is very interesting on its own, but I do want to say that I don't think Matt Parker was suggesting in his video that the ferro shuffle (spelling?) occurred through completely random means - with the shuffler never having performed one before. If I remember right, the situation was that a group of people claimed that they had this perfect suit of cards dealt out to each person after shuffling appropriately (and cutting the cards) and the ferro shuffle (probably with a brand new deck) was part of the answer to how they could have got that outcome. Now, the group of people in question had no idea that this would happen, so they probably used that type of shuffle (or a similar structured shuffle) while deliberately trying to randomise the cards, without realising they were unwittingly creating this setup. They didn't know using such a structured shuffle would create this outcome (accidentally rigging the deck), and if they were habitual card players (which seems to be the case), they probably had learnt and were using different shuffling mechanisms (whether deliberately or subconsciously). That's another factor that can bias randomisation with actions like this: once someone learns some card tricks and shuffling tricks, it does become far more likely that they will accidentally repeat these tricks or use variations of them when playing cards. Muscle memory and repetition contributes significantly to the learning of voluntary musculoskeletal movement, and this can become ingrained in the subconscious, becoming more likely to be repeated absentmindedly (or out of habit). The human neurological system is always biased according to previous experiences and repeated actions, making it somewhat difficult for real randomisation to occur in human actions - unless you're deliberately repeating actions in a systematically randomised fashion. Anyway, great video again.
Okay, so I'm thinking something like: There is a variable amount of pressure you put on the cards, and they are a variable distance to the edge of your finger they need to overcome. These together both contribute to the amount of charging needed to start flipping cards However the cards are at a set distance from eachother, making a very reliable factor. But as the deck goes down, there's less and less cards adding spring force, so potential charge goes down more and more rapidly. This actually starts from the number of cards cut to each side, but is much more noticeable when get to the point where you do something like half the number of cards left between flips. These are things I might isolate for for a practical test, or thy to be aware of when trying to do this without even knowing if that's how it works because that sounds like a lot of experiment setup.
Depends on the person. There are card tricks done by magicians on stage that require 6 or more perfect splits in a row without missing a beat to double check.
It's these kinds of observations of completely mundane things like the probability of a specific order of cards in a deck, wondering about it and finding patterns, rules and a complex system that facinates me. How do you start thinking about these things? How do you come up with material that's interesting to you for videos?
Shuffling cards is impossible to be random. This is because cards are being placed next to each other. The amount of randomness of a deck of cards is a function of the current order and the probability of a card being displaced from its current location as a function of the total randomness, which by the limited species of items being organized, only 52 cards, perfectly random will not occur. Or may only occur rarely, which then become a form of organization, thereby creating a form of predictable pattern or other anomalies which in any event may be only considered limited.
At 13:30, you have measured the probability of ONE perfect shuffle. You need to square that to get the probability of two in a row -- necessary to turn a fresh deck into four perfect hands. Not many people play 900k^2 hands in their lifetime. Even fewer open 900k^2 fresh decks; but, some initial arrangements allow the possibility that two specific shuffles in the right order might yield a similar sorting.
First, _any_ arrangement where the suits are completely segregated will do, it doesn't matter what order the cards are in _within_ each suit. This is often done just to make sure all the cards are there. Second, if I were _actually trying_ to do a Faro Shuffle _and conceal it,_ my odds would be about 50/50 to do it once, so about 1 in 4 to do it twice. This is why it's generally required to shuffle a minimum of four times, and five or six is not at all unusual. I read a long time ago that it takes 7 shuffles to ensure any bias from the initial deck order is eliminated, but I don't know how true this is if the shuffler has a tendency to perform perfect or near-perfect Faro shuffles _without trying._
The only way to determine these probabilities for real people is to perform real experiments. However, there is an idealized model of the riffle shuffle called the Gilbert-Shannon-Reeds (GSR) model that is usually used when analyzing this mathematically. This cuts the deck according to a binomial distribution (which matches the intuition that cuts into roughly equal stacks are far more probable than extremely lopsided cuts) then riffles the stacks together by dropping cards one at a time as a series of Bernoulli trials. Each time, the next card could come from the left hand or the right hand, and the probability of coming from one or the other is equal to the fraction of cards remaining in that stack. So if partway through shuffling, there are 10 cards remaining in your left hand and 5 cards remaining in your right hand, the probability that the next card will come from the left is 10/15 = 2/3. This model is qualitatively similar to a real riffle shuffle and optimizes some key indicators of randomness. Specifically, after any number of riffle shuffles, this model on average will produce a deck with lower total variation distance from the uniform distribution than any other model, and it will maximize entropy. So it's kind of the "best" riffle shuffle. The probability that you get a Faro shuffle in this model is extraordinarily small. First, one must cut the deck into two equal stacks, which has probability (52 choose 26)/2⁵² = 0.11. Then, to get an "out" shuffle, one must first drop the card from the stack that started on the bottom, with probability 26/52, then from the other stack with probability 26/51, then from the first again with probability 25/50, etc. You can see that after going through all 52 cards, I will have multiplied together the fractions (26/52)(26/51)(25/50)(25/49)(24/48)(24/47)...(1/2)(1/1) = (26!)²/(52!) = 1/(52 choose 26). Multiplying these two together, we achieve the overall probability of 1/2⁵² = 2.2 * 10⁻¹⁶. Thus, someone following the GSR model precisely would on average get one "out" Faro shuffle out of every 4.5 quadrillion shuffles. (They would get the same number of "in" shuffles.) But this only tells you how to reproduce a _shuffle,_ not how to reproduce a permutation. There are many different shuffles that all end up putting the cards into the same permutation. The strictly most likely permutation to end with is always the one you started with. Any other permutation will always be less probable. For a single shuffle, every other possible permutation is equally likely. (Of course, most permutations are not possible at all after a single shuffle.) The go-to source for this topic is a paper by Dave Bayer and Persi Diaconis.[1] Their Theorem 1 on the first page gives an exact formula for the probability that one achieves a given permutation after shuffling n cards m times. Setting n = 52 and m = 1, we find that the probability of leaving a 52-card deck totally untouched after a single GSR shuffle is 53/2⁵² = 1.18 * 10⁻¹⁴, while the probability of any other particular possible permutation (i.e. any permutation with two "rising sequences" as defined in that paper) is 1/2⁵² = 2.2 * 10⁻¹⁶. The probability of getting more than 2 rising sequences after a single shuffle is exactly 0, which should be obvious from how the shuffle works. But how many of these would result in a "perfect Bridge deal"? Well, if the deck started sorted by suit, then exactly none of them. But what if you shuffle _twice?_ Then it's possible (and very likely) to have four rising sequences, which is the minimum necessary to reorder a deck arranged by suit into one which will deal out by suit. If you think about it, with just four rising sequences, there is one and only one way to perfectly segregate the cards by suit, since if you just look at the cards of any one suit, they all must be in ascending order. (Otherwise there would be five rising sequences.) We can apply Theorem 1 again and get the probability of this unique permutation after two shuffles, which is a whopping 1/2¹⁰⁴ = 4.93 * 10⁻³². You can look at more shuffles, where many more possibilities open up. For instance, with 3 shuffles, there are many possible ways to get rising sequences of length 4-8, and many of those are perfect deals. But the denominator grows exponentially, and things only keep getting worse. Needless to say, it is not plausible that anyone has ever opened a new pack of cards (or any deck sorted by suit), shuffled it twice while following the GSR protocol to the letter, and then dealt a perfect Bridge deal. Something else must be going on. I think it is likely that experienced dealers are much worse at shuffling cards than less experienced ones. They tend to shuffle more "perfectly" in the sense of alternating cards far too often and almost never getting large clumps. Diaconis discusses this in an interview with Numberphile.[2] It is likely that some people suffer from this affliction more than others, and so that for some people, shuffling this way twice is within the realm of possibility, especially when you consider the variety of other possibilities. On top of all that, it is always possible that some of the news articles discussing this were simply not true, i.e. that the cards had not been shuffled at all, or the alleged deal never happened. That type of deception is not all that rare, so when we're discussing rare events, it's always going to be a concern. ------- [1] D. Bayer and P. Diaconis. "Trailing the dovetail shuffle to its lair." _The Annals of Applied Probability_ 1992, Vol.2, No. 2, pp. 294-313. statweb.stanford.edu/~cgates/PERSI/papers/bayer92.pdf. [2] Persi Diaconis video interview. Brady Haran. Numberphile2. Mar 23, 2015. th-cam.com/video/c_Hunaf0tWw/w-d-xo.html.
