In the previous article in this series (‘Introducing ICM’), we discussed how the Independent Chip Model can help you translate your stack size in a given Sit & Go situation into a real-money value. Now we will look at an example of how this is worked out, supposing you are playing a standard Sit & Go with payouts of $50, $30 and $20 with stacks of 6,000, 4,500, 3,000 and 1,500. In order to calculate the real-money values of these stacks we must consider the possibility of each player finishing in each position and multiply each value by the corresponding payout, then add them together. There are programs available that will do the calculations for you, but getting a rough grasp of ICM calculations will help you in the long term.
Number crunching
Deciding how often each player comes first is easy, as that is simply represented by the percentage of the chips they have (so 40/30/20/10). However, the other percentages are more complex to assign and require some number crunching.
For example, for a player to finish in second we need to assume another player wins and then see what percentage of the time our player is likely to beat the others to come second based on the chip percentages between them. So if the 4,500 stack wins (which happens 30% of the time) the 6,000 stack will have 6,000/10,500 of the remaining chips, so 0.3* 6,000/10,500 = 0.1714. Doing this for the situations where the two short-stacks win and the 6,000 stack finishes second gives values of 0.1 and 0.444 respectively, which added together gives a total probability for the big stack of finishing second 31.59% of the time.
Third-place finishes are even more complex, as now you must consider the possibility that a given player wins, then among the three remaining our player comes second as in the above example. There are six possible combinations for this (for example the probability of the stacks finishing in the order 4,500, 3,000, 6,000, 1,500 is 0.3*(2/7)*(4/5) = 0.0686) and adding them together gives a total of 20.64%. With those values calculated we can then simply multiply by the corresponding payouts to get a real-money value. So for example the 6,000 stack is currently worth (0.4 * $50) + (0.3158 * $30) + (0.2064 * $20) = $33.60.
If we do this for all the stacks we get the following results: 6,000 chips = $33.60; 4,500 chips = $29.49; 3,000 chips = $23.59; and 1,500 chips = $13.32. As we can see therefore, the fewer chips you have the more they are worth individually and vice versa. By calculating different situations you can then determine whether a certain call is profitable or not, but as all this maths demonstrates it’s a lot easier to use an online program to do the number crunching for you!