"We should kill 2.22 Xenos, brother." "Excelle- wait, .22? How can you only kill .22 of a xeno?" "He'll only be a little bit killed." *From the other side of the field, an elder calls* "Thats awfully nice of you!"
My favorite moment in 40K was way back in third edition playing at a friend's house. I had a big ol' mob of Grots that my opponent completely ignored because they were weak, even as I surrounded his big bad daemon prince with them. Thirty shots hitting on 5's: 25 hits. 25 hits wounding on 6's: 15 wounds. 15 wounds saving on 3's: 10 go through. 10 failed saves ignored by an invulnerable save on 4's (he was a bit of a cheater): 9 failed invulns. 9 invulns ignored by Feel No Pain on 5's (he was a filthy cheater): 8 wounds went through. MathHammer states those 30 shots would have only caused 1.11 wounds, 0.185 taking his cheating into account, but thanks to the luck of the dice it was more than enough to SPLAT his prized model. But yeah, math hammer is great for determining what can be generally expected of a unit. I certainly would not expect a repeat performance of that caliber from my Grots, nor did they ever deliver such a glorious beat down ever again. They mostly stayed in my list so the Boyz could survive an extra turn of shooting, and as a scare tactic against that particular friend. Ain't no Distraction Carnifex as effective against him as a 90 point mob of Grots!
sounds like me playing space marines. i can't roll 3+s with them to save my life. my smash captains charge 5 man scout squads with a heavy bolter and lose half their wounds to overwatch. i have legitimately never won a game of 40k with space marines to this date. yet put me in front of an ork shooting list and i'll roll 5s and 6s all day. lol math.
So to add various nerd maths stuff here: Due to how probability works, if you don't want to continue having to put in 4/6 or 3/6 all the time, the multipliers for each of the results required as such (to 2 decimal places): 2+ = 0.83 3+ = 0.67 4+ = 0.5 5+ = 0.33 6 = 0.17 Each number on a D6 has roughly a 17% chance of rolling, fyi. Extra stuff: If you have to pick between hitting an extra time or having +1 to a roll for any reason (ether better wounding bracket, better AP, etc.) then the extra attack is always worth more not withstanding other factors (such as damage which acts as a total multiplier instead of a result multiplier). This is why for Tau, the advanced targeting system is often worse to take over just another copy of the weapon you want to improve with the only exception being Cyclic Ion Blasters purely because of points. Fun: Having an attempt that has a re-roll for failure makes that roll effectively better than having the next best chance. For example, a 4+ re-rollable is better than a 3+ with no re-roll. This applies to all rolls EXCEPT when needing a 6, in which case a raw 5+ would be better than having re-rollable 6s. If you are wondering, a 2+ re-rollable is about 97% accurate.
Extremely useful information, never seen a breakdown like this. Gives me the mental shorthand to better understand dice rolls and armor/weapon values conceptually. Have been in the middle of trying to understand the mechanics of the game for the first time after reading the books for 15 years and owning around 5000pts of orks just for the joy of painting them.
PLEASE make more of this math hammer explanation! I want to be able to understand the numbers and how to evaluate such odds and damage, but I do not know where to start. This is a godsend to new players, please do a full series and I will watch every one!
@@jodylathwell4886 Oh, it does, my friend, it does. However, for each 1 you re-rolled into a 1, someone else on this planet re-rolls his 1 into a 6. You just drew the short stick on the dice roll average.
Actually, he’s at least -28,000 years old because Magnus hasn’t been born yet so he’s a thousands sons sorcerer sending a message back in time to awaken skynet to turn the world into chaos worshippers Just a thought
To reiterate and expand on Mik Low's point, a 5+ save is only 20% better than a 6+ save (as in, it reduces incoming damage by 20% compared to the 6+), but a 5+ to hit or wound is twice as good as a 6+ to hit or wound. Essentially, 1 point has the biggest impact when the odds of the attack's success on that roll are low.
@@andrewpye7459 probability is the science that says that a person can have his feet in liquid nitrogen and his head inside a steel furnace and be fine cus... average... the body temperature is a luke warm 36'C
I have an excel sheet that I use for almost exactly the sequence you're describing here. Just enter the odds of the attack succeeding at each step, then the average damage (adjusted for things like a d6 damage weapon only doing 1 damage against a 1 wound infantry squad), and multiply through. Very easy.