Great video. The only thing is that the usual way of shuffling is not that good at shuffling cards, if you get what I mean. People playing bridge usually try to do a pharaoh shuffle, which is not hard to do perfect once you are used to doing it. Even by chance I usually do perfect shuffles, without actually trying, learning to do it without effort is just a result of training your shuffling technique, and I mean just shuffling while playing, and having a decent deck of cards.
We could try to measure the conditional probabilities of getting a card from left or right bases on the number of cards on both sides | a few previous cards. This would give way more data points for every recorded shuffle while still accounting for the conditional nature of these events
A suprising number of fields bloom from just the principle of obfuscation, and if you put encryption into the mix, you've got a recipe for either world domination or disaster. Like encrypting something twice has the potential of making the message less secure. Thus, sometimes when trying to codebreak, it's beneficial to re-encrypt the message, giving you a less entropic source to let your analysis loose upon. Funny how that works.
I designed and built a "random" number generator for my small children to replace throwing a dice. My design used a clock circuit driving a binary to 7 segment display driver set to start at one and roll over before 7. I used a switch to freeze the display at whatever count was shown at the time the button was pushed. There was never any randomness to the circuit as the numbers flowed consecutively but the clock speed was very high and randomness was achieved from the human intervention of the button that froze the display. Try as we could, we were never able to trick the device to anything but random numbers.
If you believe that people are fundamentally quantum systems then if the clock rate is high enough I feel like there's a fair degree of true randomness going on here.
I suspect there are a lot of activities where the more you practice them, the less random they get. Shuffling cards might be one of the more obvious ones, but also painting, playing Mario, heck even walking would exhibit similar behaviors.
Another way to make a random number generator is to have a radio receiver thats picking up static noise. Connect it to an oscilloscope and measure the amplitude of the static signal at certain times, thats your random number.
Seemingly random, yet still a decent attempt. The data could be crunched to show how or at which points or delay the seemingly random generator for numbers could be plotted probabilistically. The spans. But, that the span is by an unpredictable higher energy particle interaction I do concede would be exceedingly difficult to accurately track and model to see if certain factors would be more or less predictable for the overall result. It's, in my opinion, more fair than many other algorithmic rng calculation setups, like those in slot machines or video games as examples, seeing as how those systems have to implement what appears to be randomness. Nice job. A couple times in my life after playing solitaire I got some predictable results after shuffling, so I'd have to cut and reshuffle in varied ways seemingly randomly to avoid getting very similar patterns in gameplay. Mostly, I noticed, because I'd gotten to a decent shuffling ability, and would always place my aces in the same order when finishing a round, pretty much putting the cards back in an unshuffled state every time. This was pretty similar.
Have you considered that matlab's Rand function is not completely random in the sense that if two separate machines are each running Matlab, when told to output the same Rand function they will be the same. You do need to have never used the function before, but when the conditions are met, both machines will output the same random numbers for as many times as you run the code. In a Matlab course we ran into this during a class project.
I once played a game of magic the gathering with someone who could perfect shuffle. He saw me mana weave my deck before the game, and took advantage of knowing every third card was land. Separated all the lands together while shuffling my deck, so that I could not draw a decent hand for the life of me. Even trying other shuffles after that, you're gonna end up with a lot of lands clumped together, making it both difficult to draw a good hand, and difficult to draw decent cards later in the game
8:09 that glitch really isn't avoidable with a simple GM tubes setup like that. After an event is recorded, the GM tube needs time to reset its fill gas to a neutral charge before it's able to record another event. The time required for this reset is referred to as dead time and there's a couple techniques to avoid it. The easiest is probably to have some logic that shuts off the detector for the duration of the dead time (and just display the number for that duration) and then turn it back on when the numbers start cycling again.
Yeah the dead time is just longer than I wanted it to be - it’s like a second… But shifting the distribution over like I did is basically what you describe. I absolutely love that that just works with Geiger tubes - you can glance in it’s direction at any time and see the same probability distribution of future ticks. I wanted to talk about it more but just had time to throw in the onscreen text about memorylessness…
Vsause has a grate vid on how shuffled cards are impossible to get the same shuffle 2x its a 1 in 52 factorial chance and thats a bigger number then the human mind is able to understand intuitively
If you did shuffles and monitored how often you create "runs" of perfectly interleaved cards, you would only be measuring the likelihood that YOU produce a perfect shuffle... magicians and card mechanics can reliably perform perfect shuffles, as it is an entirely trainable skill. That makes it very dubious to apply statistics to. You might find that you get better and better and they become more frequent depending on the type of shuffling you're attempting. I know that years ago someone measured how many shuffles are necessary to ensure a deck is 'well shuffled' and the answer they came up with was 7. I believe that was accounting for a lot of individual variation. I imagine the paper they published (it was legit peer-reviewed research) would have a lot of relevant information to determining the likelihood of a perfect Pharoah shuffle, and might even include their own observation of it. It's been quite a few years since I read it, though, so I don't remember anything except they came up with 7 as the number of times you should shuffle a deck to ensure it is 'well shuffled'. edit: Heh, I obviously commented before I finished the video, you did address the trainable skill issue.
I imagine the edge effect at the start may be due to the difference between the static friction of you holding the cards still vs the rubbing friction of you letting them roll through your fingers. At the end I don't have any ideas though.
I always wondered about the gambler fallacy when we talk about stuff like odds. The gamblers fallacy states that if you have a 1 in 50 odds of winning with each slot machine pull, then each pull has a 1 in 50 chance of winning. That means you can pull 50 times and not win even once. But eventually if that string of bad luck continued it would get less and less likely for you to lose, simply because your odds of winning is still 1/50. with 1/50 odds, a losing streak of 0/50,0000 would be impossibly unlikely. Each pull is still individually a 1/50 odd of being a win, but the longer the streak of losing (or winning for that matter) the lower the chance that the streak will continue.
I am sorry to disagree but your reasoning sort of implies that pulls are not independent, but they are: every new pull doesn't "know" what happened before. Suppose you are tossing a coin, 1 is heads, 0 is tails. If you toss it 10 times, you can say that the sequence 0000000000 is very unlikely to happen (1/1024), but any other particular sequence like 0000010000 or 0110001000 or 1100110011 has the exact same probability to happen. If after 10 draws the result is 0000000000 then after 11 draws you have exactly the same probability of getting 00000000001 or 00000000000: you do NOT have more chances of getting a 1 just because you already got ten times 0. It is true that long streaks of winning or losing are less likely, but this is true ONLY before you start playing. Once you have pulled N times, this has no influence on the (N+1)th pull because the N first one have already happened and are predetermined. The past pulls have no influence of future pulls and there is a contradiction in your last sentence: you cannot say that the odds of each individual pull is still 1/50 but at the same time that you are less likely to lose after some time.
Would you be willing to post the data? There is a famous problem in probability theory on how many shuffles it takes to throughly mix a deck (it has some characteristic "mixing time" one can calculate). They usual assume a certain model for the runs for this and go from there. So it would be cool to see if your data matches this model
Oooh this would be fascinating but unfortunately I didn’t keep the entire deck order each time, just the runs of “1s”, so I doubt we would be able to pull the relevant info. If we find a way to easily enumerate the stacking order post shuffle this sounds like an awesome thing to crowdsource to get loads of data
@@AlphaPhoenixChannel The famous Bayer and Diaconis "Trailing the Dovetail Shuffle to its Lair" paper cites Diaconis's earlier "Group representations in probability and statistics" as establishing that Gilbert-Shannon-Reeds (GSR) model is reasonably accurate. More specifically, chapter 4 mentions an experiment where Diaconis and Reed performed 103 and 100 shuffles respectively, recording the permutations. Persi Diaconis loves exploring the conditions for whether things are "effectively random," with a lot of experimentation to develop and validate models… In approachable YT videos, the interviews on Numberphile are lovely, and his lecture "The Search for Randomness" is delightful. IIRC, some of the Numberphile videos discuss the effectiveness of different shuffling techniques. I suspect you'd also enjoy his discussion of flipping coins.
