cEV

1. Chip Expected Value.

The Big Idea

The prevailing school of thought for approaching poker tournament strategy in a theoretically optimal way involves "cEV," an analysis of whether the play being made or discussed is likely to allow the player to win or lose chips.

Discussions of cEV tend to disregard the notion of "tournament life" and ICM considerations.

Discrepancies

A common misconception regarding tournament play is that cEV is always equal to real money EV ($EV). While cEV is roughly equal to $EV in the early and middle stages of an MTT, the discrepancy between the two grows as the tournament gets nearer to the final table, and also varies further depending on the payout structure.

Calculating cEV

Let's say you're in the middle stages of a tournament and in BB sitting on a 50K stack with blinds at 1K-2K/200 antes. You get dealt Ad3d and it folds to the player in the SB who raises to 5K with 60K behind. Let's assume that you decide calling isn't an option, so it's either move all-in or fold.

Before we make any calculations, we must assign a calling range to your opponent. Let's assume that your opponent is solid and will try to steal your blinds with 70% of hands, but given that 40K is two-thirds of his stack, he will call reasonably tight. So using Poker Stove, you get:

33.941% {Ad3d} 66.059% {22+,A8s+,KQs,A9o+}

Based on these calculations, the possible outcomes are:

1. You fold: after posting the BB, your stack is now 47.8K.

2. You shove, SB folds: stack is 48K (5K + 1.8K [antes] = 54.8K] x 82.1% likelihood = 44.9K cEV.

3. You shove, BB calls, you win (17.9% calling x 33.941% chance winning = happens 6.07%): 101.8K x 6.07% = 6.8K cEV.

4. You shove, BB calls, you lose (17.9% calling x 66.059% = happens 11.8%): 0 cEV.

Now, you add up all the possible results assuming you shove and get: 44.9K + 6.8K + 0 = 51.4K.

51.4K (total cEV of shoving - 47.8K (total cEV of folding) = 3.6K (total cEV)

So, based on the assumed ranges, shoving in this spot will show positive chip expected value, but not by a very wide margin.