Independent Chip Modeling is a method of equating the expected value of a tournament decision in terms of the # of chips you’ll win (cEV) and your monetary equity associated with the decision’s outcome ($EV). The development of ICM theory was a key advancement in the “solving” of correct SNG play…as we’ll demonstrate with a classic SNG problem.

There are four players left in a single-table 9-man SNG, with a traditional 4.5x-2.7x-1.8x payout table (where “x” is the buy-in). The blinds are 200/400, and the chip stacks are as follows:

Seat #1: 800
Seat #2: 2100
SB: 5200
BB (You): 5400

Action folds to the SB, who shoves. You have Ace-King. What do you do? Sounds like a no-brainer…but let’s take a closer look.

With ICM, we assign a $EV amount to each decision, based on the possibility of payout percentages. If we call with our Ace-King, we may win and be a dominating chip leader, or lose and be out of the tournament. So let’s estimate we’re a 85% favorite to win the tournament if we with with Ace-King, 10% to come in 2nd, and 5% to come in third.

However, we also have to include our odds of winning the hand. If the SB is shoving with any two cards (and they should be), we’re a 65:35 favorite, according to PokerStove.

The $EV of a call is the sum of the value of each decision:

$EV(call) = $EV(win) + $EV(lose)
$EV(call) = (.85*4.5x + .10*2.7x + .05*1.8x) * .65 + 0
$EV(call) = 2.72x

We have to make similar outcome estimation if we fold. Let’s say, based on approximate chip equity, we’re 35% to win, 45% to come in second and 15% to come in third.

$EV(fold) = .35*4.5x + .45*2.7x + .15*1.8x
$EV(fold) = 3.06x

There is more value in a fold than a call with Ace-King, even though we’re a big favorite from a chip equity perspective.

You can make similar calculations at key points in larger tournaments as well. Let’s say you’re in a 180-man MTT on Stars. Tenth through 18th pay out 2.2x the buy-in. Seventh through 9th pay out an average of 4.7x the buy-in. Fourth through 6th pay out an average of 11.7x the buy-in. The top 3 spots pay out an average of 37x the buy-in.

The blinds are 400/800 as the money bubble breaks. You are 12th out of 18 remaining players with 8400 chips. Doubling up will move you up to 4th. A fairly loose player, who has you covered, shoves from the cutoff. You are in the BB with J9s. For the sake of this exercise, let’s assign the cutoff a starting hand range of any two Broadway, any Ace, or any pair. According to PokerStove, your J9s is a 62:38 underdog to this range.

If you win this hand and are 4th in chips, let’s estimate you are 25% to finish in the Top 3, 30% to finish 4-6, 30% to finish 7-9, and 15% to finish 10-18.

$EV(call) = $EV(win) + $EV(lose)
$EV(call) = ((.25*37x + .30*11.7x + .30*4.7x + .15*2.2) * .38) + (.62*2.2x)
$EV(call) = 5.51x + 1.37x
$EV(call) = 6.88x

If we fold and give up almost one-tenth of our stack, let’s estimate you are 5% to finish in the top 3, 20% to finish 4-6, 35% to finish 7-9 and 40% to finish 10-18.

$EV(fold) = .05*37x + .20*11.7x + .35*4.7x + .40*2.2x
$EV(fold) = 6.72x

With these results estimations, making a call with J9s, as a 3:2 underdog, provides the best financial outcome.

ICM also provides some fuel to the “always take any slight advantage” fire in MTT strategy. Let’s say you’re a successful low-to-mid stakes tournament player, with an expected ROI of 60%, so you should expect to make $15 (on a long-term average) or so by participating in this tournament. You’re in the $24+2 32k guaranteed on Full Tilt, with 1500 players and 162 spots paying.

You raise on the first hand of the tournament from the cutoff with 99. The BB shoves, and tells you he has AKs…and you believe him. Your 99 is a 52:48 favorite. From the cEV perspective, this is an easy call.

From a $EV perspective, however, you need double your expectation to justify the call. To reach this point in the payout table, you’re passing almost 10% more of the field. You have to double the likelihood of going deep, reaching the Final Table, taking the whole thing down. Is this reasonable, just by adding less than .1% of the total chips in play, at Level 1 of the tournament? If the answer is “no” for you, then reconsider the “always take a slight advantage” strategy.

I will grant you, this is a lot of math. Performing ICM calculations takes time. Even when using an ICM Calculator from a poker site, it’s tough to get the data you need to make a decision in the time bank available online. Parts of the exercise, however, are a practicable skill. You can spend a lot of time going over tricky situations, running the numbers and seeing what the right play is. ICM takes practice, both in terms of figuring out what the $EV play may be, and being willing to accept the likelihood of conflict against traditional cEV pot odds.

I also HIGHLY recommend getting friendly with PokerStove and other card calculator applications. Running the numbers on $EV(call) and $EV(fold) may be overwhelming, but there’s no reason why anyone can’t practice assigning hand ranges, and spending time learning how typical hands play against each range. We all spent most of our youth doing homework for hours, with no clear picture as to what we were getting out of it.

Poker homework is +$EV.