I think this is a perfect example of how math doesn’t always represent real world observations. The variables involved in shuffling, skill, moisture in the air and on the materials, temperature, etc etc.. combined with the basic odds.. accidentally achieving the perfect shuffle is impossible (imo).
Coming from someone who did card magic years ago, getting a perfect shuffle isn't actually too hard with a good deck of cards and the right shuffling technique. In fact, I was even able to do enough perfect shuffles in a row that it would bring the deck back to the original order. That being said, I agree that it should be random for a random person shuffling a random deck. Great video
yea I used to carry a deck of cards in school and would be permananly shuffling between classes. After a year of that I got pretty consistant at getting them.
If you do 8 “out” Faro shuffles the deck gets back to the initial state. The “out” faro keeps the top and bottom card the same every time. If you do an “in” faro where the top and bottom cards are interleaved, it takes 52 perfect shuffles to get back to where you started!
Yeah agree , Faro shuffle is not that hard as ppl may think, with a bit of practice (like 10-20h , don't actually remember how much time it took me but somewhere around that time) , you can get pretty consistent with it to the point where you can use it in magic tricks.
Had to learn it for a trick , but it was more useful for some cardistry (double fans , waterfalls etc).
Yep I was gonna say the same. Simply learning to do a perfect pharao is definitely a thing in card magic.
This is true. As someone who also dabbled in card magic as a child and is now a professional dealer, I can do a perfect shuffle almost every time just by making sure my thumbs are moving at the same rate. In my job, though, I purposefully make sure not to do this so cards are shuffled fairly.
your videos are so freakin' good. Even the ones that don't sound interesting end up being incredibly engaging and informational as always
I'd say that most channels have videos with titles and thumbnails that _sound_ interesting, but you get bored five minutes into the video. This channel is the inverse lol.
I don’t love this title yet - always looking for better packaging lol
@@AlphaPhoenixChannel why shuffling doesnt actually hate you
@@AlphaPhoenixChannel Card shuffling is deeply related to mixing of Markov chains. In addition, there is a rather simple way to model faro shuffling. Here is the most famous reference on the subject (proving a theorem which applies to many other Markov mixing problems: there is a critical number of shuffling below which you only explore "a few" configurations; no need to shuffle more than that number since the shuffling is already perfect)
projecteuclid.org/journals/annals-of-applied-probability/volume-2/issue-2/Trailing-the-Dovetail-Shuffle-to-its-Lair/10.1214/aoap/1177005705.full
statweb.stanford.edu/~cgates/PERSI/papers/aldous86.pdf
en.wikipedia.org/wiki/Markov_chain_mixing_time
www.ams.org/publicoutreach/feature-column/fcarc-shuffle
My first game of poker I ever played I got a Royal Flush and nothing will ever come close to that luck.
Wow, that is incredibly lucky
The odds of that are exactly the same as the odds of any other hand
I got a royal flush of hearts on the deal once when we were playing poker at school and absolutely no one believed me when I tried to tell them I didn't cheat. I was the dealer so it made it harder lol.
@@williamshea1970 true, but the odds of hitting in your first game is a hell of a lot less than hitting it at some point in your life
We used to engineer things so that poker noobs would get a royal flush, just to see how they handle the pressure.
There is something incredibly interesting (and somewhat bizarre) about random distributions.
You measured atomic decay (which are supposed to be "truly" random, at least from a quantum physics point of view) and card shuffling (which are supposed to be NOT random at all, at least from a quantum physics point of view).
What I think is very fascinating is that there the same Mathematics that can be used to study "true" randomness also works for uncertain events. Even something fully predictable (like a pseudo-random generator) becomes more and more indistinguishable from "true" randomness the less and less you know how it works.
If it was possible to know everything, nothing would be random.
@@ZackXa I'm not sure quantum physics would agree with that statement 🥲
@@ZackXa Good ole' Laplace's Demon.
@@AlanZucconi Do people actually think quantum mechanics means things are unpredictable? lol.
@@treyt6474 That is exactly what quantum mechanics means. A system can be both deterministic and also unpredictable if the state of that system cannot be measured without altering it in a predictable way.
To be more precise, by "predictable" I mean an experimenter could correctly call out in advance an arbitrary series of future states with better accuracy than random chance. Flipping a coin and calling out "it will come up heads about half the time" doesn't count any more than saying "it will definitely be either heads or tails": those are facts about the system as a whole and do not demonstrate an ability to predict the behavior of the system. To be predictable, one would have to be able to beat random chance. In the case of a coin flip, one would have to be right more than half the time. How much more would indicate how predictable the system is.
QM says you can't predict the decay of a nucleus any better than random chance. You can predict that it will decay and you can even calculate an element's half-life, but if you try to call out the numbers coming from Brian's box, you won't get the answer right any more often than someone else just calling out the numbers from another similar box or another person just calling out the same number over and over.
Somewhere in the multiverse, 10,000 monkeys are taking a break from randomly writing Shakespeare, and playing a perfect game of bridge after shuffling way too many times. 😅
I love how you edit over parts with editing Brian. Takes a lot of self reflection to be like "that was ass, I'm gonna dub over it" and then tell the viewers that. 😂
Chad move
But then we're not getting "Plan A".
If he edits over parts like in this video, he needs to change the channel name to *BetaPhoenix.*
@@ddegn Remember his quote is plan A always goes up in flames
@@pirateofthebeans_2393 And I want to see those flames.
Seriously, I love this channel.
I haven't watched the video yet, but I am aching to share my story.
Basically in 2015ish I was adjudicating a debate competition. While we were waiting for the next round me and a few judges started playing a board game called "Ne se surdi, choveche", which is the german Mensch ärgere Dich nicht, or as Wikipedia claims also known as Parcheesi, Ludo, Trouble etc. We were just killing time and this was just a game that happened to be laying around in the resting room we were provided with at the school, the venue where the competition was hosted. It's a basic and heavily luck dependent game with the players moving their pieces by rolling a six sided die and eliminating opponent figures. If you roll a six, you can move six spots and roll again. That's basically 90% of the rules.
I don't really know how to best tell this story and explain everything that happened. All I can tell you is that it was extraordinary, there was laughter, maniacall laughter, there was sadness, there were offended friends and there were astronomical probabilities, which led to personal confusion and disappointment.
One thing to note: we decided to roll two dice instead of one so as to at least be able to finish the game in time. I'm not convinced now that this was the best option to finish the game early as, as we soon found out it meant that doubling or tripling of your turn happened way less frequently. And that chance to do things twice or to use special features is the only "strategic" moment of the entire game.
Now on to the story proper. A few rounds in the game and on my turn I rolled two sixes. This wasn't the first time it happened in the game, I think, but it was amongst the first ones and definitely many rounds in. I moved my pieces and rolled again:
12.
We laughed and my friends told me I was very lucky.
I played, I rolled again. Guess what: another 12.
Everyone was amazed. We were beside ourselves laughing our asses off.
I rolled yet again. 12. Now I was laughing pretty maniacally, but my friends were in disbelief. One of them, especially.
I played my turn and rolled again. 12 as expected. Now the guy that was pissed last time, asked me directly: "how are you doing this?" His tone revealed curiosity, little anger. People were confused, but not yet agitated. I told him I haven't done anything, but I was still laughing and pretty much shaking. I was more confused than amused tbh.
I didn't want to anger anybody while also being a bit annoyed at being suspected of something. On retrospect if I was somehow cheating and confessed about it AND showed them how I did it, I am certain that people would have even taken it in jest and be entertained by my skill. The reality, however, was that I was in fact not faking it and was just being lucky.
I guess thinking that it would ease the tension or at the very least move the game along when the time came to roll, I just dropped my dice on the table without rolling them, from about 30~40cm.
Well... it did not help. They spun and settled on 12. Sixth time in a row.
I was still chuckling, but inside I did not know what to do. People were reeeally annoyed. I said that this was my final roll and will pass on to the next person.
Now that I think about it this might have made me even more sus, but oh well hindsight is 20/20.
Next time my round came people were convinced I couldn't possibly roll 2 sixes again. We were joking about my incr. luck and being friendly again. Things were getting back to normal.
That is until I rolled 12. One of my friends said: "Here we go again", in a friendly manner, but some undeclared threat or tension was present.
After I played my turn and was ready to roll again, people were on the edge of their seats. The tension was very palpable.
