# Sit N Go Tournament Math

You can improve your win-rates dramatically in Sit N Go tournament using math. With the help of unique calculators which you can use between playing sessions, you can get a whole new perspective on play at the bubble – which will help you make better decisions than your opponents. This look into the math of Sit N Go tournaments focuses on 1-table games, however you can easily adapt these ideas for other variations including Multi-Table SNGs and variations like Double-or-Nothings.

First up, I have outlined how to think of the bubble in terms of ‘prize pool equity’ – which shows your average winnings for different stack sizes over 1000’s of games. Calculating this involves math known as the ‘Independent Chip Model’ which is covered next. In order to get the most out of this math, you need to assess the ranges of hands different opponents are likely to play. I discuss this and the concept of equilibrium between two or more players considering playable ranges at the end of this article.

Even if you prefer to play by ‘feel’, understanding Sit N Go math is important – this will help you see how your opponents are thinking and the logic in their plays.

## Thinking In Terms Of Prize Pool Equity

To demonstrate how prize pool equity changes your thinking at the bubble of a Sit N Go, I have created a simplified example of a bubble situation with 4 players left. In this example everyone has the same stack size, the blinds are ignored and the prize pool is a nice round \$1000.

3 people will get paid in the standard 50%, 30%, 20% format with the 4th place finisher getting nothing. With 2000 chips each, on average each player will win \$250 over 1000’s of games – enough time for short-term variance to even out. That is to say their ‘equity’ in the prize pool is \$250 each.

Now we imagine an all-in between two players. Player 1 shoves all-in, player 2 calls and one of them busts out.

The question is – what does the equity of each player look like now?

This is where the math comes in. I’ll show you the answer and then explain it.

Player 1 \$0 (this guy just busted)

Player 2 \$375 (he doubled his stack to 4000 chips)

Player 3 \$312.50c

Player 4 \$312.50c

What happened here is that player 2 doubled his chips, but did not double his average equity in the prize pool. To do this he would need to win 100% of the time after doubling, and poker is never that simple. The other players gained \$72.50c each in equity without doing anything. They are now guaranteed \$200, and at least one of them will win \$300 or \$500.

The key point to consider is that in order to increase his prize pool equity by \$125 (50%), player 2 had to risk his entire current equity of \$250.

This is important, he risked twice as much as he gained.

Because of this disparity in risk and reward, in order to call the all-in he needed to be sure that he not only beat the hand of player 1, but beat it enough times to justify the lop-sided risk and reward.

The question is, how do you know which hands are good enough to justify this gamble?

## The Independent Chip Model

Fortunately, there is a mathematical model which gives you the answer to this. It is too complex to use at the tables, so you will need to use a special calculator while offline. Examples include SNG Wizard and ICMizer.

What you do is plug in the stack sizes and the range of hands you expect your opponent to play. The calculator then shows you what hand(s) you can call the bet with and which ones you can fold. You will be surprised how few hands justify calls at the bubble. Even if you ‘know’ your opponent is pushing all-in with a wide range of hands, you need to fold most of the time. Remember, calling with the ‘best hand’ is not enough – you’ll need to have enough of an upside to justify risking more equity than you gain.

With an ICM calculator you can adjust the stack sizes of the different players and work out the ranges that you can profitably push all-in with yourself, and call bets with. It does take some time to get to know all the numbers, though once you have done this you will have a significant edge over your non-mathematical opponents.

## Working Out Ranges And Equilibrium Models

The output you get from an ICM calculator is only as good as the information you put in. For example if you work out the math assuming an opponent pushes 60% of hands in a given spot, but their real range is just 25% – then you will make mistakes which cost you money.

This means you have to start with default ranges and work on fine tuning them. This can be achieved using a method known as ‘NASH Equilibrium’. Here is an example:

Your starting point is a range of hands you think a knowledgeable opponent would push all-in with. Let us say 50% for the sake of an easy example. You can then use an ICM calculator and work out that you can call with 8% of hands in this situation. The next step is to assume that your opponent knows you worked out that you can profitably call with 8% of hands. Working backwards from here, he sees that this can be exploited by cutting his range down to 35%, giving him a profitable edge. You know that he has considered this, and so calculate a profitable calling range against this instead – and so on.

Eventually the differences get smaller and smaller, and you reach an equilibrium point.

Remember that this only works against thinking opponents. Against average players you have to get inside their heads with the ‘I have an ace, so I’ll call’ and work out how to best play against that.

Using math in Sit N Go tournaments will give you a huge edge at the tables as long as you make good assumptions about how each opponent will behave. I recommend you study ICM, and watch your bankroll grow.