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Many people shy away from Independent Chip Modeling at first.  I find that the biggest hurdle people face is that ICM seems to be too "math-intensive."  However, ICM is the biggest reason that you should play the SNG bubble much differently than cash-game poker, so it is well worth learning. 

ICM brings to the SNG world The Law of Diminishing Returns, as each chip in your stack has a diminishing value.  In a stack of 5000 chips, the value of your first chip is worth more than the value of your 5000th chip.  Usually those two values are very close, but four-handed, the disparity of those values is huge!

My focus today will be to illustrate a type of hand that occurs frequently where ICM is critical, and to teach you, using that example, how to play from the chiplead, from second, third, and from the shortstack while exploiting the unique dynamics that occur on the SNG bubble.

Definitions for the purpose of this discussion:
 
cEV - (expected value, in terms of chips)
$EV - (expected monetary value)
Equity - (the amount of money that the SNG is currently worth)
C-Bet - (continuation bet, a bet made postflop by the preflop aggressor regardless of whether he hit the flop)
Fold Equity - (the mathematical chance that your opponent will fold)

 
The hand example will be from a $20+2 10-man SNG where the prizes are $100 for the win, $60 for second place, and $40 for third place.

The stacks are:
 
Chipleader - 7000 (cutoff)
Hero - 5000 (button)
Third - 2500 (big blind)
Fourth - 500 (small blind)

Blinds are 50-100.

The chipleader has been pushing all-in nearly every hand since the action became four-handed fifteen hands ago.  The action is on the chipleader, who pushes all-in once again, and we expect that his total range is any two cards. 

Let's determine what we, as the Hero, can call with:
 
Before the hand, here is how the equity is split up:
 
Player           Chips        Equity
Hero             5000        $65.63
Chipleader     7000        $73.95
Big Blind        2500        $49.16
Small Blind      500        $11.25

If we call the push and lose, our equity is $0.00 because we finish fourth, so we lose all of our $65.63 in equity! (also take note that in this scenario, the shortstack has nearly quadrupled his equity without moving a chip):
 
Player        Chips        Equity
Chipleader    12150        $92.19
Hero                   0         $0.00
Big Blind         2400        $63.34
Small Blind       450        $44.47 

If we call and win, we take a nice lead, but our equity only moves up $19.87 in the right direction:
 
Player           Chips        Equity
Hero            10150        $85.46
Former CL      2000        $48.58
Big Blind        2400        $52.66
Small Blind      450        $13.30

So in this case, we risk $65.63 to potentially win $19.87.  Given this info, we must call with cards that will win 76.74% (3.3/4.3) of the time to make this call +$EV.
 
The mistake people make a lot of the time in this spot is calling with hands that will usually win them chips (cEV), such as AJ, 99, etc.  It is +cEV to call with hands as bad as K10 in this spot, meaning that we will, on average, win chips calling with K10.  However, it is only profitable in this instance to call with AA and KK.  Your risk is too large to call with QQ, as it does worse than the 76.74% required against any two cards.  Please note that if you could narrow the pusher's range to any ace or any pair, KK would be a clear fold in this instance.  This is one of many situations in bubble play where a play that wins you chips more often than not can be a very unprofitable play (+cEV but -$EV).
 
Here's how to use this information to your benefit, and how to play four-handed (Please note that these are general rules that work a majority of the time, but circumstances may exist that alter your optimal strategy):


If you are the chipleader:
 
- Shove all-in with any two cards from the button or the small blind if 2nd or 3rd is in the big blind, and all players left to act have very solid stats, and therefore understand ICM. (mostly high limit)

- In lower limits, against players who aren't good, simply raise 3x the bb with any two cards in this instance.  They will fold often enough to warrant a raise, because most have a fear of not cashing.  If they are clueless players, they may tend to call, and a 2/3 pot c-bet will work the 70% of the time they miss the flop. (The c-bet only has to work 40% of the time to be profitable here, a figure you can reach against even the worst players.)

- Do not make any efforts to keep the shortstack alive unless 2nd and 3rd place are very tight and your chiplead is significant.


If you are in second place:
 
- Call a shove by the chipleader with only AA or KK, and if the fourth place player is very short and the pusher most likely has an ace, only AA.

- If the chipleader simply raises, use care in which hands you shove with.  If you feel you have fold equity, you may still fight back with AK or JJ.

- If the chipleader is shoving every time it's your big blind, then make efforts to kill the shortstack, even if you give away some equity on that hand.(-cEV)  The small amount of equity you risk by shoving the shortstack's big blind could make the action three-handed, which effectively unties your hands.(+$EV)  Don't make extra efforts to kill the shortstack if the chipleader is not doing this.

- Raise passive players' big blinds, including the chipleader.

- Pick on third place's big blind, raising any two against it from the button or the cutoff.

If you are in third place:
 
- Call a shove by the chipleader with QQ or better; KK or better if the shortstack is extremely short.  Your fold equity is limited, so keep the same range if you are only raised instead.

- If the chipleader shoves and the second place guy calls, call with AA only.

- Steal from passive players, including those that have you outchipped.
 
If you are in last place:
 
- You have two strategies to choose from: waiting out an elimination so your equity can skyrocket or getting in there and fighting hard.  Here's a good rule for choosing your strategy:

Wait it out and try to sneak into the money if:

- The others are being extremely aggressive, and a confrontation of the other stacks is likely to ensue (common in very low-limit SNGs).  The blinds must also be relatively small, in order to ensure that you have several hands remaining before you are eliminated.

- Your stack is too short that it barely matters if you triple up (if your stack is less than 30 chips, folding AA UTG or on the button is usually the best option!)

- There is another stack that will take the blinds before you and is likely to go out first.

If those conditions don't exist,  get in there and fight!

Although ICM is most useful four-handed in a SNG, it exists at all times, except for heads-up and winner-take-all situations. 

Hopefully this helps bring your game up a notch and gets you more of those first place finishes we all desire!

Jennifear

Jennifear is a proud Contributing Writer for Pocketfives.com and a Presto Award Winner.  She teaches private poker lessons, and you can find the details at Jennifear.com.  A discount on these lessons is available by supporting pocketfives.com by joining a poker site through one of their links.