12. Again. "Bullshit" I heard. ("Gluposti") ''Impossible" someone said, "Nee, ti se ebawash", ( "You are messing with us") another one exclaimed.
They politely, but firmly on the edge of ordering told me to roll with another set of dice.
I did willingly, almost eagerly. One of dice was green and very small like for backgammon and the other was regular size. (The new ones)
I rolled with them. The green bounced and shoot up from the wall of the cardboard lid we were throwing them in. I immediately regretted changing dice as I felt as if I was admitting smtg. The dice spun wildly, but when they settled both were sixes.
The guy that originally was quick to get annoyed said "You must be spinning them somehow? Tell us how you are doing this? Come on..."
I again, declined of having done anything illegal or mischievous. He told me next time I want you to roll with my phone. Now that really pissed me off, both the demand, which I found demeaning and also bcs of my rolls, bcs I just wanted a casual game with just jokes and having a good time and not having this "cross-examination" and seriousness.
Ultimately I did "roll" with his phone. It was an app of some sort or just a random number generator. Well I got 12 regardless. For the tenth time.
Another friend accused the person who handed me the phone, the one who has been so far the most vocal, and myself of staging the whole thing. Saying it "wasn't funny" and that it was all quite "boring", while being visibly upset. We were all vaguely aware of how miraculously improbable was for the rolls to happen naturally.
I told him earnestly and trying to calm things down that I was not cheating and that our first friend has nothing to do with it. Inside I was bitter and perhaps some of that showed.
I told him if he wanted me to I can use his phone and whatever app he wanted me to next time I roll. I again said that I am passing my turn to the next player to ease the tension. This time it was less effective as no one really wanted to keep playing.
He said I should just stick to the original dice and not to do stupid stuff. He clearly meant that I was so far HAVE BEEN doing stupid stuff. Words were heated now. People were not having a good time.
We agreed that henceforth if you roll two sixes you get one extra roll PER TURN and not as originally each time you roll a set of sixes.
Play continued. People really did not want to play, or talk, or interact. The vibe was dead.
Next time it came my turn, I rolled and I rolled 12.
People now just accepted it with quiet judgement.
I felt miserable. I felt like I was just purposefully hurting my friends. I did not enjoy it one bit. Now thinking back I was a bit like an automaton. I didn't really have a say in what was happening, yet I was causing this distress. I had no control over the rolls, I could only try and deal with the outcome of each one. I felt powerless in a moment in which I should be feeling powerful. I am in the context of the game winning after all. And AND we are all witnessing smtg. Incredible.
I rolled for the 12th time and for the 12 time two sixes stared at me from the bottom of the cardboard.
Sharply the second friend said: "Go on, roll a third time." I told him it wasn't my turn anymore, but I ultimately agreed.
Finally it was 5 and 3.
Next turn it wasn't double sixes. The magic was gone. We carried on for a few more rounds, but we never finished the game. We ended it early and just did other stuff for the remainder of the time. For the rest of the day people were bitter with me.
Later when I came back home I reflected on the day and I thought about how astronomical were the odds of this happening. To me it became abundantly clear that I would never witness another event of such a rarity. Or to put it less fatally the chances of me seeing or participating in two events of such rarity are infinitecimally significant.
I felt and still feel like I have "wasted" my luck, which is bull, but it still feels like it.
Of course from the POV of the dice there is one six in a row 12 roll, a 4 of sorts in a row and a 2 in a row, bifurcated by the turns of other players, (provided you count the changing of the dice and the phone as a valid rolls). But from my POV you have 12 times I have rolled consecutively, one after the other the same set of two, the chances of which optimistically is 1 to 4.73838134e18. This might be the first and only time this will happen in the history and the future of the universe and for all it's worth it was "wasted" on a stupid board game, observed by no one but the participants, which were largely pissed for unwillingly taking a part in the event.
Ultimately I rolled 12 times two sixes and felt bad about it.
Just wanted to say that I had a great time reading this and will be bookmarking this video so that I can find this comment again. Thank you.
@@TheHackysack Thanks man!
Sounds like God was messing with you
Wow. Just wow. "Čovječe ne ljuti se" is called around here. Lots of fond memories with that game. Yeah, randomness sometimes laughs you in the face with a strange grin. Devil's business.
Lol how TH-cam keeps deleting my comments 😁
One thing I think is extremely important that you didn't mention when talking about physically doing the tests instead of simulation, is the cards you used. The cards you used are pretty thin cards with a glossy looking top. They will bend more easily, stick to each other slightly more, and most importantly stick to your thumb more. I think it might surprise you how drastically the probability would increase if you used newer decks of slightly higher quality cards like bicycle cards. I would guess with your level of shuffling after this project that it would already by down by nearly 2 orders of magnitude from your 1 in 119k number. This is assuming you use the same method of course, as a better method for perfect shuffling where you count out 26 and sort of just shove them into each other can get a perfect shuffle every time with practice, but I'm sure you know this.
Interesting! I just bought cheap cards - didn’t even stop to think the surface finish would affect the result but you’re totally right
@@AlphaPhoenixChannel Casino cards is the only way to go
@@AlphaPhoenixChannel I feel like you need to make a Shuffling machine to check the results against human error as issues like surface finish would be far less important. Obviously if someone wanted to go balls to the wall it could get a perfect every time but if one simply simulates the motion of it in machinery and compares the statistics of that against your current batch it could take any error bars to virtually zero.
@@seditt5146 There are battery powered card shuffle machines...
@@kylone1 Yeah I know but for the most part that does perfect shuffle every time which is not really close to the error humans experience.
It's really sobering to realise someone probably ended up with a perfectly shuffled deck at some point but they never knew about it because they continued shuffling before dealing.
I used to do magic as a kid for about 6 years and was shuffling cards constantly, and as I was watching this video I tried to shuffle a deck and I noticed that my shuffles almost never had a run more that 4 and rarely had one that was 3, so I agree that more shuffling makes you better at ferro shuffling. And great video love it as usual!
I really enjoy nerding out to your content. Thanks for sharing this with us.
This kinda simple question bugs me to the point of making a video cause I just gotta know the answer
I was sitting here with a wide grin on my face for the entire video lol. you just radiate enthusiasm and it brightened my day immensely. tyvm!
Speaking of underlying threads of mathematics, I just happened to randomly spend my entire day fiddling with card shuffling in the context of random number generation, within 24 hours of you posting this video, having not known about it prior to now. What an excellent and informative end to a perfect day of post-holiday putzing this video was, and a fun coincidence too.
My god man... I want you to know the hours of tedium you endured making this video were not wasted I appreciate your work.
The outro reminded me of a story: Back in high school, I was really into Dungeons and Dragons. I had an idea for a certain campaign that involved giving the players actual, genuine loaded dice as a puzzle mechanic. This had me looking into internet articles on loaded dice, and how to get them to a certain degree of “unfair,” and how to analyze… But most of what I found was how to tell if a die IS fair - the chi squared test, where getting a really low value means the die is fair. I thought “Huh, neat!” and then moved on.
Years later, in college, I was talking with a friend about their research. They mentioned trying to raise their chi squared value, and I said, “Wait, don’t you want that to go DOWN?” And they said, “No? You always want it to go up, for more precision!” It turns out they’re both two sides of the same (fair) coin - you can use chi squared to prove a set of data is remarkably precise, but you can use it for the opposite purpose, to prove a set of data is remarkably IMPRECISE. We just came at it from opposite ends of the same problem.
Also, just found you from your Algorithmic Gerrymandering video, and I really love what I’ve seen so far. Definitely sticking around!
(I am at 16:16) I mean, yeah! I do card magic as a hobby, and I am actually very good in faro shuffle. I can pull perfect faro shuffle almost any time I want, and even when I don't want. I can do that 8 times in a row, and then the deck just unshuffles itself. Idk, shuffling the deck of cards stopped to be some kind of random process for me at one point.
Wooo, Math! Love the conclusion. How many times have people asked me, "why is that important" or "why are you learning that?" when it is completely unrelated to my specialties. Well, because the more you know about the nature of the universe, the more connections you can make. It's the opposite of the saying "when all you have is a hammer".
The universe is so beautiful
rhus when you can predict random numbers, money is not a problem, you can do whatever you want to enjoy life XD
Because it's interesting!
