My last article, Our Own Poker Calculator - The Perfect Application, introduced the Independent Chip Model (ICM) calculator, an online tool designed to help us mathematically understand the correct play in common end-game situations. The calculator has been a tremendous boost to anyone looking to improve, but it's not perfect for all ICM situations.

The calculator I use only supports five paying places in the payout structure. Would you like to analyze a Final Table spot in a 45-man SNG on Stars, with seven places paid? You can try, by incorporating the first couple min-cash spots into the rest of the structure. After all, you shouldn’t be caring about min-cashing anyway.

But your modifications will make the end result inaccurate. Not horribly wrong, but inaccurate nonetheless.

The calculator is even less valuable when trying to analyze situations in 180-man SNGs or large-field MTTs. Tournament players often find themselves in a spot deep in the money – 27 players left out of a starting field of 2000 – with a push/fold stack of 15 BB. Doubling up at this point will go a LONG way to make the final table, and is likely to be worth a certain amount of gamble. What situations may be monetarily advantageous (+$EV), while having negative chip equity (-cEV)?

Traditional ICM calculators cannot address this situation. The math model is just too expansive, and there is not a way to simplify hand ranges.

The calculator is also not flexible enough to handle odd payout structures, which are becoming more prevalent online. Are you playing in a Knockout tournament? One of those new Cashout structures, recently launched by Full Tilt? Are you playing heads-up or a shootout, where the payout from winning this match is not the entire equity in the tournament? In each of these cases, what you get out of an ICM calculator will be inaccurate, to varying degrees.

The last drawback to an ICM calculator (and the one most vehemently raised by its critics) is the direct assignment of chip equity to a dollar expectation. Let’s take a look at the full ICM calculation from the hand we used in the last article…for the following spot:

PokerStars Game #44920618027: Tournament #278651732, $20+$5+$2 USD Hold'em No Limit - Level VI (100/200) - 2010/06/01 13:49:56 ET
Table '278651732 1' 9-max Seat #5 is the button
Seat 1: Small Blind (970 in chips)
Seat 3: Big Blind (6400 in chips)
Seat 4: Under The Gun (2370 in chips)
Seat 5: The Button (3760 in chips)
Small Blind: posts small blind 100
Big Blind: posts big blind 200
*** HOLE CARDS ***
Dealt to Under The Gun [X X]
Under The Gun: raises 2170 to 2370 and is all-in
The Button: folds
Small Blind: folds
Big Blind: calls 2170
*** FLOP *** [Tc 2s 5h]
*** TURN *** [Tc 2s 5h] [7h]
*** RIVER *** [Tc 2s 5h 7h] [Qd]
*** SHOW DOWN ***
Big Blind: shows [X X]
Under The Gun: shows [X X]

…the ICM equity analysis is:





---


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Explanation:

• Stack: Players stack before posting blinds.
• Push%: Percentage of hands a player open-pushes.
• EQPre: ICM equity before blinds.
• EQPost: ICM equity after hand.
• EQDiff: ICM equity change during hand.

The calculator determines the break-even point between each player winning the pot in an all-in situation, and losing the pot, potentially being eliminated in the process. Against each player, if your hand is better than a given range, you have positive equity. If you shove or call below the break-even point, it’s a negative equity situation…all other things being equal.

The problem is, all other things are never equal, are they? Hopefully, we are better players than our opponents, and have an overall positive expectation of profit in the game. We should find an adjustment based on our opponent’s leaks.

Doing so, however, across a generic sampling of shoving and calling ranges, is incredibly complicated. It’s another set of variables to work into an already complex game theory model. Which opponents will over-defend their blinds? Who will shove too light? Is the guy on your left waiting for AA, and happy just to min-cash?

Rather than trying to figure out every TAG/LAG/weak/passive/psycho/nit combination, I am more than happy just using the ICM calculator to do a range analysis. The egotist in me thinks, “But I’m better than them, so why use a tool that says I’m not?” The realist tells the ego to shut up and live with the range the tool gives me.

To soothe the ego, you can also learn how to do ICM estimations manually. For a specific hand, it really isn’t that complicated. You do what the calculator does, and come up with three values:

- $EV(win)…your dollar-equity in the tournament if you win the pot at showdown
- $EV(lose)…your dollar-equity in the tournament if you lose the pot at showdown
- $EV(fold)…your dollar-equity in the tournament if you choose to fold and not play the hand

Doing the ICM work manually allows you to account for all kinds of situations outside the realm of a basic calculator. You can determine possibilities beyond all-in pre-flop decisions: is it worth chasing a flush or straight draw on the flop if you’re only getting 3:2 on your money? You can work out your own ranges against an opponent on tilt who is sure to be shoving Any Two Cards.

Going through these exercises require being proficient with a utility like PokerStove, which anyone serious about the game should be anyway. And the process can be tedious if you don’t like math.

But at its essence, poker is a mathematical game. Sure, you may have “reads” and “tells” and gut instinct…this information simply provides a range of hands for your opponent. Where you stand against that range, and what you can do with the chips after you rake the pot, is all about the numbers.

Embrace ICM as a methodology, and the calculator as a tool, and your game will benefit.


EPILOGUE:

I intentionally avoided giving a specific example of doing a $EV estimation and ICM calculation by hand, because I did so a year ago, in a previous article. You can follow the link:

http://www.pocketfives.com/articles/...cation-398479/

…or I’ll copy it below. It should be noted, as it was in some discussion back then, you may disagree with the percentages I assigned. That’s fine. To be honest, as I often do, I used examples which highlight the difference between +$EV and –cEV. Disagreeing with the numbers I’ve used does not invalidate the mathematics, or the strength of ICM as a useful analysis tool.


Let’s say you’re in a 180-man MTT on Stars, in which 10th through 18th pay out 2.2x the buy-in, and 7th through 9th pay out an average of 4.7x the buy-in while 4th 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.

grapsfan Paul Herzog

*Opinions expressed in this article and all member-submitted content belong solely to the author, and do not necessarily reflect the opinions or views of PocketFives.com, its staff, or administration.

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