This article will show you how to calculate expected values in real money or as I like to call it: the real money EV. This article is the basis for any ICM calculation. I am using several math expressions in this article – you are warned For a simple introduction to ICM (Independent Chip Model), please see my article ICM.

### ICM recap

To quickly recap, ICM is used to getting the real money value of a stack given the other stacks and a payout structure.

### EV in cash games

Lets look at the traditional way of calculating your expected value. Assume for this we are playing a cash game. Let Pwin be the probability that you win a hand, Cwin the amount of chips you will have should you win the hand. Let Plose, Close be the according variables should we lose the hand.

We can calculate our expected value (EV) in chips after the hand:

EV = (Pwin * Cwin) – (Plose * Close)

### EV in real money with ICM – EV$

Now lets assume we are playing a tournament with a given payout structure and given stack sizes of all the other players. Let ICM(C) be the map of stack sizes C to its value of real money given the payout structure and all other stack sizes.

Wen can calculated our expected value in real money (not in chips!). I will call this EV$:

EV$ = (Pwin * ICM(Cwin)) – (Plose * ICM(Close))

This is it, that is the only change in calculating your EV from cashgames to tournaments.

### ICM – Why it is not as easy as it looks

The main reason why ICM is so hard to grasp is because the function is anything but linear. This means gaining and losing chips with equal probability is not resulting in a neutral EV$ difference.

This is exactly what you would expect from a good model for tournament chips evaluation: Winning chips has to be weighted against survival in a tournament.

I will follow up with a real life example on how to calculate the real money EV in my next article to give you a better idea of how to actually do any calculations.

### Summary

Real money EV (EV$) is calculated as:

EV$ = (Pwin * ICM(Cwin)) – (Plose * ICM(Close))

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