6. Search: Games, Minimax, and Alpha-Beta
ฝัง
- เผยแพร่เมื่อ 9 ม.ค. 2014
- MIT 6.034 Artificial Intelligence, Fall 2010
View the complete course: ocw.mit.edu/6-034F10
Instructor: Patrick Winston
In this lecture, we consider strategies for adversarial games such as chess. We discuss the minimax algorithm, and how alpha-beta pruning improves its efficiency. We then examine progressive deepening, which ensures that some answer is always available.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
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Patrick Winston, the professor of this lecture, pass away this July... Thank you Patrick.
Oh sorry to hear that. RIP
is it because of Corona?
So sad hearing that, true jem of a teacher. RIP
@@ThePaypay88 His McDonald's belly
,,🙏🏻🙏🏻🙏🏻 respect from India
Rest in peace 🕊️🕊️🕊️ A great professor....
Minimax : 16:17
alpha beta simple example : 21:51
alpha beta big example : 24:54
thx
@@ahmedmamdouhkhaled8750 welcome, good luck ^^
didn't pay attention in my classes, now here i am at 4 am watching a lecture from 7 years ago......
thank you for saving my ass.
also, Christopher impressed me at the end lol
same boat here mate
This was 3 year ago... this isn't 2021!
Viral Villager I came from the future
Nafolchan O.o
R.I.P. Patrick Winston, your work will last forever
One of the best lectures in the series, fantastic professor and amazing didactic. Many thanks to MIT for this contribution.
Are u serious? The class and professor disappointed me. The small dwarf guy explains very well. But this professor...Not even close.
@@Atknss can you tell me where i can find this mestirious dwarf that can help me understand AI, would be much appreciated, thank you in advance :)
I dont know where u study or what u study but this is an amazing lecture abt AI. If u cant follow thats allows seriously conclusions about you tho
@@MrEvilFreakout I think he plays in Game of Thrones. Ask George R.R. Martin. LOL no seriously I would like to know too. Although I think this lecture was pretty good.
This is the Breaking Bad of AI lectures. Epic beyond comparison. I've watched it more than once and I've learned something new every time.
Amazing professor. My hat off to you sir
what a great explanation. Elaborated very well! thank you
Great lecture. Very clearly explained alpha beta pruning. I liked the greater than and less than comparisons on each level. This was much clearer then just defining alpha and beta at each level.
Love these lectures - think about them throughout my day. Well seasoned Lecture. Sad to hear about his passing.
Came here for a good explanation of alpha-beta pruning, and got what I came for. Fantastic lecture!
...but what really blew me away was how *absurdly clean* that blackboard is. Just look at it!
Wowwww I've never seen anyone evaluate the time cost of brute forcing chess the way he did! Amazing! This guy is just amazing.
He’s only off by 10^10. While still being right. See my other comment.
He is an amazing professor. I would have considered myself lucky to be in his class.
Love this professor. Calm clear explanation. Smooth voice. And humour.
This was an excellent lecture. The explanation of alpha-beta pruning was so clear and easy to follow, and Prof. Winston is excellent at presenting the material in an engaging fashion. And I loved how Prof. Winston goes the extra mile to tie in these concepts to real life situations such as Deep Blue. Thank you so much!
Greetings from the Politecnico di Milano; thank you for these beautiful lectures!
Great explanation! It's basically everything you need to build any game with AI opponent in one lecture. And you can easily determinate the level of difficulty by limiting the depth level of calculating.
This lecture is so good. It clears the concept on a theoretical and practical aspects both.
This lecture is awesome...such a great professor he is...I absolutely love him
This prof explains stuff so well. Respect.
Amazing teacher, thanks to engineers of yesterday, and MIT, we have access to these gems.
Patrick Winston has a great teaching style with a subtle humor , childlike playfulness, enthusiasm , energetic and engaging lecture, enjoyed thoroughly :)
This is such a great video, I am pretty amazed at how anyone could have came up with this. Great lecture.
Amazing lecture, I am very grateful that this has been recorded, thank you for spreading knowledge for free
best minimax and alpha beta pruning explanation i ever see!
You gave me a great inspiration. Rest in peace my teacher.
For those who want to know where he talks about Min Max go to 25:00. It saved my ass.
+Mares Fillies Thanks , World needs more people like you.
bless you
fuck you. it starts around min 16.
thats alpha-beta part, not the original min-max.
no such thing as savex about it, doesnt matter, schoolx, scox, these gamex etc. meaningless, cepit, do, be can do,be any nmw and any be perfx. also buyer not seller, always test profx not for test
Excellent, very helpful for my Artificial Intelligence exam. Greetings from Germany.
Thank you for this great speech. RIP professor.
Seems like a really nice professor. My AI professor also nice and good teacher but leaves out some details which I learn it from here. Thanks for great courses!