So glad I found this channel. I had a realization while watching through your videos that I wasn't as smart as I thought I was. It's given me great motivation to see the things you can accomplish with an extensive understanding of science. I put this channel right next to Ben at Applied Science in terms of helping me push my understanding of the universe forward. I sometimes spend an hour on Wikipedia afterwards. Great stuff.
Can't know everything! Accepting that you need to learn is infinitely smarter than holding the mindset that you don't need to learn.
There's another factor you weren't considering: the split of the deck. The Farro shuffle is possible if and only if you split the deck perfectly in half, i.e. 26 and 26. The likelihood of that in a typical shuffler's hands isn't tiny, but it'd probably still add another order of magnitude or so.
Came here looking for this comment. Can't believe he didn't mention it!
This is exactly what I was wondering from your geiger meter random number generator video. That is awesome, such a cool concept! I just ordered all the stuff to make something like this!
You know, i always add your videos to my watch later, look at them for months, finally convince myself to watch it, and its always good
for an example in a given playing card game, you don't need to perfectly Faro shuffle all 52 cards. If 4 players are only dealt 4 cards each, you only need to have perfectly shuffled the top 16 cards.
This should make the likelyhood significantly higher, as possibly a majority of the time, your "error" in a non-perfect shuffle comes from the lower majority of the deck, which can be disregarded.
This is true, but the motivation behind this he explains is about bridge, in which you deal the entire deck to the four players.
Thanks for the insight! Your sincere joy for math and science shines through in every video.
Your excitement for math and how it describes our physical world is great. I have the same excitement. Unfortunately, I struggled with it in school and never pursued it after.
I loved how when you explain the machine it gives the sequence 0, 1, 2, 3.
You are making some of the best content on TH-cam. Thank you!
Here's an idea for a convenient and money saving way to use quantum mechanics to generate random number. Get one of the older smoke detectors, most of the circuitry is done, and mod the board, so that the Americium decay detection timing is conditioned and shown on one of those 7-segment blocks
It can also be done solely with monolithic clock generators and flip-flops. Feed 32 clock generator outputs into D-inputs of 32 flops which are all clocked by the same clock at some fairly high rate. The first stage flops will go metastable with a fairly high frequency. Clock the output of each first flop stage into a one or more flops in series to capture a 32-bit value, some bits of which may be random as the metastabilities are resolved. It isn't necessary to feed different frequencies into the first stage flops as the clock generators will come up in completely unrelated phases to each other.
@@garymartin9777 you know, you could probably do a sample and hold of RF tuned to the cosmic background microwave, whether or not that truly is random is something well outside my knowledge!
Fun video. My own tendency is to consider almost anything with mathematical precision, and it is brilliant, entertaining, and very educational to instead have this fast-paced hands-on approach that adds in bits of mathematical modeling later.
There's a simple model of a riffle shuffle that I have used in teaching where a card is equally likely to fall from the left hand or the right hand at each instance of a card falling. Of course it is a simplification, but I never thought of the physical reason for why it is wrong. As explained in the video, the relative motion between fingers and deck on the side where a card has not fallen is continuing, creating a negative correlation.
The discussion of edge effects is a great lesson for trying to learn from empirical data. Very nice.
This was way more interesting than I expected from the title.
This is the best kind of nerdiness.
This was surprisingly interesting. Can't believe i got so invested in card shuffling statistics
Magicians use a type of shuffle called a Faro shuffle which is performed by splitting the deck in half, holding each half in separate hands, then carefully interleaving the two halves so that you alternate a card from the top half, then a card from the bottom half, and so on. It is exactly the same as a perfect riffle shuffle where the cards alternate, card from left hand, card from right hand and so on. Magicians like doing the Faro shuffle because it takes skill and is showy.
So, here is where this is leading. An out shuffle is a shuffle where the top card stays on top, and the bottom card stays on the bottom (they stay on the OUTside). An in shuffle is where the top card goes to the second position, i.e., it moves down one position, and the bottom card moves up one position.
It only takes 8 perfect out shuffles to restore the deck to its original order. It does not matter if it is a Faro shuffle or a riffle shuffle as long as the cards are interleaved in alternating order and the top card remains on top.
Here is the math.
Let n = number of cards in deck, in this case n = 52, but any number can be used.
Let k = position a card in the deck. k = 1 for the top card, k = 52 for the bottom card.
The top half of the deck has a different rule for the movement of the cards than the bottom half of the deck.
1) Top half, k 26, the card moves to 2k - 52
The card in position 1 remains in position 1. 2 x 1 - 1 = 1
The card in position 52 also remains in position 52, 2 x 52 - 52 = 52
What about the rest? let's look at the cycles.
2 -> 3 -> 5 -> 9 -> 17 -> 33 -> 14 -> 27 -> 2
It should be obvious that that a card in any of the positions this sequence will end up back in its starting position in 8 shuffles. If we do this for the remaining positions, we find it takes 8 shuffles for any card to return to its starting position. Ther is one odd exception, 18 -> 35 -> 18. This cycle has two steps, but that is okay because the cards will be back in the original positions in 8 shuffles.
He gets longer runs in the middle because of the sound/feeling that gets easier to identify with a rhythm (getting “in the groove”) and with a musical pitch (440 cycles per second = A).
I’m sure that given an infinitely tall deck mechanically fed to his hand that he could eventually and intuitively “hear” and “feel” the perfect rhythm… like learning to bounce a basketball without looking and even with your eyes closed by hearing the bounce and contact slap steady rhythm.
Human hearing is amazing.
you are shuffling in the right direction
Regarding a unifying thread of physics that belies disparate things, it seems that if you take any set of things and look hard enough you will find some mysterious connection. Not that one creates their own correlation, but rather that ultimately there is really only one 'thread' that ties every perceivable thing together no matter how disparate. "What is it that breathes fire into the equations and makes a universe for them to describe?" I love your insight and passion for exploration of both the fantastic and (seemingly) mundane. Keep manning the bellows. 😉
apologies if i'm doing a cunningham's law here, but shouldn't the geiger tube setup be a textbook poisson distribution? the probability mass function does have an exponential in it. but that low part toward the start isn't a glitch, it's a natural part of the distribution
It _should_ be a textbook Poisson distribution, since arrivals at the Geiger tube are uniformly distributed in time, given an average rate. I think wait times in that case would then be exponentially distributed, so the glitch at the start is indeed a glitch. If you looked at the number of arrivals within time periods then that would indeed be the way you describe it iirc.
At 7:58 he shows the results of the actual Geiger tube and it IS a Poisson distribution. Only now he calls the low part a glitch because he expects an exponential instead of a Poisson distribution.
Isn't it a textbook Poisson *process*, which would result in an exponential distribution? The definition of an exponential distribution is that it represents the time between events of a Poisson process. The Poisson distribution represents the number of events within a fixed period of time, which is not what he was measuring.
Yes, you are right, I was wrong. It is a Poisson process and the distribution of wait times between events should have been an exponential distribution, not a Poisson distribution. So the glitch must be caused by his setup, just like he said.
It is important for viewers to know that any random numbers generated by a computer are not at all really random. Rather they are a predictable sequence of numbers, which taken over their entire range (usually 32-bits), are random or close to it. But number-to-number there is little to no randomness. This is called pseudo-random. Depending on the quality of sequence seed, the sequence may repeat with far fewer than the maximum possible number of entries. A good seed is a large prime number of equal or close to equal the number of bits of the sequence generator (e.g. 32). If you have the option to select the seed, lists of primes can be found online. Two calls to the sequence generator starting with the same seed gets exactly the same sequence. This is handy when testing because the pseudo-random sequence used by an application will probably cause the same output, time after time, given that nothing else changes. It is possible to generate truly random numbers for use with an application but this requires extra hardware not found on a p.c.
As I watched I realized that you display an incredible scientific honesty about your own work; self evaluation leading to low marks for performance displayed is, sadly, increasingly rare in public performance. I suspect you are your very harshest critic.
The number e is a cool example of something that shows up in a bunch of seemingly unrelated places!
Once I heard about perfect shuffles leading back to the same deck and how it could be used for some of the most ultimate card tricks I started trying to perfect doing a casual perfect shuffle. It was super hard and really boring so I eventually stopped focusing on it but I continued having a deck of cards at my desk. I have ADHD so when I am thinking about something at my desk, I like to keep my hands busy with something so I have a lot of things on my desk to mess with and even though I stopped trying to do a perfect shuffle, I did start just casually shuffling to keep my hands busy as it is immensely satisfying to shuffle cards well. Over time I got to a point where I could perfect shuffle about half the deck and do about a dozen shuffles in a minute. I haven't done any statistical analysis but I could probably get a perfect shuffle in less then a hundred attempts, but I am still far from being able to do it to the level required for insane magic tricks.