I do the same when I need to compare two units/gears precisely. But for a rough idea that I can calculate in my head, I round each dice roll to an integer result (as it would with real dice). If the result is a half (for example 2.5), I round to my disadvantage. In your example it would be: 10 shots on 3+ = 6 hits 3+ to wound= 4 wounds 6+ save = 3 damage So I get rid of the extra decimals of each phase, that can benefit to the end result. In real life, you don't have 4.44 dice to wound, you have either 4 or 5 (and 4.44 is closer to 4). However, mathematically your approach is the correct one.
I feel one aspect people sometimes do not factor in is how variation effects different units. Most players are familiar with the concept that d6 shot, d6 damage weapons are high variance, but it goes a bit further than that. If you take a very reliable unit, like almost anything Custodes, then your average damage is going to be much closer to your maximum, while your minimum is going to be much further away from your average. This can create the feeling of being unlucky, when in reality you expect some deviation from the mean, and that deviation can be greater when it is downward. The exact opposite applies to most Ork units (at least when shooting). Understanding this can be important, both because you want to try to factor in likely variations from mean results and because it can help avoid a negative mentality when the dice go slightly against you.
Comparing two units in a match is usefull too. let us have to units A and B, Na number of models in unit A, Nb number of models in unit B. As it is hard to know which unit will strike first before the battle I usually use a simultanuos strike model (but it can be modified to take first strike into account). With Pa the average damage of a model of A on B and Pb the average model of B on A, balance is reached when. Na/Nb = (Na - Nb Pb)/(Nb - Na Pb). => Pa Na² = Pb Nb² This model works fine enough for 1 wound, 1 damage untits. Multi damage can be taken into account in Pa and Pb. Multi wounds can be taken into account this way (but it is more complicated than that). Wa Pa Na² = Wb Pb Nb² Then using points, it is easy to choose for instance between two weapons configurations or two units to fight the best a specific unit. Note : All these statistical models do not take into account overkills (ex: damage 2 shots on 3 wounds models, saturation fire which have a (usually low) probability to kill more models than there is in the target unit). The real average damage is thus very often lower than the calculated one.
I do 'enjoy' the idea of the D6 shots, D6 Damage weapons. If all hit, wound and none are saved the range is 1-36 wounds. I do wonder if people play expecting they're going to roll the 36 every time.
I have an ingrained spite for "math-hammer" as a practice because it takes away from the enjoyment of the game to think about it that way. I dislike the idea that I would have a need to use the arithmetic I was taught in high school after my young self informed mh teachers that I would never need to use what they were attempting to teach me on a daily basis. Math-hammer makes them right... Damn. Plus, I play Orks in a narrative play environment and math-hammer is the most un-Orky thing I can think of. If their ever was something akin to heresy for Orks, it would include math-hammer. 🤣
as an ork player, you can count very high... 1, 2, lots! =D and that's enough! always aim for lots! lots of Daka, lots of crumpin' and lots of figtin'! sounds like lots of fun! or so does my boss nob tells me and he is bigger than me so I'll do as he says else he's punching me gob in and taking me teff!
"we should kill 2.22 xeno's brother!" I have no idea why this is soooooo funny to me, hahaha
"David?"
"Got one sir!"
"Kevin?"
"Killed one two, sir!"
"And Larry?"
"I got the bastard's feet, sir!"
"PERFECT!"
"We should kill 2.22 Xenos, brother."
"Excelle- wait, .22? How can you only kill .22 of a xeno?"
"He'll only be a little bit killed."
*From the other side of the field, an elder calls*
"Thats awfully nice of you!"
I like to imagine this is just shrapnel and General battlefield shenanigans going on. Anything to support... THE MATH-HAMMER”.
My favorite moment in 40K was way back in third edition playing at a friend's house. I had a big ol' mob of Grots that my opponent completely ignored because they were weak, even as I surrounded his big bad daemon prince with them. Thirty shots hitting on 5's: 25 hits. 25 hits wounding on 6's: 15 wounds. 15 wounds saving on 3's: 10 go through. 10 failed saves ignored by an invulnerable save on 4's (he was a bit of a cheater): 9 failed invulns. 9 invulns ignored by Feel No Pain on 5's (he was a filthy cheater): 8 wounds went through. MathHammer states those 30 shots would have only caused 1.11 wounds, 0.185 taking his cheating into account, but thanks to the luck of the dice it was more than enough to SPLAT his prized model.