The most clear explanation of Alpha Beta Pruning and Minimax
Came for just the minimax but I stayed for the whole lecture. Thanks MIT
I am into AI and Game Theory now with Columbia Engineering, I really enjoyed this presentation. So long professor.
I wanted to say a huge thank you, this was an amazing lecture!
I can only imagine the elegance of modern chess engines like StockFish and LC0... StockFish being a brute force and neural network hybrid and LC0 being a pure neural netword powerhouse... The amount of knowledge someone could get from studying them would be extraordinary! If only I could had the pleasure...
Thanks to the guy who wrote the subtitles. It clearly made me understand beter.
Thank you Professor Patrick! I wish I have had some professors like you!
Great video and lecture! Required viewing from my AI professor at Pace University. Worth every second!
Phenomenal lecture. Thank you.
I wish I had such a lecturer in my university :)
Especially I liked the moment about cloud computing at 11:07
Prof Winston is quite a genius in giving funny Memorable names for algorithms - British Museum, dead horse, Marshall Art etc. Also the way he explained how Deep Blue applied minimax + alphabet prune + Progressive Deepening etc immediate relate the material to real-life applications. Good Job! But I hope he could explain more on how paralleled computing helped alpha beta punning in DB.
Perhaps it can be organized by branch: one process takes a branch, then when it splits it also splits the process in two. Of course when b=15 that can become cumbersome I guess.
I pray every day for more lectures
Cleared the outlook for Games search
Thank you for these great lectures
Good lecture. Elaborated very well.
Beautiful lecture. Thanks very much.
Pruning explained in the perfect way !!
Such a great, clear lecturer!
Excellent instructor ever. Love from Comsats Islamabad
Very well explained. All my doubts got cleared
perfect lecture!
The dude with leg up just reinvented a whole damn idea in a class. No wonder he is in MIT and I am not.
Sir u R Great !
Really This is Excellent Lecture :)
Thanks
I'm glad I never went to a university, someone like me needs to hear or see something done a few times, this is better for me video lectures from MIT xD
Thank you very much for these.
you saved my life , thank youu
Great lecture!
This is beautiful. he explained it in simple terms very vell
Great and impressive lecture.
Finally. Someone explained this stuff in a way I could understand
thanks for this lecture :)
Since school is online anyways and the whole course is project-based for me. I'm going to MIT online for my Fall semester.
Damn, this was good. I ended up skipping the proof like stuff and could only really understood the actual algorithm. Might watch more of these.
Very clear and concise.
This professor is perfect. It is waste of time to attend the same classes in other school.
wonderful lecture
great lecture!
Great lecture
Human chess players do use the alpha-beta approach (even if we don't recognize it by name), we just have a lot of additional tricks like heuristics about which moves to explore and the order in which to do so.
I didn't think anyone would call a bulldozer sophisticated, but they are! This course is quite eye-opening.
This is really helpful! Great lecture :)
Awesome lecture, I have a test on these topics today. :D
How'd you do on it?
thanks mr winston. This is so good :)
I got thrown off a little on the alpha beta part. So at each level we when we make comparisons do we look at the values from both the min and max perspective?
@ 29:34, for the deep cut, did he compare two Max nodes? or compared the bottom Min node with the root Max node?
very nicely explained the concepts my ai lecturer couldnt teach
rip. great explanations!
A problem I can not understand about the minimax algorithm is about the other player. Do we consider the other player can make the same calculation of the tree to a similar depth? What if they can not and made some decisions to different branches... Will that be a problem? Or not a problem?
I find something here about alpha & betha, what if we're changing the position between 3 and 9 on the left tree...then the first cut off wouldn't happen... so the interesting thing is the alpha betha depended on the evaluation method... For example if you're doing evaluation from the right position so the cut-off will be different :D ... anyway thank you for the explanation... it's really clear
I feel proud that I've been watching MIT lectures enough to have gotten the "celebration of learning" reference. xD
What does it mean?
@@axelkennedal5656 Euphemism for an exam?
Great explanation minimax saved my ass! thankssss
Jeez this prof is so cool in the way he talks about things wish I have a teacher like that so I don't have to watch this in a class with a super bad teacher lol
I have a few questions. The first one is, is Minimax considered as a state space search? If it is is there a Goal state/node?
Great lecture, but I hope that AI has advanced far enough now to automatically filter the coughing noises out of the audio. It sounds like a TB clinic in there.
Lectures like this make me wish I didn't screw around so much in high school :C should've gone to MIT instead of my crappy uni
24:59 man had a tree prepared like a G
30:29 Shouldn't the root then be = 8 ?
When exactly does A-B prune the most nodes?
39:02 "unfortunate choice of variable names" lmfao
R.I.P Patrick Winston
Can anyone explain how the deep cut off works at 28:13? Is the maximizer making a comparison from the root to the minimizer value just above the leaf?
Whenever u get a fixed value of a node (here 27 at the top) , you compare that fixed value to the next deepest first node(here 1) and then again the usual way of checking nodes...