Dear Brian, I think the histogram at 08:00 is actually perfect as is. Yes, gas detectors have a bit of dead time, which might cause this attribute, but I think it is a necessary feature of this compound probability density function. Since the particles are coming from random directions and sources, the pulses should follow a Poisson distribution that has a root at t=0. After the peak it will indeed resemble the exponential distribution, but it should be 0 at t=0. Don't take this to heart, though, I'm not a statistician, but I remember doing an experiment resulting in pretty much the same histogram as yours.
People get very adept at training their ear to make a good sounding shuffle, so it's more likely
I "liked" this video pretty immediately which means about 2/3 times thoughout the video I wanted to "like" it again and got disappointed because I saw I already "liked" it lmao. It's just a good video and I love your hilarious attitude
So we're really predicting random number generator that's powered by universe feelings huh
Next what brian? A computer using 0,1,2 instead of just 0,1?
Wait no....
next up, a computer that uses 0,1,2,3 !
Ternary computers were a thing! They could count either -1, 0, 1, or 0, 1, 2 depending on how it was implemented. The soviets built some in the early days of computing, the US and Canada both built one, and Samsung recently funded research on a silicon ternary computer.
15:23 the thing about clumps at the end of the deck (as I am sure has been pointed out by now) is that it (in part) happens because one side has to run out before the other. This can be by one card, but often more. This leads a whole stack to be deposited on top.
This actually had a very interesting effect when I simulated shuffling. Because about half the time the card that was on the very top, remains on the top (as well as the cards close to the top) it is very likely for it to just not move. This can be fixed simply by moving a portion to the bottom between every riffle (which is what I now do)
Coming up on 2^17 really fast now. Looking forward to your new buttons
I'd be intrigued to get my hand on that data and try to linearize the exponential. Would be intriguing to see how close to perfect the linearization actually is as to predicting the probabilities.
In the case of shuffling cards and ticks of a Giger counter, the underlying common thread is Poisson statistics.
When shuffling cards, the shuffling of cards isn't the randomness, but we, as the shuffler, are. You are measuring the randomness of human beings.
Nice Video
Just a comment on randomness. The exponential shape has nothing to do with random behavior, You can create an exponential distribution from non random processes. Randomness means that within the distribution, the last number does not affect the result of the next number.
thouch seeding with the previous number makes it more unpredictable, so wouldn't it be more random?
I think the claim in this case is that, of the plausible/likely physical explanations for what is causing the clicks for the device, that the “it is through this particular random process” is most supported by the gaps in the times being exponentially distributed.
Of course, one could use the sha2 hash of an incrementing value to produce a sequence of pseudorandom bits, and use those to sample from an exponential distribution repeatedly, but that clearly isn’t what is happening with this particular device.
The randomness test here is, I think, ruling out other explanations for the observations that would be compatible with his knowledge of how the device is made.
I don’t think any physical + statistical test can ever confirm that something is truly random, because, if physics is computable, then one could imagine a modification of the laws of physics where everything which is random is replaced with a pseudorandom number generator with a cycle time much too long for us to notice.
Of course, if one allows certain additional assumptions, such as strictly requiring locality (not just “local-as-far-as-we-can-tell”. Like, if the only possible form of faster than light communication was by influencing the internal state of a random number generator, but in a way that was so complicated that we could never figure out the correlation, then we wouldn’t be able to observe any non-locality, but it would technically still be there. So, by saying assuming locality, I mean assuming nothing like that is the case.), then with things like quantum entanglement and the EPR paradox, one might be able to rule out things like that,
but that requires an additional assumption which we can’t truly test.
That being said, it does feel somewhat implausible to me that all the randomness in the world is only nonlocal pseudorandomness?
I suppose the assumption that randomness is actually only pseudorandom might make some theological questions easier? Like, in the area of “interpretations of quantum mechanics”+”how that fits in with theology” (the many worlds interpretation feels sorta weird theologically?)
Some might say that true randomness would make the concept of free will easier to defend, but I think insofar as that is true, it is only because it makes it easier to defend it poorly. A good defense of free will should not rely on randomness per se.
It should either be compatibilist, or be some third kind of thing, separate from both determinism and randomness.
(I’m not an incompatibilist, though, I’m not sure whether free will is compatible with determinism, or is instead a concept so confused/broken/invalid of a concept that the question of whether it is compatible with determinism is a nonsense/ill-defined question .
But I’m confident that *if* having free will is both a valid concept and such that whether or not we have free will is an important question, *then* we have it.)
@@satibel something can be effectively random if it is sufficiently hard to predict, but when people talk about something being truly random, they generally mean in an objective sense, not just in terms of it being subjectively unpredictable.
Generally people will not say that something which uses its previous outputs as part of the process of generating its next output is more “truly random”. “Truly random” is usually meant as like, there isn’t anything that determines the value (only things which contribute to a probability distribution over the value).
There is also a notion of algorithmic randomness, where a sequence of bits is algorithmically random when any (deterministic) program (in a given encoding scheme) that generates that sequence of bits, would be longer than the sequence of bits.
So, for example, Chaitin's constant, which is the probability that a randomly selected Turing machine (from a particular distribution over Turing machines) will eventually halt, if run on a blank tape,
expressed in binary (or whatever other base) is algorithmically random.
Cool.... Really f'n cool... Thanks for thanking the time to do it. Keep up the great work! from a recent subscriber
if you leave the experiment runnign for an infinite amount of time you will also see gaps between pulses with an infinite length between them
god thinking about that just make me brain hurt. Thinking about such unintuitive subjects is truly a mental workout
Prove it
This is very interesting on its own, but I do want to say that I don't think Matt Parker was suggesting in his video that the ferro shuffle (spelling?) occurred through completely random means - with the shuffler never having performed one before. If I remember right, the situation was that a group of people claimed that they had this perfect suit of cards dealt out to each person after shuffling appropriately (and cutting the cards) and the ferro shuffle (probably with a brand new deck) was part of the answer to how they could have got that outcome. Now, the group of people in question had no idea that this would happen, so they probably used that type of shuffle (or a similar structured shuffle) while deliberately trying to randomise the cards, without realising they were unwittingly creating this setup. They didn't know using such a structured shuffle would create this outcome (accidentally rigging the deck), and if they were habitual card players (which seems to be the case), they probably had learnt and were using different shuffling mechanisms (whether deliberately or subconsciously).
That's another factor that can bias randomisation with actions like this: once someone learns some card tricks and shuffling tricks, it does become far more likely that they will accidentally repeat these tricks or use variations of them when playing cards. Muscle memory and repetition contributes significantly to the learning of voluntary musculoskeletal movement, and this can become ingrained in the subconscious, becoming more likely to be repeated absentmindedly (or out of habit). The human neurological system is always biased according to previous experiences and repeated actions, making it somewhat difficult for real randomisation to occur in human actions - unless you're deliberately repeating actions in a systematically randomised fashion.
Anyway, great video again.
I would be curious to see some auto correlation ( lags 1 to 3) analysis on the Geiger counter random number generator.
Okay, so I'm thinking something like:
There is a variable amount of pressure you put on the cards, and they are a variable distance to the edge of your finger they need to overcome.
These together both contribute to the amount of charging needed to start flipping cards
However the cards are at a set distance from eachother, making a very reliable factor.
But as the deck goes down, there's less and less cards adding spring force, so potential charge goes down more and more rapidly. This actually starts from the number of cards cut to each side, but is much more noticeable when get to the point where you do something like half the number of cards left between flips.
These are things I might isolate for for a practical test, or thy to be aware of when trying to do this without even knowing if that's how it works because that sounds like a lot of experiment setup.
Great video! I would be interested to see how the probability of perfectly splitting the deck into 26-card halves affects these results
Depends on the person. There are card tricks done by magicians on stage that require 6 or more perfect splits in a row without missing a beat to double check.
My answer to the title before watching: Probably a lot better than we could imagine. 🤞🤪🤙
It's these kinds of observations of completely mundane things like the probability of a specific order of cards in a deck, wondering about it and finding patterns, rules and a complex system that facinates me. How do you start thinking about these things? How do you come up with material that's interesting to you for videos?