But yeah, math hammer is great for determining what can be generally expected of a unit. I certainly would not expect a repeat performance of that caliber from my Grots, nor did they ever deliver such a glorious beat down ever again. They mostly stayed in my list so the Boyz could survive an extra turn of shooting, and as a scare tactic against that particular friend. Ain't no Distraction Carnifex as effective against him as a 90 point mob of Grots!
me: the math says the master crafted bolter won't even hit my custode captain haha
dice: hehe double ones armor save goes dead custodes captain
xenos rejoice! every dead captain is a good captain!
sounds like me playing space marines. i can't roll 3+s with them to save my life. my smash captains charge 5 man scout squads with a heavy bolter and lose half their wounds to overwatch. i have legitimately never won a game of 40k with space marines to this date. yet put me in front of an ork shooting list and i'll roll 5s and 6s all day. lol math.
So to add various nerd maths stuff here:
Due to how probability works, if you don't want to continue having to put in 4/6 or 3/6 all the time, the multipliers for each of the results required as such (to 2 decimal places):
2+ = 0.83
3+ = 0.67
4+ = 0.5
5+ = 0.33
6 = 0.17
Each number on a D6 has roughly a 17% chance of rolling, fyi.
Extra stuff: If you have to pick between hitting an extra time or having +1 to a roll for any reason (ether better wounding bracket, better AP, etc.) then the extra attack is always worth more not withstanding other factors (such as damage which acts as a total multiplier instead of a result multiplier). This is why for Tau, the advanced targeting system is often worse to take over just another copy of the weapon you want to improve with the only exception being Cyclic Ion Blasters purely because of points.
Fun: Having an attempt that has a re-roll for failure makes that roll effectively better than having the next best chance. For example, a 4+ re-rollable is better than a 3+ with no re-roll. This applies to all rolls EXCEPT when needing a 6, in which case a raw 5+ would be better than having re-rollable 6s. If you are wondering, a 2+ re-rollable is about 97% accurate.
Extremely useful information, never seen a breakdown like this. Gives me the mental shorthand to better understand dice rolls and armor/weapon values conceptually. Have been in the middle of trying to understand the mechanics of the game for the first time after reading the books for 15 years and owning around 5000pts of orks just for the joy of painting them.
PLEASE make more of this math hammer explanation! I want to be able to understand the numbers and how to evaluate such odds and damage, but I do not know where to start. This is a godsend to new players, please do a full series and I will watch every one!
You may have done the math, Kai'Ba, but there's one thing you didn't account for: *THE HEART OF THE DICE!*
*A SPITEFUL, TWISTED, HATEFUL, SADISTIC, SHRIVELLED-UP HEART, BUT A HEART NONETHELESS!*
You should do a video on the top 3 or 5 most durable infantry units in the game.
Lmao that thumb nail
Step one: do the math
Step two: remember you're playing a real game, so subtract d6 models actually killed compared to the math
Step three: cry
Step two playing Orks: any 6's?
Step three: WaaaaRRGGGGH
Soooo true! /cry
Don't trust any statistics that you haven't faked yourself.
The amount of times I've rerolled my Chaos Lord's 1's for overcharged plasma into another 1 is ridiculous.... Maths has no place within these walls!
@@jodylathwell4886 Oh, it does, my friend, it does. However, for each 1 you re-rolled into a 1, someone else on this planet re-rolls his 1 into a 6. You just drew the short stick on the dice roll average.
Last time I was this early, Magnus still had 2 eyes
So you're over 10,000 years old. Wow 😜
Actually, he’s at least -28,000 years old because Magnus hasn’t been born yet so he’s a thousands sons sorcerer sending a message back in time to awaken skynet to turn the world into chaos worshippers
Just a thought
Your voice is always brimming full of emotion
I know you're joking around, but his voice is honestly nice to paint listening to
Watching these videos makes me feel like I'm attending a uni/lectures about warhammer 40k and I love it!
I tried to use my "Math-Hammer" at a local casino and got kicked out for counting cards
Remember that a 2+ save is twice as good as 3+! Same as 6+ is twice as worse as 5+.
6+ is only half as good as 5+ if you talk about bs and ws.
To reiterate and expand on Mik Low's point, a 5+ save is only 20% better than a 6+ save (as in, it reduces incoming damage by 20% compared to the 6+), but a 5+ to hit or wound is twice as good as a 6+ to hit or wound. Essentially, 1 point has the biggest impact when the odds of the attack's success on that roll are low.
Great breakdown of your process.
Also, if your dice hate you, then take a third of the result of your math & that’s a more representative estimate.
The Law of Maths says I won't fail this 2++ on my Archon. Sods Law on the other hand...
It says you *probably* won't fail.
