Today we are going visit a concept that is derived out of game theory and the Nash equilibrium which you may be familiar with from the popular film starring Russell Crowe about Mathematician John Nash’s life “A Beautiful Mind”.

We are still being +$EV

In poker we strive to make +EV decisions regardless of risk when the $ value to our chips is the same in dollar value, however in certain situations with payout structures and chip stack depths these situations vastly differ, with $ value on our chips changing, thus meaning we need to be risk-averse with our stack in certain situations and more risk-averse in other spots.

We need to make sure to draw a distinction between not minimising dollar risk and the fact we are only minimising our tournament risk, which is what will maximise our $EV, which is what we are always looking to do in Poker.

Payout jumps

ICM stands for Independent Chip Model and is a way to calculate exactly what stacks in tournaments are worth.

If there are 3 players left in the tournament with payouts at:
1st $500
2nd $300
3rd $200

Your chances of winning the tournament is proportional with the % of chips you hold in the tournament and if this is true, we can make equations to calculate our equity in tournaments.

If the chip stacks of the players left are as follows:
A: 5000
B: 3000
C: 2000

And we have 2000 chips as player C, then we have a 20% chance of winning because we have 2000 of the 10,000 chips in play.

Calculating our equity

However this isn’t our equity, to work this out we can use a handy tool from the team at ICMizer the ICM calculator to work out how much equity we have with our stack. Give it a try here: https://www.icmpoker.com/icmcalculator/

As you can see from this calculation we have $288 in equity with our short stack, this is because we still have a chance to win and there are scenarios that see our equity boosted by player A beating player B for example.

When do we not have to worry about ICM?

ICM does not come into play from early game tournament poker, early in tournaments you will just want to acquire as many chips as possible, ICM is most relevant when we get to the bubble and payout jumps on final tables.

Bubble play

There are going to be spots in tournaments where you have a small stack and there are not many players to bust until we receive a return on investment (ROI) by cashing in the tournament.

Now in normal circumstances we are going to be looking for any +EV spot to gamble, for example, if during Mid game of a tournament a player moves all in for 11bbs from the button and we hold ATo in the BB we will call this all in, this is because we have a range advantage vs them and allow we may be in a flip or sometimes beaten by hands like AJ, AQ, AK, AA, KK, QQ, JJ, TT the most likely scenario is that we will have good equity against the range of hands they will move all in with this stack in this position, so it is a +EV call to make in the long run.

Say we get this exact same situation on the bubble of a tournament where 12 players are paid and we are 8th in chips and the player that is 7th in chips moves all in from the button with the same stack and we are in the big blind with ATo, well then ICM would dictate that this would make a good fold, the reason being is that if we fold the hand we are almost a lock to make the money and cash the tournament with many other players shorter stacked than us, however if we call here and say we are a favourite we may only have say 60% equity against our opponents hole range, then 40% of the time we will bust the tournament with no cash payout and no chance of climbing further in the payouts.

Sometimes ICM pressure means we have to play like a Maniac

ICM doesn’t always mean we have to play tight, if we have a big stack and have players covered in chips then we are going to want to be more aggressive, putting our opponents to the test as they will need watertight hands to be able to risk their tournament life in spots like this, so if they can only call with say the top 10% of their range, they will be folding 9/10 times to our aggression… this is where we can print money on the bubble.

However you are going to want to be wary of “Fuck ICM” type players, they are out there and will take any spot to build big stacks in tournaments, they will either not be aware of the correct math or just won’t care about the strategy due to having a heavy bankroll and wanting to build a big stack regardless of risk.