Shuffling cards is impossible to be random. This is because cards are being placed next to each other. The amount of randomness of a deck of cards is a function of the current order and the probability of a card being displaced from its current location as a function of the total randomness, which by the limited species of items being organized, only 52 cards, perfectly random will not occur. Or may only occur rarely, which then become a form of organization, thereby creating a form of predictable pattern or other anomalies which in any event may be only considered limited.
At 13:30, you have measured the probability of ONE perfect shuffle. You need to square that to get the probability of two in a row -- necessary to turn a fresh deck into four perfect hands. Not many people play 900k^2 hands in their lifetime. Even fewer open 900k^2 fresh decks; but, some initial arrangements allow the possibility that two specific shuffles in the right order might yield a similar sorting.
First, _any_ arrangement where the suits are completely segregated will do, it doesn't matter what order the cards are in _within_ each suit. This is often done just to make sure all the cards are there. Second, if I were _actually trying_ to do a Faro Shuffle _and conceal it,_ my odds would be about 50/50 to do it once, so about 1 in 4 to do it twice. This is why it's generally required to shuffle a minimum of four times, and five or six is not at all unusual. I read a long time ago that it takes 7 shuffles to ensure any bias from the initial deck order is eliminated, but I don't know how true this is if the shuffler has a tendency to perform perfect or near-perfect Faro shuffles _without trying._
The only way to determine these probabilities for real people is to perform real experiments. However, there is an idealized model of the riffle shuffle called the Gilbert-Shannon-Reeds (GSR) model that is usually used when analyzing this mathematically. This cuts the deck according to a binomial distribution (which matches the intuition that cuts into roughly equal stacks are far more probable than extremely lopsided cuts) then riffles the stacks together by dropping cards one at a time as a series of Bernoulli trials. Each time, the next card could come from the left hand or the right hand, and the probability of coming from one or the other is equal to the fraction of cards remaining in that stack. So if partway through shuffling, there are 10 cards remaining in your left hand and 5 cards remaining in your right hand, the probability that the next card will come from the left is 10/15 = 2/3. This model is qualitatively similar to a real riffle shuffle and optimizes some key indicators of randomness. Specifically, after any number of riffle shuffles, this model on average will produce a deck with lower total variation distance from the uniform distribution than any other model, and it will maximize entropy. So it's kind of the "best" riffle shuffle.
The probability that you get a Faro shuffle in this model is extraordinarily small. First, one must cut the deck into two equal stacks, which has probability (52 choose 26)/2⁵² = 0.11. Then, to get an "out" shuffle, one must first drop the card from the stack that started on the bottom, with probability 26/52, then from the other stack with probability 26/51, then from the first again with probability 25/50, etc. You can see that after going through all 52 cards, I will have multiplied together the fractions (26/52)(26/51)(25/50)(25/49)(24/48)(24/47)...(1/2)(1/1) = (26!)²/(52!) = 1/(52 choose 26). Multiplying these two together, we achieve the overall probability of 1/2⁵² = 2.2 * 10⁻¹⁶. Thus, someone following the GSR model precisely would on average get one "out" Faro shuffle out of every 4.5 quadrillion shuffles. (They would get the same number of "in" shuffles.)
But this only tells you how to reproduce a _shuffle,_ not how to reproduce a permutation. There are many different shuffles that all end up putting the cards into the same permutation. The strictly most likely permutation to end with is always the one you started with. Any other permutation will always be less probable. For a single shuffle, every other possible permutation is equally likely. (Of course, most permutations are not possible at all after a single shuffle.) The go-to source for this topic is a paper by Dave Bayer and Persi Diaconis.[1] Their Theorem 1 on the first page gives an exact formula for the probability that one achieves a given permutation after shuffling n cards m times. Setting n = 52 and m = 1, we find that the probability of leaving a 52-card deck totally untouched after a single GSR shuffle is 53/2⁵² = 1.18 * 10⁻¹⁴, while the probability of any other particular possible permutation (i.e. any permutation with two "rising sequences" as defined in that paper) is 1/2⁵² = 2.2 * 10⁻¹⁶. The probability of getting more than 2 rising sequences after a single shuffle is exactly 0, which should be obvious from how the shuffle works.
But how many of these would result in a "perfect Bridge deal"? Well, if the deck started sorted by suit, then exactly none of them. But what if you shuffle _twice?_ Then it's possible (and very likely) to have four rising sequences, which is the minimum necessary to reorder a deck arranged by suit into one which will deal out by suit. If you think about it, with just four rising sequences, there is one and only one way to perfectly segregate the cards by suit, since if you just look at the cards of any one suit, they all must be in ascending order. (Otherwise there would be five rising sequences.) We can apply Theorem 1 again and get the probability of this unique permutation after two shuffles, which is a whopping 1/2¹⁰⁴ = 4.93 * 10⁻³². You can look at more shuffles, where many more possibilities open up. For instance, with 3 shuffles, there are many possible ways to get rising sequences of length 4-8, and many of those are perfect deals. But the denominator grows exponentially, and things only keep getting worse.
Needless to say, it is not plausible that anyone has ever opened a new pack of cards (or any deck sorted by suit), shuffled it twice while following the GSR protocol to the letter, and then dealt a perfect Bridge deal. Something else must be going on. I think it is likely that experienced dealers are much worse at shuffling cards than less experienced ones. They tend to shuffle more "perfectly" in the sense of alternating cards far too often and almost never getting large clumps. Diaconis discusses this in an interview with Numberphile.[2] It is likely that some people suffer from this affliction more than others, and so that for some people, shuffling this way twice is within the realm of possibility, especially when you consider the variety of other possibilities. On top of all that, it is always possible that some of the news articles discussing this were simply not true, i.e. that the cards had not been shuffled at all, or the alleged deal never happened. That type of deception is not all that rare, so when we're discussing rare events, it's always going to be a concern.
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[1] D. Bayer and P. Diaconis. "Trailing the dovetail shuffle to its lair." _The Annals of Applied Probability_
1992, Vol.2, No. 2, pp. 294-313. statweb.stanford.edu/~cgates/PERSI/papers/bayer92.pdf.
[2] Persi Diaconis video interview. Brady Haran. Numberphile2. Mar 23, 2015. th-cam.com/video/c_Hunaf0tWw/w-d-xo.html.
Can't wait to watch this one!
Thanks for doing this experiment. I can use your results to program a realistic card shuffler
That KSP audio sample triggers a weirdly strong pavlovian reaction in me every single time I hear it.
Great video. The only thing is that the usual way of shuffling is not that good at shuffling cards, if you get what I mean. People playing bridge usually try to do a pharaoh shuffle, which is not hard to do perfect once you are used to doing it. Even by chance I usually do perfect shuffles, without actually trying, learning to do it without effort is just a result of training your shuffling technique, and I mean just shuffling while playing, and having a decent deck of cards.
We could try to measure the conditional probabilities of getting a card from left or right bases on the number of cards on both sides | a few previous cards.
This would give way more data points for every recorded shuffle while still accounting for the conditional nature of these events
I wonder if the length of runs of only one side follows an interesting distribution
A suprising number of fields bloom from just the principle of obfuscation, and if you put encryption into the mix, you've got a recipe for either world domination or disaster.
Like encrypting something twice has the potential of making the message less secure. Thus, sometimes when trying to codebreak, it's beneficial to re-encrypt the message, giving you a less entropic source to let your analysis loose upon. Funny how that works.
I'm using double ROT-13 right now. Good luck reading this!
I designed and built a "random" number generator for my small children to replace throwing a dice. My design used a clock circuit driving a binary to 7 segment display driver set to start at one and roll over before 7. I used a switch to freeze the display at whatever count was shown at the time the button was pushed. There was never any randomness to the circuit as the numbers flowed consecutively but the clock speed was very high and randomness was achieved from the human intervention of the button that froze the display. Try as we could, we were never able to trick the device to anything but random numbers.
If you believe that people are fundamentally quantum systems then if the clock rate is high enough I feel like there's a fair degree of true randomness going on here.
I suspect there are a lot of activities where the more you practice them, the less random they get. Shuffling cards might be one of the more obvious ones, but also painting, playing Mario, heck even walking would exhibit similar behaviors.