@@andrewpye7459 probability is the science that says that a person can have his feet in liquid nitrogen and his head inside a steel furnace and be fine cus... average... the body temperature is a luke warm 36'C
Math hammer is strong till you roll nuthin but 1s.
*Laughs in Captain and Lieutenant*
I have an excel sheet that I use for almost exactly the sequence you're describing here. Just enter the odds of the attack succeeding at each step, then the average damage (adjusted for things like a d6 damage weapon only doing 1 damage against a 1 wound infantry squad), and multiply through. Very easy.
I do the same when I need to compare two units/gears precisely. But for a rough idea that I can calculate in my head, I round each dice roll to an integer result (as it would with real dice). If the result is a half (for example 2.5), I round to my disadvantage.
In your example it would be:
10 shots on 3+ = 6 hits
3+ to wound= 4 wounds
6+ save = 3 damage
So I get rid of the extra decimals of each phase, that can benefit to the end result. In real life, you don't have 4.44 dice to wound, you have either 4 or 5 (and 4.44 is closer to 4). However, mathematically your approach is the correct one.
I feel one aspect people sometimes do not factor in is how variation effects different units. Most players are familiar with the concept that d6 shot, d6 damage weapons are high variance, but it goes a bit further than that. If you take a very reliable unit, like almost anything Custodes, then your average damage is going to be much closer to your maximum, while your minimum is going to be much further away from your average. This can create the feeling of being unlucky, when in reality you expect some deviation from the mean, and that deviation can be greater when it is downward. The exact opposite applies to most Ork units (at least when shooting). Understanding this can be important, both because you want to try to factor in likely variations from mean results and because it can help avoid a negative mentality when the dice go slightly against you.
5:06 My heart when I roll snipers to get that last wound off an important model
Comparing two units in a match is usefull too.
let us have to units A and B, Na number of models in unit A, Nb number of models in unit B.
As it is hard to know which unit will strike first before the battle I usually use a simultanuos strike model (but it can be modified to take first strike into account).
With Pa the average damage of a model of A on B and Pb the average model of B on A, balance is reached when.
Na/Nb = (Na - Nb Pb)/(Nb - Na Pb).
=> Pa Na² = Pb Nb²
This model works fine enough for 1 wound, 1 damage untits. Multi damage can be taken into account in Pa and Pb. Multi wounds can be taken into account this way (but it is more complicated than that).
Wa Pa Na² = Wb Pb Nb²
Then using points, it is easy to choose for instance between two weapons configurations or two units to fight the best a specific unit.
Note : All these statistical models do not take into account overkills (ex: damage 2 shots on 3 wounds models, saturation fire which have a (usually low) probability to kill more models than there is in the target unit).
The real average damage is thus very often lower than the calculated one.
Huh. Funnily enough just minutes before I saw this video, I was math-hammering what weapon to give a World Eaters daemon prince....
I do 'enjoy' the idea of the D6 shots, D6 Damage weapons. If all hit, wound and none are saved the range is 1-36 wounds. I do wonder if people play expecting they're going to roll the 36 every time.
Remember when aggressors where a thing? RIP
Thank you! This is very useful
i wonder if there's any places I could go where there's a lot of different matchups between units and common wargears
I have an ingrained spite for "math-hammer" as a practice because it takes away from the enjoyment of the game to think about it that way.
I dislike the idea that I would have a need to use the arithmetic I was taught in high school after my young self informed mh teachers that I would never need to use what they were attempting to teach me on a daily basis. Math-hammer makes them right... Damn.
Plus, I play Orks in a narrative play environment and math-hammer is the most un-Orky thing I can think of. If their ever was something akin to heresy for Orks, it would include math-hammer. 🤣
Da only numbah dat mattahs is ow' many barrels on me deffgun
as an Ork player i rely on my opponent to do da sumz
as an ork player, you can count very high... 1, 2, lots! =D and that's enough! always aim for lots! lots of Daka, lots of crumpin' and lots of figtin'! sounds like lots of fun! or so does my boss nob tells me and he is bigger than me so I'll do as he says else he's punching me gob in and taking me teff!
@@MagralhoPT my boss nob iz betterer dan your boss Nob. sounds like you want a 6 off !!
So are heavy flamer sternguard squads going to be bad ass in 9th?
specially if salamanders... oof but then again... heavy D6, only 2 guys and low AP low damage... so... no... its still mediocre
5 Eldar Guardians disliked this...
Woo MATH!
Unless you are me then you only rolls 1s except morale then its 6 always 6
POOPOO PEEPED CACA