Another form of Future Game Simulation is found when you take the coming blinds into account (when you are UTG, for example). This is a much more difficult situation to make such assumptions in, however, since you need to have very accurate information on your opponents' ranges. If you are feeling uncertain, don't bother making your decision even more complicated. Card Removal Effect As players fold in front of you, it becomes less and less likely that an opponent behind you will have a better hand. If three players ahead of you each fold an ace, you don't have to worry about running into pocket aces and probably won't be facing an ace behind you, either. Of course, you can never know what the players in front of you folded, but the card removal effect is still important, as the following example will show: EXAMPLE 4 CO 10 BBs BU 10 BBs SB 10 BBs Hero with 32o BB 10 BBs You are on the bubble in a standard 10 seat tournament with a $100 buy in. Each player has 10 BBs, the blinds are at 200/400. The CO and BU fold to you. The BB is likely to call with any hand in the Nash range. This gives your push with 32o an expected value of +.02%, or +$2. An obvious push?
http://resources.pokerstrategy.com/Strategy/SnG/ICMadv/ICMadv03.jpg ICMadv4 No. You haven't made use of all the information available to you. All players in front of you have folded hands that weren't good enough for a push. Each time a player folds, it becomes more likely that the player behind him has a better hand. This effect is normally ignored in cash games, but can you do the same in a SnG? After all, you have to make a lot of marginal pushes in a tournament. The example above shows us that the decision to push with 32o is actually very marginal once you take the other players' Nash ranges into consideration.
http://resources.pokerstrategy.com/Strategy/SnG/ICMadv/ICMadv04.jpg ICMadv5 If you simply rely on the ICM and pushed with a very wide range while ignoring the other information available to you, you will fail to realize that you are actually in a very marginal spot. It only takes two folds in front of you to dramatically change your EV. Always keep the card removal effect and other information given to you by your opponents' actions in mind. A good approach to the example above would be choosing an edge of 0.2% in the SNG Wizard to account for the card removal effect. Pushing with any two is still profitable, but the weakest hands are much more marginal than they appear to be in the ICM. Edge The ICM assumes that all players are equally good, meaning it fails to give players an advantage/disadvantage as the SnG goes on. If you know that you will be able to find much more profitable spots later in the tournament, you should avoid marginal pushes and calls at times. If, for example, the player behind you is very weak and folds too much of his range in a blind vs. blind push, you should at least consider refraining from a marginal resteal, since there is a clear danger of being called. Problems when analyzing a hand with the ICM The ICM wouldn't be perfect even if there was a way to take all the factors we have mentioned into account. All ICM programs (except for SnG Power Tools) work with set pushing and calling ranges, which, in reality, are rarely the same ranges that most players actually have. Some players prefer pushing with 76o, others with A2o... A marginal call may be right against the one range, but wrong against the other. You also have to ask yourself how well you can actually put your opponent on a range. Your range can vary greatly by simply adding or removing a few hands from your opponent's calling range. If you have trouble putting your opponents' on a range, you should tighten your range to ensure that your pushes are, in fact, profitable. How to improve the ICM There are a number of improvements you can make to the ICM. The ICM relies on conditional probabilities, as we said above. Player A's probability of taking 1st place is defined as Stack(PlayerA)/Stack(total number of chips at the table). A second assumption must be made to determine the further outcome of the tournament. When calculating the probability of winning, the ICM assumes that Player A will take 2nd place if Player B takes 1st: P(A,2| B,1) = Stack(A)/(Stack(total) – Stack(B)) This assumption tends to favor the small stack. A diffusion model presents a better approach, as described in the book Kill Everyone. Such a model relies on random walks. In other words, one chip is moved from one stack to another (selected each time at random), until one stack is completely depleted. The result is that a short stack's equity is not as overestimated as it is in the ICM approach. Kill Everyone gives you the following result when calculating the probability of Player A taking a given place based on the distribution of chips among the three players: Chips Diffusion ICM A B C A 1st A 2nd A 3rd A 1st A 2nd A 3rd 10.0% 10.0% 80.0% 10.0% 40.5% 49.5% 10.0% 41.1% 48.9% This gives us a better impression of the actual situation at hand. This allows you to estimate an opponent's equity more accurately, but it doesn't solve all of the problems we've discussed. Using such a model is also much more demanding, which raises the question of the practicality of relying upon such a model. Another issue is the fact that the ICM program works with exact ranges, when, in reality, you will not be able to put your opponent on his exact range all too often. One way of combating this is to use a distribution of ranges instead of set ranges.
