ICM IS Easy To Understand – Yet Easily Misunderstood.
Here We Look At The Basics, The Math and When Not To Use ICM in SNG Tournaments.
In its simplest form ICM is a way of representing your current equity in a prize pool based on the relative stack sizes of the remaining players and the distribution of that prize pool among them.
At the start of a 10 player SNG with equal stacks of 1000 chips and a prize pool of $100 distributed in the standard 50%/30%/20% format everyone has an equity of $10. Skill differences, cards and blinds are not involved - the numbers simply state what each player’s current stack is worth.
By the time we get to the bubble there are usually 4 players with different stack sizes, now each player’s equity in the $100 prize pool is different, we can work out a snapshot of each players equity by calculating their chance of finishing in each of the 4 remaining positions (see next section).
This is where ICM starts to have a practical application. If you know what your current equity is you can use this to make decisions based on how much extra equity you will either gain or lose by taking certain actions (usually pushing all in or calling an all in at this stage). For example if you have 24% equity and will lose all of this by calling an all-in you need to balance this with what equity you potentially gain by winning the hand. This is often less than you stand to lose – for example doubling up might increase your equity by 12%, now instead of judging your winning chances against the range of hands your opponent could have pushed with you instead judge your equity risk against equity reward then look the range of your opponents hands compared to your holding. If you think you are 60% favorite against your opponents range but are risking $24 to win $12 then it makes sense to fold your hand – the equity risked is not compensated by the potential gain in this situation.
This is the key to using ICM: If you take positive expectation situations you will win over time. Conversely if you take negative expectation situations you will lose... lets put it in numbers to be even clearer!
You have 24% equity and are 60/40 favorite (an estimate of course) to your opponents range when he pushes all in ahead of you. If you win and double up you gain $12 additional equity, if you lose you are out in 4th (equity = $0).
So after 100 hands....
60 Times you win and have $36 equity 60*36 = $2160
40 Times you lose and have $0 equity.40*0 = $0
So at the end of 100 tries you have $2160/100 or $21.6 in equity - the play costs you $2.40c each time you make it when compared to folding!!! Let me ask a question - is your ROI above 24%??
How is Prize Pool Equity Calculated?
No mystery here, each remaining player at the bubble has a chance to finish in any of the 4 remaining positions... to work out current $ equity we need to calculate the chance of each position for the 4 players.
Here is how it is done (will try to keep as simple as possible), the 4 players have stacks of 5000 / 2500 / 1500 / 1000. We Start with the big stack, based on chips alone he has a 50% chance of finishing 1st and taking the $50 for 1st place, that is $25 in equity.
Next we assume big stack indeed got 1st and work out what % chance the other players have of finishing 2nd / 3rd / 4th (based on % of chips in play after we exclude the big stacks chips). So the guy with 2500 chips now has 50% of the remaining chips and thus a 50% chance of finishing 2nd. Repeat for each place.
We are now part of the way there! Next we start over and look at the 2nd stacks chance of finishing 1st (25%) and then work out the other stacks chances of taking 2nd / 3rd / 4th based on their chip stacks. Repeat for the other stacks...
At the end of the exercise you have worked out each stack’s chances of finishing in each position and can so calculate their total equity as an average of their chance of each finishing position and the payout for that position.
No need to calculate this manually, there are many on-line ICM calculators available. Link below is an excellent example.
http://www.chillin411.com/icmcalc.php
If you take one thing from this section it should be that doubling your chip stack does not usually double your prize pool equity... I strongly suggest readers who are new to this change stack sizes in a calculator and see what effect moving the chips around has on each players $ equity... this understanding is vital to the next step - using ICM at the table!
What Other Information is Needed in order to use ICM at the bubble?
The first thing to mention is that some information is missing here - you can not base decisions on $ equity calculations without having an understanding of relative strength of hands against ranges of hands that your opponents might push with.
For example, you have pocket 10's and face an all in from the big stack at the bubble, based on $ equity you need 65% against his range of hands and estimate that range as any pair, any ace, K7 suited + or any 2 cards 10 or above... you need to know whether you have the required edge in advance. We Suggest ‘Pokerstove’ as a good starting point if you have not learned these.
Secondly you need to estimate that range of hands which your opponents will push all in with or call your all in bets with. Without this your $ equity knowledge is useless. For example if player A will call with 65% of hands you can not profitably push into him to steal blinds with as wide a range as someone who is only calling with top 10%. Accurately estimating bubble push and call ranges is a key component of profitable SNG play – see the other SNG Planet Articles on this topic.
Once you can estimate ranges the next step is to get an ICM calculator such as Sit and Go Power Tools (several others available such as ‘SNG Wizz’). You input the stack sizes, blind sizes and your estimates of pushing / calling ranges and these tools tell you whether your push or call has a positive or negative expectation. These Tools are worth the $80ish price tag many times over. For more information see our comprehensive Tools section.)
What ICM Can Not Do
Important - ICM is no magic bullet, it helps you make good bubble decisions based on prize pool equity decisions that will give you an edge long term - but that is all!
ICM does not account for Blinds properly, for example the short stack is next in the BB and is all-in, you are fairly sure of 20% equity if he busts... ignore the range ICM tells you to call the big stack with, tighten up further!
ICM does not take skill differences between the players. If you are outclassed at a table you may have a better chance of winning by taking a gamble early, conversely if you outmatch your opposition it may pay to decline a small +$ev move early to wait for a better spot later.
Understanding ICM can not save you from hideous bubble calls. We have all seen them right, someone gambling with their 23% equity with J6 suited when the math would show clearly that they needed 70% against their opponents range.
It is up to you to spot these players and adjust accordingly - nothing is going to stop some people from spewing both their equity and yours to the players not in the hand!! Be particularly aware of your own image at the table, pushing all in 2 or 3 times in a row and winning the blinds is great - be aware that the 3rd or 4th push might very well be called by a weak holding and make sure that your $equity edge justifies the risk against a much looser calling range.
Link:
ICM
The Independent Chip Model for SNGs 