Your example of Ohm's Law makes me remember the Generalized Fractional Calculus version of Ohm's law. Shit's cray.
Another way to make a random number generator is to have a radio receiver thats picking up static noise. Connect it to an oscilloscope and measure the amplitude of the static signal at certain times, thats your random number.
Seemingly random, yet still a decent attempt. The data could be crunched to show how or at which points or delay the seemingly random generator for numbers could be plotted probabilistically. The spans. But, that the span is by an unpredictable higher energy particle interaction I do concede would be exceedingly difficult to accurately track and model to see if certain factors would be more or less predictable for the overall result. It's, in my opinion, more fair than many other algorithmic rng calculation setups, like those in slot machines or video games as examples, seeing as how those systems have to implement what appears to be randomness. Nice job. A couple times in my life after playing solitaire I got some predictable results after shuffling, so I'd have to cut and reshuffle in varied ways seemingly randomly to avoid getting very similar patterns in gameplay. Mostly, I noticed, because I'd gotten to a decent shuffling ability, and would always place my aces in the same order when finishing a round, pretty much putting the cards back in an unshuffled state every time. This was pretty similar.
You for sure have to do the Fazeau Apperatus measuring the speed of light video follow up over a longer distance!
Just discovering your channel, loving it! Great work!
I love the destroyed play buttons
Up until now I was under the impression that random by definition is unpredictability
Nixie tubes look so good.
Two vídeos aaaaaauahhhhhhhhhh thank youuuu
I had wondered the same thing back when I watched Matt's video.
I kept expecting him to answer it every time he says something like “and THEN I wondered…” but he left my curiosity hanging 😂
Have you considered that matlab's Rand function is not completely random in the sense that if two separate machines are each running Matlab, when told to output the same Rand function they will be the same. You do need to have never used the function before, but when the conditions are met, both machines will output the same random numbers for as many times as you run the code. In a Matlab course we ran into this during a class project.
I once played a game of magic the gathering with someone who could perfect shuffle. He saw me mana weave my deck before the game, and took advantage of knowing every third card was land. Separated all the lands together while shuffling my deck, so that I could not draw a decent hand for the life of me. Even trying other shuffles after that, you're gonna end up with a lot of lands clumped together, making it both difficult to draw a good hand, and difficult to draw decent cards later in the game
Is mana weaving allowed? I’ve never played mtg
You could try shuffling a smaller deck to test edge effects to some degree.
8:09 that glitch really isn't avoidable with a simple GM tubes setup like that. After an event is recorded, the GM tube needs time to reset its fill gas to a neutral charge before it's able to record another event. The time required for this reset is referred to as dead time and there's a couple techniques to avoid it. The easiest is probably to have some logic that shuts off the detector for the duration of the dead time (and just display the number for that duration) and then turn it back on when the numbers start cycling again.
Yeah the dead time is just longer than I wanted it to be - it’s like a second…
But shifting the distribution over like I did is basically what you describe. I absolutely love that that just works with Geiger tubes - you can glance in it’s direction at any time and see the same probability distribution of future ticks. I wanted to talk about it more but just had time to throw in the onscreen text about memorylessness…
That dead time is like burning a card while dealing poker, it should ensure a random gap by letting a few pings slip by.
This feels like a mathematician's thesis.
Minor detail for 3:28
You wouldn't expect a normal distribution of numbers - you would expect an equal distribution.
Gary PLayer once said, “The more I practice, the luckier I get”
Vsause has a grate vid on how shuffled cards are impossible to get the same shuffle 2x its a 1 in 52 factorial chance and thats a bigger number then the human mind is able to understand intuitively
I'd love to see a data set featuring some of the card magic people in the comments!
If you did shuffles and monitored how often you create "runs" of perfectly interleaved cards, you would only be measuring the likelihood that YOU produce a perfect shuffle... magicians and card mechanics can reliably perform perfect shuffles, as it is an entirely trainable skill. That makes it very dubious to apply statistics to. You might find that you get better and better and they become more frequent depending on the type of shuffling you're attempting. I know that years ago someone measured how many shuffles are necessary to ensure a deck is 'well shuffled' and the answer they came up with was 7. I believe that was accounting for a lot of individual variation. I imagine the paper they published (it was legit peer-reviewed research) would have a lot of relevant information to determining the likelihood of a perfect Pharoah shuffle, and might even include their own observation of it. It's been quite a few years since I read it, though, so I don't remember anything except they came up with 7 as the number of times you should shuffle a deck to ensure it is 'well shuffled'.
edit: Heh, I obviously commented before I finished the video, you did address the trainable skill issue.
you could have setup a camera, an acrylic focal plane, butt cards up, then later just run a script on it to count
Brute forcing something is maths! Just look at Monte Carlo simulations for a really elegant use of maths of brute force.
I imagine the edge effect at the start may be due to the difference between the static friction of you holding the cards still vs the rubbing friction of you letting them roll through your fingers. At the end I don't have any ideas though.
I always wondered about the gambler fallacy when we talk about stuff like odds. The gamblers fallacy states that if you have a 1 in 50 odds of winning with each slot machine pull, then each pull has a 1 in 50 chance of winning. That means you can pull 50 times and not win even once. But eventually if that string of bad luck continued it would get less and less likely for you to lose, simply because your odds of winning is still 1/50. with 1/50 odds, a losing streak of 0/50,0000 would be impossibly unlikely. Each pull is still individually a 1/50 odd of being a win, but the longer the streak of losing (or winning for that matter) the lower the chance that the streak will continue.
I am sorry to disagree but your reasoning sort of implies that pulls are not independent, but they are: every new pull doesn't "know" what happened before. Suppose you are tossing a coin, 1 is heads, 0 is tails. If you toss it 10 times, you can say that the sequence 0000000000 is very unlikely to happen (1/1024), but any other particular sequence like 0000010000 or 0110001000 or 1100110011 has the exact same probability to happen. If after 10 draws the result is 0000000000 then after 11 draws you have exactly the same probability of getting 00000000001 or 00000000000: you do NOT have more chances of getting a 1 just because you already got ten times 0. It is true that long streaks of winning or losing are less likely, but this is true ONLY before you start playing. Once you have pulled N times, this has no influence on the (N+1)th pull because the N first one have already happened and are predetermined. The past pulls have no influence of future pulls and there is a contradiction in your last sentence: you cannot say that the odds of each individual pull is still 1/50 but at the same time that you are less likely to lose after some time.
Would you be willing to post the data? There is a famous problem in probability theory on how many shuffles it takes to throughly mix a deck (it has some characteristic "mixing time" one can calculate). They usual assume a certain model for the runs for this and go from there. So it would be cool to see if your data matches this model
Oooh this would be fascinating but unfortunately I didn’t keep the entire deck order each time, just the runs of “1s”, so I doubt we would be able to pull the relevant info. If we find a way to easily enumerate the stacking order post shuffle this sounds like an awesome thing to crowdsource to get loads of data
@@AlphaPhoenixChannel The famous Bayer and Diaconis "Trailing the Dovetail Shuffle to its Lair" paper cites Diaconis's earlier "Group representations in probability and statistics" as establishing that Gilbert-Shannon-Reeds (GSR) model is reasonably accurate. More specifically, chapter 4 mentions an experiment where Diaconis and Reed performed 103 and 100 shuffles respectively, recording the permutations.
Persi Diaconis loves exploring the conditions for whether things are "effectively random," with a lot of experimentation to develop and validate models… In approachable YT videos, the interviews on Numberphile are lovely, and his lecture "The Search for Randomness" is delightful. IIRC, some of the Numberphile videos discuss the effectiveness of different shuffling techniques. I suspect you'd also enjoy his discussion of flipping coins.
I think this is a perfect example of how math doesn’t always represent real world observations. The variables involved in shuffling, skill, moisture in the air and on the materials, temperature, etc etc.. combined with the basic odds.. accidentally achieving the perfect shuffle is impossible (imo).
the more you riffle shuffle, the more likely you are to get a faro shuffle
Shocking right?
I thought I was going to learn how to beat the lotto. OH WELL!
You made me curious with the unexpected applications of Ohm's law :-) I wonder what these could be!
If you haven’t already, an expanded ohms law vid would be awesome
Filming next weekend if my wire finally arrives
Wait what do you mean by expanded?
Cool stuff, delivered well. Thank you!