Tuesday, February 13, 2007

ICM for SNGs - Basics and Building Blocks

This post comes from a reader request... To go 'Back to Basics' with The Independant Chip Model (ICM) for SNGs, look at how this is calculated and how it can be used. The maths is actually fairly simple once you look into it - my thought is that the key to using ICM in your game is not just to understand how it can help, but to clearly understand what it can not do too!!

What is ICM?

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 everyones current stack is worth.

By the time we get to the bubble there are usually 4 players with different stack sizes,here everyones equity in the $100 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 and all in you need to balance this with what equity you gain by winning. This is often less than you stand to lose so doubling up might increase your equity by 12%, now instead of judging your winning chances vs the ranges of hands your opponent has pushed with you instead judge your equity risk vs equity reward vs the range of your opponents hand. If you think you are 60% favourite vs your opponents range but are risking $24 to win $12 then it makes sense to fold.

This is the key to using ICM, as with all poker, if you take positive expectation
situations you will win over time. Conversely if you take negative expactation
situations you will lose... lets put it in numbers to be even clearer!

You have 24% equity and are 60/40 favourite (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!!! 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, thats $25 in equity.

Next we assume biggy 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.

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 stacks 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 reward for each position.

No need to calculate this manually, there are plently of on-line calculators available. Link below was suggested by a reader and is a good example.


If you take one thing from this section it should be that doubling your chip stack does not 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 $ev... this understanding is vital to the next step - using ICM at the table!

Another thing to note is that the prize pool difference between 4th and 3rd is the same as the jump from 2nd to 4th... will save this discussion for another day.

What Other Information is Required in order to use ICM at the bubble?

Have already written several articles on SNG Bubble play and ICM (these can be accessedvia the 'jump off' page which is in the links on the right hand side) so will just summarise here.

Firstly thing to mention is that some info is missing here - you can not base decisionson $equity calculations without having an understanding of relative strength of hands vs ranges of opponents hands. For example, you have pocket 10's and face an all in from the big stack at the bubble, based on $ev 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. 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 or call your all ins 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%. Article on estimating ranges available va jump-off page.

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 postive or negative expectation. Worth the $80ish price tag many times over. These tools are not much use at the table but using them to analyse bubble situations after the game really helps!

What ICM Can Not Do!!

Important - ICM is no magic bullet, it helps you make good bubble decisions based on
prize pool equity 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 guarenteed 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 maths would show clearly that they needed 70% vs 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.

Longer than expected to will stop here... happy to answer any queries on the above,
please leave a comment. If you enjoyed this series of articles please tell your friends about the Plan3t Gong Poker Blog!

Cheers, Mark


Cell 1919 said...

I've got a great deal out of your articles and especially 'A Comedy of Errors'.

It's taken me far too long to link to you, but I've finally got round to it.

Thanks for all the effort :)

MrTynKyn said...

Again , great job Mark !!!

"Please leave a comment. If you enjoyed this series of articles please tell your friends about the Plan3t Gong Poker Blog!"

All the people here speak spanish and think that shove with 72o is a totally mistake. What can I do if not take their money ?

BTW , great session with your $T .

Mark , How about to write some in order to get some "rules of thumb" in the middle of the sits . For example:
I saw people let themself down to 800/900 , I think is too risky , I start to steal blinds at 50/100 and 1000 chips stack . But they have better ROI than I . I dont know if Im doing well.

Always appreciate your comments

Keep it up !!