Math in Sit and Go Tournaments

Beating Sit N Go Tournaments Is Easy Once You Know the Math

Sit and Go tournaments have their own pay structures which can be quite different to a standard tournament. In an average multi-table tournament, every time you move up the pay chart, the jump becomes a bigger one, but this isn’t the case with many sit go and tournaments.

In a standard one table game, the payouts might be $25, $15 and $10 for 1st, 2nd and 3rd and. This uses a 50%, 30%, 20% payout structure. You’ll notice that the difference between finishing on the bubble and 3rd is exactly the same as the difference between 1st and 2nd (20% in both cases). In this article, the math behind sit and goes is examined, starting with a basic example, before delving a little deeper into Independent Chip Modelling.

Although you can do these calculations for all types of sit and go, this article concentrates on single table tournaments with 9 or 10 players. These are by far the most popular format.

Sit n Go Math - Equity and the Bubble

When you are playing a sit and go you should always aim to think in terms of equity. Equity is the actual value of your stack. If the game were played out thousands of times, the amount of money you would win with the stack you have is the prize pool equity of those chips. What you will find is that the value of chips is not linear. That is to say that doubling your chip stack does not double your long-term winnings. An example of this will show you why:

There are four players left in a sit and go and each of the four has exactly 2,500 chips (an unlikely situation, but one that works very well as an example). The total prize pool for the single table tournament is $50, with the payout structure as described in the introduction to the article. At this point it is easy to work out that each player has an equity of $12.50, which is the total prize pool of $50 divided by four. Over 1000’s of games, all else being equal, everyone wins $12.50c per game.

The next hand sees the cutoff and the button both fold, but the players in the small blind lands a strong-looking QQ, while the player in the big blind hits Ace-King. Neither player manages to fold and all the chips go in - one player exits the tournament, leaving the other three players all in the money.

Now consider the new situation. The player who won the coin-flip now has double the amount of chips than the other two players have. All things being equal, this gives the player a 50% chance of winning, a 25% chance of coming second and a 25% chance of coming third. When you do the math, you’ll see that 0.5*$25+0.25*$15+0.25*$10 is equal to $18.75. Despite doubling their chip stack, the equity in the tournament has only risen from $12.50 to $18.75. The other two players share the other $31.25 between them, meaning their equity is now worth $15.62.

As you can see from this example, while two ‘uninvolved’ players have remained on exactly the same number of chips, their equity has risen from $12.50 to $15.62. While the player who won the showdown, risked everything and only increased their own equity by 50%.  

The reason this happens is determined by the way the prize pool is structured. All players are now guaranteed the minimum prize, and all players still have a shot at first place. Importantly, the player who ends up with all of the chips will only get 50% of the total prize pool.

The Independent Chip Model (ICM)

The situation above begs a further question. In these situations, should you be willing to risk all your chips in a coin-flip situation? The answer is a simple no. In the example above, the equity for the players all-in was $12.50 before the hand, but effectively $9.37 the moment the hand goes to showdown (an average of $0 equity for the player who loses and $18.75 for the player who wins). In fact, you should only be willing to go to showdown in this example if you were 75% favorite.

While this was a very straightforward example (and the hands were now known to the players), to even do these calculations while in the thick of the action would be tricky.  

Fortunately, you can find ICM calculators online – simply head to google and you’ll see a number of commercial options. With these calculators, you’ll plug in the stack sizes and the potential ranges that players will both push with and call with. The ICM calculator will tell you whether you can then push yourself or call profitably. What you will find is that calling ranges are very narrow, especially when your opponents are selective about their pushing ranges. This makes sense, you’ll be risking $12.50c in equity to win less than $6 more.

You won’t be able to use these ICM calculators during play, but they can prove to be very useful learning tools. You can plug in particular hands to see if you played them correctly, or you can set up various different situations to see what your next move should be. The more you use these calculators, the easier making the right decision will become. At first you might be surprised at just how small a range of hands you can call with. There will be many occasions when you have to fold AK and sometimes it’s not even close to a call.

ICM calculators can be used for all types of tournaments, including multi-table tournaments. However, the unusual set up of the single table sit and go makes it ideal for use in this format.

Keep in mind that you will need to adjust your own ranges depending on whether you believe your opponent understands this concept or not.