ICM isn’t Gospel
Monday, 8 April 2013
I’ve noticed an increased tendency recently among players on forums and in tournaments towards the bubble. They seem to be taking ICM too literally. They seem to be forgetting that the “M” in ICM stands for “model”. Your true equity in bubble situations is not exactly as ICM predicts. I’d like to recap the known shortcomings of the model, and consider some rules of thumb to help with decision making in the heat of battle.
ICM doesn’t take into account the following:
1. When you’ll be posting the blind. If you’re under the gun, you’ll be posting the blind next hand. Hence, you should be less likely to fold than ICM predicts (as you’ll have a shorter stack very soon, and the shorter your stack the wider the range of hands you should be playing).
2. Your relative position. Having bigger stacks (who can bust you) to your right is advantageous because you’ll know in advance of playing your hand whether you can go bust this hand.
3. Stack equity/Skill equity. It’s unclear how much of an advantage it is having a large stack, both in relative terms to other players and in absolute terms to the blinds. As Kill Phil suggests, if you are a weak player, you should try to play for stacks more often (when you are first to act) because it reduces better opponents’ skill advantage.
This cuts both ways, as more skilful players have an advantage when stacks are deeper. How to model this skill advantage has proven difficult, and ICM does not go this far.
Most advanced tournament players are now capable of making adjustments on the fly which take account of these issues, based on experience. They’ll peg the weaker players who are clearly playing Kill Phil strategy and avoid marginal situations with them. They’ll adjust their opening ranges based on relative position and the skill level of their opponents.
What I don’t see a lot of in discussion – even among advanced tournament players – is game theoretical savvy. They seem to be taking concepts such as “Nash equilibrium shoving ranges” as concrete, as if they are formalised “answers” to the question of what ranges should be played in certain situations.
In reality, the shortcomings of the model are significant enough that there are no concrete answers as to what should be shoved and when – merely guidelines as to how one should be thinking. The central concept here is the “non-linearity of chip values”, or to put it more plainly, that the dollar value of the chips in your stack are not constant – they vary according to how many you have, and the differentials in the next prize jump.
The discrepancy is expressed using two terms: chip equity (cEV), which is your equity in a pot in terms of the number of chips you expect to win or lose based on your odds (so like pot equity in cash games); and true equity ($EV), which is the real money value of your chips in the pot (plus those in your stack), based on whether you win or lose the pot, and the resulting prize money if you bust (your prize for coming in nth place) or stay in the tournament (your percentage of the total chips in the tournament expressed as a likelihood of winning, coming second, third . . . etc. multiplied by the value of each prize.)
When you are playing cash games, or are heads up in a tournament, your cEV is equal to your $EV. In other words, chip values are linear. Chips are only non-linear when the amount of chips you have is not directly proportional to the amount of money you can win. This is the case in a tournament with more than two players left, because even if you have almost all the chips in the tournament, you cannot guarantee yourself more than the first place prize.
The question I’ve seen posted many times on forums is of how to use ICM on the fly, ie, during a tournament – especially a live one – when you can’t use ICM tools to model the situation more accurately. The following rules of thumb should help with decision making:
The bigger the next pay jump, the higher the bubble factor
When bubble factor is high, the less cEV translates into $EV, so the less difference adding more chips to your stack will increase your true equity in the tournament. Be more prepared to push a larger stack, less likely to call off a larger stack, and narrow your range in both cases.
If players to your left can bust you, narrow your range
Bubble factor is highest when you can bust, so push better hands if the players left to act have bigger stacks than you.
If you’re less skilful than your table, be more likely to be the first to get your stack in
But remember to leave your opponents the correct odds to fold. If you don’t have much fold equity (including noting whether the big stacks at the table are loose), tighten up regardless. The converse also applies: if you feel you have a skill advantage, be less likely to get involved without a decent hand.
If players are being too tight, loosen up, preferably by not committing your whole stack
This is the old-school advice, but there’s a caveat in the modern game: more people, even tight players, know the value of the reraise all in. Raise small more often, fold to the reshove more often, and keep a tally of how profitable this strategy is at the table. If it’s not working, tighten up a bit and wait for a good hand to raise/call with.
Keep an eye on the next level jump
Even the players savvy of ICM will get lost in the endless fold, fold, shove, fold. Many level jumps can reduce your M by a third, or as much as a half. The players who are aware of the next pay jump will be looser and more aggressive than those who aren’t. Adjust your play accordingly.