About ICM. an explanation, and two questions

this forum has two reasons. 1: to teach players who don’t know what ICM is what it is and how to use it. 2: two questions i don’t know myself about it i ask to the other players that do know to teach me.

for the people who don’t know what ICM is. it means independant chip model, and it is a formula that proves that lost chips are worth more then won chips by changing the chip value to money value. it is used to know how much equity you need to make your play profitable. you don’t have to actually make this formula after every hand you play (players won’t gonna like you if you do :stuck_out_tongue:) but understanding it will help you to make more good decisions.

here an easy example:
you are in a 6max sng with a buy in of 50. the 1st place gets 70% (210) and the 2nd place gets 30% (90)

there are three players left and player A has 500 chips. player B has 300 chips. player C has 200 chips

the first thing you have to do is calculating the first place equity.
the only thing you need to do is this: (player chips/total chips=winning odds) * (1st place prize)
so player A has 500 of the 1000 chips in game so 500/1000= 0,5. the first prize is 210. so
210 * 0,5=105. this means player A has 105 1st place equity. (0,5 also means 50% chance to win)
player B has 300/1000. so it’s 0,3 * 210= 63 (0,3 also means 30% chance to win)
player C has 200/1000. so it’s 0,2 * 210= 42 (0,2 also means 20% chance to win)

the calculation of the second place is much more difficult to do, but still very doable if you get how.
this is what you have to do:
(((player A second = ((B winning odds * percent of A’s chips to (total chips - B’s chips) * 2nd place prize))+((C winning odds * percent of A’s chips to (total chips - C’s chips) * 2nd place prize)) ))).
same formula counts with the other second places.
player A second place equity: player B has 30% winning odds. A has 500/700 chips, which = 0,714285714285714285 etc. so i just call it 0,714. the 2nd prize is 90. so when ptting it all together you get 30% (is 0,3) * 0,714 = 0,2142 (i’l just say 0,214) * 90= 19,26…player C has 20% winning odds. A has 500/800 chips, which = 0,625. the 2nd prize is 90. so when putting it all together you get 20% (is 0,2) * 0,625 = 0,125 * 90 = 11,25. now put the 2 together, 19,26 + 11,25 = 30,51. this means player A has 30,51 second place equity.
player B second place equity: A has 50%. 300/500 = 0,6. so it’s 0,5 * 0,6 = 0,3 * 90 = 27… C has 20%. 30/800= 0,375. so it’s 0,2 * 0,375 = 0,075 * 90 = 6,75. so 27 + 6,75 = 33,75
player C second place equity: A has 50%. 200/500 = 0,4. so it’s 0,5 * 0,4 = 0,2 * 90 = 18… B has 30%. 200/700= 0,2857142857142857142 etc. (so i’ll just say 0,286). so it’s 0,3 * 0,286 = 0.0858 (i’ll just say 0,086) * 90 = 7,74. so 18 + 7,74 = 25,74

now to put it al together:

player A has 5000 chips. this means he has 105 + 30,51 = 135,51.
so he has 5000 chips but it’s the same as 135,51 money equity

player B has 3000 chips. so 63 + 33,75 = 96,75.
so he has 3000 chips but it’s the same as 96,75 money equity

player C has 2000 chips. so 42 + 25,74 = 67,74
so he has 2000 chips but it’s the same as 67,74 money equity.

now that everything is clear i’ll give an easy ICM example (no blind values to keep it easy):
assume you are player C. player A pushes all-in and player B folds. now it’s your turn. if you only look at chip value, you only need more then 50% equity to get +EV. so let’s just say your and your opponents hand have an 55/45 chance. this means normally calling is +EV. but now look at it again with ICM involved.

  • when you call and lose, you lose 67,74 equity
  • when you call and win we get a new amount of chips
    player C (you) 4000. player A 3000. player B 3000.
    so C has 0,4 * 210 1st place equity which is 84
    so A and B has 0,3 * 210 1st place equity which is 63
    now the second place again:
    C second place equity: A has 0,3. 400/700 = 0,571428571428571428 etc. (or 0,571). so it’s 0,3 * 0,571 = 0,1711 (or 0,171) * 90 = 15,39. since B has the exact same stack as A we can just double it. so 15,39 + 15,39 = 30,78.
    A and B had the exact same stack so this is the second place equity for both: C has 0,4. 300/600 = 0,5. so 0,4 * 0,5 = 0,2 * 90 = 18… AorB has 0,3. 300/700 = 0,428571428571428571 etc. (or 0,429). so it’s 0,3 * 0,429 = 0,1287 (or 0,129) * 90 = 11,61. so A and B has 18 + 11,61 = 29,61.

so when putting it all together:
C (you) get 4000 chips which is 84 + 30,78 = 114,78
A and B have 3000 chips which is 63 + 29,61 = 92,61

this means that with the call of the all in. you would lose 2000 chips if you lost and won 2000 if you won. which is exactly the same. but the looking at the ICM. you know now that losing 2000 is a real loss of 67,74. and winning 2000 is a real win of 47,04. so this means your 55% chance hand is actually -EV. so +chip EV may sometimes also be real -EV.

i hope this formula will help :slight_smile:

now that the explanation is done, i will ask my own questions:
since i also have a few things i don’t know about ICM, perhaps people that got this already can help me with my questions.

