Independent Chip Modeling Part 2: Positive Chip EV Doesn’t Mean Positive Monetary EV

By Tony Guerrera

Brief Synopsis of Independent Chip Modeling

The following expression is your monetary EV (mEV) in a tournament (the amount of money you expect to make on average in the long run if you were to play the tournament repeated times):

P(1st)(Payout For First) + P(2nd)(Payout For Second) + … + P(nth)(Payout for nth)

Assuming that all the players in the tournament are of equal skill, independent chip modeling (ICM) calculates your finishing distribution solely as a function of everyone’s stack size. Many players play as though all positive chip EV (cEV) decisions are necessarily +mEV. ICM shows that this is not actually the case.

+cEV Is Sometimes -mEV

Let’s take a standard single table tournament in which 1st pays $500, 2nd pays $300, and 3rd pays $200. The blinds are 200-400, and you’re in the big blind with J2o. Action folds to the small blind who pushes all-in. Before posting blinds, the stacks in this tournament were as follows:

Big Blind (You): 7,500
Under The Gun: 2,500
Button: 2,500
Small Blind: 2,500

Assuming that everyone is of equal skill (it’s pretty tough to have an edge in skill with stacks this short), should you call or fold?

Poker Stove tells us that your probability of winning is .4205, your probability of tying is .0460, and your probability of losing is .5335. If you call and win, you’ll have 10,000 chips; if you call and tie, you’ll have 7,500 chips, and if you call and lose, you’ll have 5,000 chips. Your expected chip count after calling is therefore (10,000)(.4205) + (7,500)(.0460) + (5,000)(.5335) = 7217.5. 7217.5 is greater than 7,100, so this call is +cEV. Those using cEV as their only metric for calling or folding would call here.

Let’s now apply ICM to this situation. The different possible tournament scenarios that can exist after this hand are outlined below. Your stack size appears first in each set of stack sizes. Additionally, the mEV corresponding to each outcome is also included in parentheses.

Call and win: {10,000, 2,500, 2,500, 0} ($426.67)
Call and tie: {7,500, 2,500, 2,500, 2,500} ($370)
Call and lose: {5,000, 2,500, 2,500, 5,000} ($303.33)
Fold: {7,100, 2,500, 2,500, 2,900} ($360.22)

Using the winning, tying, and losing probabilities cited earlier, your mEV for calling is ($426.67)(.4205) + ($370)(.0460) + ($303.33)(.5335) = $358.26. Your monetary EV when you fold is $360.22. Therefore, ICM suggests that you should fold despite this call being +cEV.

The Big Idea

You obviously can’t do the calculation I just performed while playing in a casino, and analysis like the above doesn’t mean much if it doesn’t produce results that you can take with you to the tables. In that spirit, the important point of this analysis is that +cEV situations can be -mEV. One class of situations especially susceptible to this is hands involving skewed stack sizes and marginal +cEV.

+cEV yet -mEV plays exist in other circumstances as well…circumstances in which you don’t need to apply rigorous ICM calculations to arrive at proper decisions. Suppose you’re in a single table tournament satellite. Top two places pay $500, and everyone else gets $0. Action is down to 4 players, and you’re dealt AA in the big blind. Blinds are 200-400, and everyone started this hand with 3,000 chips. UTG goes all-in with [AA,TT]||[AK], B calls with [AA,JJ], and SB calls with [AA,QQ]. Do you call or fold?

FOLD! You win this hand over 50% of the time, meaning that you’re definitely +cEV. However, by folding, you automatically get a top 2 finish 93.9% of the time (there’s a 6.1% chance of a tie)! I know this seems obvious, but it’s a fact that people make horrible calls like these in satellites all the time.

Traditionally accepted lines of play are sometimes bad, and traditionally unaccepted lines of play are sometimes good. Today’s most successful players are willing to think outside of the box and are bold enough to stick with their well-founded convictions despite the potential for being called a donkey by the general poker-playing community. Be creative, and remember that bold thinking is important…without it, we’d still think that the Earth was flat and that the Sun orbits around the Earth!

May your mEV always be positive!

Tony Guerrera is the author of Killer Poker By The Numbers.

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