I was also confused for a while there..
In the alpha-beta example, the branch that doesn't actually get created is just the right-most one that leads to the terminal node (not computed, because of the "cut"). Is that right?
If it's right, than the statement "it's as if that branch doesn't exist" (24:00) must be interpreted such that the algorithm will never choose the action that leads to the right-hand node (the one
yes
On full depth search (13:44 ish) he says 10*(80+10+9+7) = 10^106 but it’s actually 10^116. Sure his point holds but he’s just off by a factor of 10^10=10 billion.
anybody got what the student said at 42:00 ?
The game tree depth is just one factor. I bigger problem is the evaluation of the board at each level. That is what makes current chess engines winners.
I wonder how much you save by using the tree of the last move as a basis for the next one, since the min player can be a human, and he might not take the branch you predicted. So the alpha beta algorithm assumes the min player will always take the option that is most in the min player's own interest, which is not always the case in computationally "flawed" humans.
If the computer is the superior player, then it doesn't matter when the human makes a poor move. The computer, when doing the initial search, decided that the branch in question was "too good to be true." Thus when the human makes that move, the computer can re-discover the path that was originally "too good to be true" with less effort than it took to find it the first time (because we are one level deeper in the tree).
Bottom line: Computers (when properly programmed) spend the bulk of their time analyzing the game under the assumption that the opponent is just as good as the computer. Whenever the opponent makes a poor move, the computer can recognize and capitalize on that gain relatively quickly, making the time wasted earlier irrelevant.
@@richardwalker3760 Probably caching values or entire trees can be of value? Otherwise you are recalculating things you've seen before.
When the intro didn't said "This content is provided under MIT open course ware...." I thought my earphone broke.
Finally I understand this :O
21:36 It's not "branching down", he says "branch and bound" from previous class.
I have a question: At 36:22 he says what if we don't have enough time and we went only till the (d-1) th level. And then he also suggests we can have a temporary answer at every level as we go down as we should have some approximate answer at any point of time. But!! How can we have any answer without going to the leaf nodes because it's only at the leaf nodes we can conclude who can win the game. Think this for tic-tac-toe game. At (d-1)th level we don't have enough information to decide if this series of moves till this node at (d-1) will win me or lose me the game. At higher levels say at (d-3) it's so blur! Everything is possible as we go down! Isn't it? So, if an algorithm decides to compute till (d-1) th level then all those path options are equal!! Nothing guarantees a win and nothing guarantees a lose at (d-1)th level because if I understand correctly wins and losses are calculated only at the leaf nodes. This is so true especially in pure MinMax algorithm. So how exactly are we going to have an 'approximate answer' at (d-1)th level or say (d-5)th level?
You are correct in sense that the any levels less than d do not 'guarantee' a winner. going down to d levels guarantees a winner iff both players play 'optimally'. this is feasible in games with small depth(ie. tic tac toe) but in the game like chess it is impossible to make tree that huge. (it is estimated that it would take world's fastest computer around a billion years to make first move!!) so here we don't care about most optimal but we just care about somewhat good move.and yes, technically (but not practically) you can beat it.
hope this helps.
Thanks for your response. You didn't get my question. How are you going to decide if a certain move is a "somewhat good move"? Only leaf nodes can tell you what is a good move and what is a bad move. Forget about the win move at (d-5) level, think about not choosing a lose move, at (d-5)level how can you decide that a certain move isn't going to lose you the game down the road?
Heuristic function is used.
That function(given the current state of the game) returns a number which measures how LIKELY it is for me to win.
How that function is constructed depends on the nature of the game and analytics which conclude how easy for other player is to respond to my move(this comes from the power of searching the tree).
The quality of that function we may change dynamically during the game because it will greatly influence our success.
In chess it may look something like this:
c1 * material + c2 * mobility + c3 * king safety + c4 * center control , where c1, c2,c3,c4 are constants which tell us what thing is more important than the other.
As you can conclude, these functions certainly aren't perfect.
Humans tend to have better understanding of the field using the experience and common patterns.
Agree! It's basically determining the likelihood of winning the game based on the features f's of the current state. g(weights * features) is shown in the lecture.
I was confused about it for a little bit too. From what I can understand, in our case, each node of the tree represents a board configuration. As someone else, we must have a heuristic to determine how good a particular board configuration (node) from the perspective of min and max.
Lecturer mentioned that one of the possibilities for heuristics is the piece count for each player (just as an example). But obviously value of each piece is not equal, so that wouldn't be the best heuristics. But you get the idea of what could be used as a heuristic.
If we didn't have any such heuristic, then your only values would be -1, 0, 1 at leaf nodes. They would represent final configurations - loss, draw, win. In this case yes, you wouldn't be able to determine values at intermediate nodes because there's nothing to tell you whether min or max are closer to winning or losing.
"Marshall" Arts >_< I was hoping it was a pun, but it looks like it's not...