1: as you can see my formula is assuming there are 2 people ITM. the thing i like to know is what formula you have to apply when using 3 or more in the prize pool.

2: even while this is a big formula i used and it took me a few hours to do the math and post it all. this is actually one of the easiest examples possible. there are things like more players, difficult chip stacks (like 27319, 81624, 66392 etc.), blinds, position, more prize pools and perhaps many more stuff. so for example: things like A 2843, B 9235, C 11382, D 1980, E 25683, F 8855, G 4583, H 3399 with 5 ITM spots. this would by using this calculation probably weeks to months to find out. so my question is: are there some algorithms to make it easier to count difficult ICM? (not specificly for the hardest stuff possible but an useful algorithm for any of those things would probably help already).

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yiazmat -

ICMIZER. Here is the link to run calculations (free part of site): http://www.icmpoker.com/icmcalculator/

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thx, i see it’s a nice link and will defenitely use it.

but the questions i asked were actually based on how to calculate it by yourself. do you also have answers on that too?

I do not do these calculations free-hand, nor do I know anyone who would even attempt it. These calculators are available so people can have access to them anywhere and anytime, even in live games. My advice is to use the tools available to you.

For me, I am just doing the very rough calculations in my head as hands progress and the number of players remaining declines. Not exact by any means but close enough for me. At some point I think it falls into a more general category of “situational awareness”. What is my stack size? Who can I attack and who should I avoid? Who am I likely to outlast by folding and who is trying to outlast me? Where is the bubble line? What are the prize increments and so on.

Hope this helps a little. ICM is a great concept and very important to understand but I would think that at 99% of the levels we play, it isn’t necessary to get dead-accurate results. Once you recognize and understand the concepts of $EV vs chipEV, you should be able to incorporate enough of it into your strategy to make it work in your favor.

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Yiazmat -

One tool to help “eyeball” decisions on the fly is to use a push/fold program to run through tons of possible hands. Just by looking at these potential scenarios, you become a lot more adept at making the mathematically correct decisions. At least for me it is helpful in that I don’t need to have the exact ICM calculation done to have a good idea what the correct play would be because I’ve run through enough simulated hands.

Probably not explaining this well but there are programs that will allow you to develop ICM decision making without actually having to run the math each hand. The one on ICMIZER is behind their paywall but I imagine there are other ones out there for free.

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  • the two questions i gave had as reason because when make an calculation of your own helps to get the right feel behind the math, because of that i like doing so.

  • the tips you gave me may not be answering my original 2 questions but they are very useful tips and i will defenitely use it. so thanks for all the information.

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don’t know if it is a stupid question, but i believe i’m missing the joke :slight_smile:

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I agree. Its just that here the math is so cumbersome that it isn’t practical. However, if you want to go through the math line by line, just use the ICMIZER free solves that you are allowed and it will run the entire solution line by line for you to review. It is doing the math but since the results are detailed step by step, it may work for your purposes.

Always good topics. Wish I had something better for you in terms of help.

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thanks for the tip, but i can’t find anywhere where the math is explained. i only see the results. do you know what i’m missing?

thanks and np. you already help the best you can, and am grateful for that.

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Digging way back to 2008, we have this thread on the math that may help. Its not that the math is hard, its that calculating every possible outcome for more than 2 players is a pain in the rear. This is the closest I could find to a good explanation with the math included, most were just the coding for the algorithms to set up your own calculator.


An example used:

Poker Stars $55+$5 No Limit Hold’em Tournament - t200/t400 Blinds - t25 Antes - 4 players

Hero (UTG): t1585
BTN: t1925
SB: t6785
BB: t3205

Pre Flop: Hero is BB with X X
_Hero raises to t1200, Button raises to t1900 all in, SB calls t1700, 1 fold, Hero? _

EV = EV(call) – EV(fold)
EV = ( P_winP_BTN_win_sideEQ_BTN_win_side + P_winP_SB_win_sideEQ_SB_win_side ) - ( P_BTN_winEQ_BTN_win + P_SB_winEQ_SB_win )

And 1 more thread for you on the algorithm and math:

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thx, when i have time i defenitely gonna look at them.

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