bonycamel's poker diary

Those guys who know ICM, and the principles I’m discussing here, well will find this very yawnsome. Those who don’t might like it and they might find it useful to see figures. I am trying to make some of the posts I wish I had been able to find six months or a year ago. They may exist but if they do, I haven't found them.


These are two common setups on the bubble. You have 3000 chips. In one example the chips are reasonably evenly shared out; in another there is a shorty and a bigstack. Compare these tables, which show stack size and equity (share of the prizepool):

3000 0.251
3000 0.251
1500 0.147
6000 0.351

3000 0.232
3000 0.232
3500 0.257
4000 0.278



You can see straight away that you have more equity when there is a shortstack. This is a feature of ICM that it’s important to grasp: even though you have the same number of chips, you have more equity if someone else is short. And you'll notice that it's quite a decent chunk: 1.9% in this example. The shorter he is, the better. If he has 500 chips and the bigstack has 7000, your share is .278, even though you still have the same share of the total chips: .222

And note that the chipleader having a bigger stack is only partly what affects your equity (so long as the chips he is gaining are not yours, obv.). Give the 1000 chips to the other stack and your equity is .274.

Well, it’s because he will blind out quicker, right? Not really. Here’s something that may not be obvious (or at least its implications might not be): the blinds don’t matter. You have the same equity no matter what the blinds are in ICM. Some people think this makes it a poor model when blinds get higher, because it doesn’t account for what the blinds eating your stack does to your equity. But that’s not a problem with the model as such; it’s just something you have to understand and account for.

ICM is static. It measures your equity right now. This is something you’re well advised to bear in mind when using SNG Wizard to work out whether shoves are +EV. If blinds are reasonably low (say t200), your change in equity after eating the blinds will rarely be huge. Let’s say the bigstack stole both your blinds in these scenarios. Your equity will drop to .238 with the shortstack, and .217 with the more even distribution. That’s not too bad. If the blinds are higher, it starts to be painful quite quickly.

So let’s say that you play a hand with the second stack, and you take 1200 chips from him. Here are the new equity tables:

4200 0.305
1800 0.184
1500 0.157
6000 0.355


4200 0.292
1800 0.16
3500 0.264
4000 0.284

Two things strike me here. One is that you do not gain all the equity the second stack loses. In the first example, he loses .67 and you gain .54. The other two stacks gain the rest. (We all understand that this happens with allins, but it’s true too of any gain or loss of chips. Look at the figures closely. The chips you gained in the first example were only worth .54/.67 = ~80% of the chips he lost. It’s an easy mental jump to imagine that you are either player and could have won or lost the 1200 chips. It’s not so easy to realise that if you play pots in this scenario, you must adjust pot odds at all points so that you will gain enough more chips to offset their lower value. It's no good taking even-money bets. Imagine that you wagered on red at roulette. There's no 0 or 00 but you bet in American dollars and are paid in Australian dollars. You are not liking that bet if the Australian dollar is buying US80c.) But the other stacks don’t share it equally. The shortstack takes nearly .1 and the big stack about .04. In the second, the second stack actually loses more equity, and you gain a little bit more. The other two share the residue more evenly.

What does that tell you? Well, it tells me three things. First, other people playing pots makes me money. Yes, that’s right. I gain if anyone else plays a pot and I don’t. (Not just when they put it all in, but any time I’m not in a pot.) That should make folding marginal hands feel that little bit better. Also, think it through: if folding makes you money if others are playing, then when you consider what you risk by entering a pot, you must add the equity you would gain if you simply folded and let others play. Second, shorties gain more when they avoid playing pots than other stacks do. Sometimes it’s frustrating when you are at, say t150, with a 1000-chip stack, and the table is really active, so that you can’t steal the blinds. But you can console yourself that you’re still making money, and what’s more, you’re making more than others who have also had to fold. And third, when stacks are reasonably even, you lose more equity when you lose. I guess that means you should be more apt to play with a medium stack when there's a shorty than you are when there isn't.


These effects are on the whole fairly small, except the disparity between equity won and equity lost. That's huge, and the bigger the percentage of your stack you are risking, the worse it gets. Look at this last table. This is the equity situation if you take 2000 chips from the second stack with the shorty in:


5000 0.337
1000 0.123
1500 0.179
6000 0.361

You gain .086 in equity. He loses .128. Your gain is worth only 67% of his loss. Meanwhile, when you make that bet on the flop, the shortstack laughs his nuts off. You just made him money, whether you win the pot or lose it. He gained 3% of the prizepool, more than $4 in a 16, because he folded and you played a big pot.