When playing Sit & Go’s every player is aware that the payouts at the end are what they are aiming for, and the majority understand that they may need to make adjustments along the way in order to maximise their profits depending on their stack size. However, what starts to separate the men from the boys is a precise understanding of when and how much to adjust, as opposed to regularly underestimating the range of hands to move all-in with and overestimating the number to call with late in a tournament. Chip values are not linear in Sit & Go’s and are often very warped by the payout structure around the bubble. Don’t make those mistakes.
Before we get into ICM let’s look at a very basic example. Consider a ten-player $10 Sit & Go with a standard 50/30/20 payout structure, where each player starts with 1,000 chips. The initial conversion rate sees one chip equalling one cent, but by the end of the Sit & Go when the winning player has all 10,000 chips, he has ‘only’ won a $50 first prize- this means the conversion rate has dropped to one chip equalling 0.5 cents. But if a player has just a single chip left when the fourth player is eliminated in an all-in confrontation, the conversion rate of his last chip is now fractionally more than $20, as he is guaranteed to finish at in at least third place.
The Independent Chip Model
The most accurate way of calculating the real-money value of tournament chips in Sit & Go situations – and therefore a very informative guide to whether you should shove, call or fold – is known as ICM (the Independent Chip Model). ICM calculates the value of tournament chips in real dollars by considering the stacks of all remaining players and the prize structure, then calculating their relative chances of finishing in certain orders and the total real-money equity they would amass by doing so. It’s quite complicated, so let's look at how it works and some of the tools you can use to help you make quicker decisions.
Let's suppose 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!
Help is at hand
If nothing else, then, we've learned that ICM calculations are extremely complicated to do by hand. Luckily, thanks to various spreadsheets and computer programs it is now possible to have all the hard work done for you and even to calculate correct all-in calling and pushing ranges based on given assumptions.
If you simply want to see how calling and shoving values change based on stack sizes and payouts, there are many ICM spreadsheets like that at chillin411 where you can enter values to your heart’s content. But, the real power of ICM is to be found in programs like Sit and Go End Game Tools and SitNGo Wizard, both of which offer similar options to help work out whether you should move all-in or fold in certain situations according to ICM.
All you have to do is find a hand history which will automatically be loaded, then by adjusting the sliders based on the calling or all-in ranges you assume for your opponents you can get readouts as to whether you are better off putting your money in the middle or folding. You can also then see how hands other than yours fare or change the parameters endlessly to get a better idea of slightly different situations.
Learning the hard way
The real power of ICM is that it allows you to constantly check up on hands that you have played, in turn giving you a greater understanding of where you are making mistakes and what the correct strategies are in tricky circumstances, like on the bubble. As you will see, there are many interesting situations that come up in Sit & Go’s that the average player using guesswork would not be able to fathom. Using a program like this can essentially teach you correct strategy very quickly.
Of course in doing this it is still important to remember that the results will be based on the hand ranges you input for your opponents, and that inaccuracies here will mislead you elsewhere. Therefore if you are unsure you may just want to set the slider to the point at which calling and folding are equal (the 0 EV point) and examine which side of that your opponent’s range is on.
Remember though, there’s no point being upset with someone for making a bad decision just because you assumed they would play perfectly!