This is the fifth part of a series of tutorials teaching people how to perform expected value calculations with a minimum amount of math. Please read through the first four parts of this series before you start into this segment on tournament calculations. While the first four parts dealt with cash game calculations, the methods used there include details that you will have to know before you can work through tournament scenarios.
The Independent Chip Model
One of the problems with performing expected value calculations in tournament scenarios is that not all of your chips are worth the same amount. For example, suppose you have a ten-handed SNG with a $5.50 entry fee, and players all start with 1,500 chips. In the beginning of the tournament, each chip is worth about $0.0037. Now imagine the player who comes in first place with all 15,000 chips who wins a prize of $25. Now each chip is worth only $0.0017. In a cash game, $1 is always worth $1, and the values of the chips do not change. The more chips you accumulate in a tournament, the less the next chip you earn is worth. This is why you can’t treat tournament calculations like you do cash game situations.
To help deal with the fact that the values of tournament chips change, there are a number of models used to approximate how much a given stack size is worth in terms of a percentage of the total prize pool. The Independent Chip Model, known as ICM for short, is probably the most popular model for these purposes. While it’s not really important to understand how the mathematics work behind producing the values that the ICM comes up with, it is important to understand why it’s needed and how to use it in your own EV calculations.
Using An ICM Calculator
A tool of some sort is needed to generate ICM values for specific scenarios. There are a number of free and paid tools available out there, but the one that we’re going to use is available at http://www.icmpoker.com/icmcalculator/. This is the most barebones one I could find that doesn’t have a lot of extra bells and whistles, and it’s free.
Here’s how this tool works. Select the number of players left in the tournament along the top with the circles. In the left-hand column, put in the payouts in terms of percentages. A standard single-table SNG payout is 50-30-20. Next, put in the stack sizes that each player hands in the middle column. After you do this, press calculate and percentages will show up in the right-hand column. These percentages are the percent of the total prize fund that each player will win, on average, with equal play from everyone. In short, it tells you how much each player’s stack is worth.
When you do typical cash game calculations, you typically need two pieces of information to find the EV of each individual outcome. The first piece of information you need is how often the outcome happens. The second piece of information is what your profit is for that outcome. In tournament scenarios, we’re not going to measure profit in terms of the number of chips we gain or lose. Instead, we’re going to measure it by the change in how much of the prize pool our stack is worth.
A Basic Example: Calling a Shove
We’re four-handed and on the bubble in a standard nine-handed SNG. The CO has 6,000 chips, the BU has 3,000 chips, the SB has 1,500 chips and the BB has 4,500 chips. The blinds are 150/300 with no antes. The CO open shoves, and both the BU and SB fold. It’s to our Hero in the BB, and he has to decide whether he should call or not. We want to calculate the EV of calling to see if we should call or not. Without giving specifics, here is how this calculation should be done. First, we set up our overall EV equation with each of the two possible outcomes:
EV of Calling = EV of Winning + EV of Losing
Now we need to assess the EV of each of those two outcomes, so we need to know the chances of winning and losing along with the profit for each of those two outcomes. The chances of winning and losing will be based on our equity against what we think our opponent’s range happens to be. That part is easy, and we’ve done that a ton of times in this series. However, the new skill we want to learn is finding the average equity in the tournament that we have after calling. We can compare this to our average equity from when we simply fold to decide which one has the best outcome.
If we fold, then we will find ourselves as the small blind in this scenario with a 28.8 percent equity in the prize pool. Notice that to find this, we just plug in the relevant stacks for each of the players starting with the big blind and working backwards to the cutoff seat. This way of organizing things makes it harder to get confused with which seat is which position.
Our equity in the tournament whenever we call and end up losing will be zero because we will bust out. That part is easy to figure out.
Now we just need to find our equity in the tournament whenever we call and end up winning. That takes a little bit of calculation because we have to figure out how the stacks change. I’ve set up the stacks for you at this link where you can see that we will have 40.8 percent equity in the tournament.
EV of Calling = (0.406)(chance of winning) + (0)(chance of losing)
We do this EV calculation and then compare it to the EV of folding which was 28.8 percent like we found above. If the EV of calling is higher than the EV of folding, then we know that we should call. If it’s the opposite, then we know that we should fold.