In part one I came up with some numbers for a few different outcomes from a specific hand. Now we'll work with putting those numbers to work in helping us make decisions. As refresher, and to have everything on one page, I was looking at a SNG situation where our hero has K2o in the SB and the button had already folded. The chip stacks were -

Button - 5,000
SB (Hero) - 10,000
BB - 5,000 <READMORE>

<SPAN>For reference I did in fact leave the default settings in the ICM, with payouts of 50%, 30% and 20%.</SPAN>

When our hero folds his SB here we found that we now have an equity of .3764 or about 37% of the prize pool. The question is whether that is the best play. Given the assumptions we made in the first article about the BB we came up with numbers for moving all-in and hoping that he folds.

Because we assumed our opponent would fold 70% of the time and our equity if he folds is .3902 we can multiply those numbers and get .3902 * .7 = .27314. We'll save that number and add it to the numbers we get when he calls.

When he calls and we still win we get an equity of .45 and we need to know how often that will happen. With the estimates we came up with we think that will happen .3 (he calls 30% of the time) * .3 (we will win 30% of the time we are called) = .09. Then we find that .09 (how often this outcome will happen) * .45 (our equity when it does happen) = .0405

When he calls and we lose the hand our equity becomes .3083, and we think from our earlier assumptions that this will happen .3 (he calls 30% of the time) * .7 (he wins 70% of the time when he calls) = .21 So we get .21 * .3083 = .064743

Now we can compare the number we got when our hero folds (.3764) to the total of the numbers we got from when our hero raises all-in (.27314 + .0405 + .064743 = .378383). It looks like we have a winner! The equity when we raise all-in turns out to be higher than the equity when we fold the hand. K2o isn't so bad after all.

What we did here was detemrine the frequency of an opponent's actions according to our best guess, and find the value of each of those actions. Let's do an even more simplified version of this so it is a little easier to understand.

Let's say that we are in an even chip position with 5k each and we are down to 3 handed in a SNG. The river has just brought a brick, and our flush draw has missed, leaving us with a hand that has no chance of winning. The pot is 3,000 so we each have 3,500 left in our stacks. The pot is heads up, and we are first to act. Is it right to put all of our chips in on a big bluff? Let's assume that our opponent will call us 40% of the time, and when he calls we will lose every time. We will also assume that if we check we can not win the hand.

Checking gives us an equity of .2333 which we find by simply entering in the stack sizes after we give up the hand into the ICM.

Raising all-in means we win the pot 60% of the time which gives us 6,500 in chips for an equity of .3649. It also means that we lose the pot 40% of the time for an equity of .2 because we will have gone out in third place and in this case third place receives 20% of the prize pool. When we add up the equity for pushing all-in we get

(.3649 * .6) + (.2 * .4) = (.21894) + (.08) = .29894

Aggression has won both battles. If our assumptions about our opponent are correct then we have determined that the all-in bluff is the best choice.

ICM calculations for more complex situations like a steal at a final table can get very complex, but they all follow

the same simple rules.

1. What are your choices?

2. How often will your opponent have each possible response?

3. What is your equity with each response, multiplied by the frequency of that response?

Add them up and you can find what the correct decision would have been.

Obviously ICM calculations are too time consuming to be doing in the heat of the moment, but using them later to find the correct play will teach you a lot about the game. ICM programs are not necessary to be a very good tournament player, but for even the best players they will yield some valuable information about the game and tournament situations. There are of course many things to be considered when using an ICM that I haven't covered here, but I'll be covering some of those things tomorrow. Things like like the size of the blinds in relation to the stacks, your skill level in relation to your opponents, and their playing styles, all change things quite a bit.

Eventually once I have all three or four articles written I'll try to put them in some coherent order and maybe make one big useful article out of them.

I'll see you at the final table,
Fox

This article sponsored by PokerFox.net where we turn players into winners and winners into pros.
</READMORE>