Independent Chip Model Part 2

written by: John

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In part II of the Independent Chip Model, I'm going to show you an example hand from a game I played not too long ago. I will cover the hand from both the hero's perspective as well as the villain's so you can see how to approach similar situations as the player shoving as well as the player calling. Once I'm done with the example, I'll provide you with some tips that you can use to get the most out of ICM in your next sit n go or tourney. Here is the link to Part I on ICM in case you haven't read it.

ICM Hand Example

Ok, this hand here is from an 18 man turbo sit n go which pays out the top 4 places using the payout structure 40%, 30%, 20% and 10%. Here is what the situation looks like:

PokerStars - Hold'em No Limit - Level XI (600/1200)
#3 is the button

Seat 2: Mrr Krinkle (8315 in chips)
Seat 3: BJCANDME (1460 in chips)
Seat 4: Hero (6645 in chips)
Seat 6: villain (6280 in chips)
Seat 8: badba_us (4300 in chips)

In this particular hand, the Hero (me) is in the small blind while the villain is in the big blind. The biggest factor in this hand here is that the player on the button has only about 2 big blinds left and is likely to be the one to bust the bubble. Here is my hand and how the action played out up until it was my turn to act:

*** HOLE CARDS ***
Dealt to Hero [Qd Ah]
badba_us: folds
Mrr Krinkle: folds

As you can see, I'm dealt a pretty good hand for being 5-handed and in a blind versus blind situation. However, I'm not invincible and if I don't asses the situation correctly, I can still be crippled to the point where cashing would be very unlikely. As mentioned in part I, there are steps I need to take in order to make sure a shove (it's a shove since I and/or the big blind have less than 10 big blinds) is a profitable play, both in terms of cEV and $EV. Here are the steps I take:

1. Put the villain on a range of hands. Most players at these stakes are going to shove much tighter and call much wider than they should. So to compensate, I will give him a range of approximately 10%. This includes 88+, A9s+, AJo+, KTs+, KQo+ and QTs+.

2. Once I give the villain a range of hands, I then need to see how AQo does versus that range. I use Poker Stove to do this and find that I'm 45.64% to win and 43.84% to lose.

3. Once that is all done, I also need to figure out the equity calculations for the times I win, lose and fold. Here they are:

Win: Mrr Krinkle: $31.33
BJCANDME: $16.25
Hero: $35.18
villain: $0
badba_us: $25.24

Lose: Mrr Krinkle: $30.96
BJCANDME: $13.82
Hero: $3.86
villain: $34.92
badba_us: $24.42

Fold Pre: Mrr Krinkle: $28.41
Hero: $24.53
villain: $26.78
badba_us: $20.27

4. It is now time to use the formula I outlined in part I. In case you don't remember, here it is:

(win % * equity when you win) + (lose % * equity when you lose)

So, now I just plug in the numbers.

(.456 * 35.18) + (.438 * 3.86) = 17.73

5. Now, compare the equity you got from the equation to the equity you would've had if you had folded. In this case, the equity the hero stands to gain (17.73) is much less than the equity he would have if had folded (24.53) - so this should've been folded preflop given the range given to the villain.

As you can see, the shove that the hero made was actually costing him in the long run. However, as you can see here, the range that the hero gave the villain was also off:

villain: calls 5005 and is all-in
Uncalled bet (365) returned to Hero
*** FLOP *** [3c 9c 5d]
*** TURN *** [3c 9c 5d] [Kd]
*** RIVER *** [3c 9c 5d Kd] [Ad]
*** SHOW DOWN ***
Hero: shows [Qd Ah] (a pair of Aces)
villain: shows [Ac 3s] (two pair, Aces and Threes)
villain collected 12785 from pot

So, assuming that A3o is the bottom of the villain's range, is the shove with AQo profitable now? Let's plug in the numbers and see using the steps above. I'm going to use 30% as the villain's range which means that the hero actually wins 58.45% of the time and loses 36.44% of the time.

(.586 * 35.18) + (.364 * 3.86) = 24.84

If you compare the two equities you'll find that with the villain's new range, AQ is a slightly profitable shove in comparison to folding preflop. You'll also notice how important it is to make the best assumption as to what the villain's range is, as it will drastically affect the hands you should be playing.

Let's look at it from the villain's standpoint now. Although I don't know for sure, for the sake of making the math easy as well as point out a few interesting things, I'm going to assume he knows that the hero is shoving 100% of hands here. Let's go through the same steps as we did above.

1. To decide whether to call a shove from the hero or not, the villain first needs to put him on a range. As mentioned above, I'll assume the villain puts the hero on a 100% hand range.

2. Once the villain puts the hero on a range of hands, the villain then needs to figure out the equity A3o has against 100% of hands. Poker Stove says that A3o is going to win 53.86% of the time and lose 42.17% of the time.

3. The villain now needs to know the equity for the times he wins, loses or folds preflop.

Win: Mrr Krinkle: $30.96
BJCANDME: $13.82
Hero: $3.86
villain: $34.92
badba_us: $24.42

Lose: Mrr Krinkle: $31.33
BJCANDME: $16.25
Hero: $35.18
villain: $0
badba_us: $25.24

Fold Pre: Mrr Krinkle: $28.53
Hero: $28.40
villain: $22.50
badba_us: $20.42

4. Once the villain has his equity figured out, he then plugs in the numbers to see if calling a shove here is profitable.

(.538 * 34.92) + (.421 * 0) = 18.78

5. Let's compare numbers! As you can see, if the villain were to fold preflop he would still have $22.50 of equity in the tournament compared to calling which nets him equity of $18.78. In short, even assuming that the hero is shoving 100% of the time, this call is absolutely horrible as it is a -$4 play on average over the long run.

I happen to dislike the villain's call a ton myself considering he called with a horrible hand, sucked out on me and I ended up the bubble boy. ;) But hey, that's poker, right?

Summary of ICM Hand Example

You are probably looking at all of this and wondering how you'll possible do all of this within the 30 seconds that the poker sites give you to make a decision and act. The answer to this is simple:

You won't.

It's just not possible. In fact, most players don't even bother with figuring out even the basic math I outlined above.

Instead, most players just use a program such as Sit n Go Wizard to tell them what is profitable and what is not. I would advise you to do the same. However, it is still important to remember that for your push/call hand ranges to be correct, you still need to put your opponents on a hand range.

Also, it's important to realize that you won't pick this up (what hands to shove or call shoves with) overnight. It takes a ton of studying away from the tables due to the unique situations such as stack distribution and player tendencies you'll face. Most crucial, however, is the fact that sit n go wiz does not take into consideration any fold equity you have or lose as the blinds increase. So, you'll need to adjust for that yourself. This may mean shoving wider in some cases which sit and go wiz won't like, but it may be necessary. As always, it'll be situation dependent.

ICM Tips

The great thing about learning ICM is learning how to use it to exploit your opponents. To better explain, here is a short list of tips to keep in mind for your next session.

Apply pressure, pressure and more pressure. Look at the real hand example above where it is blind versus blind. In this particular spot, I (hero) would shove almost any two cards here because of the pressure the big blind would face of busting out before the short stack. This is a great spot to shove and hardly ever exploitable. In most cases, the big blind can't call any wider than QQs plus and 77/AK/AQ plus if he actually put me on a 100% range.

If I still had a stack (after that hand) and the short stack folded again, I would probably shove almost any two cards again for the same reasons above. No one wants to bust before the shorty does and they must stick to an extremely tight range to avoid hurting their equity in the tournament.

Play with sit n go wiz. Don't just take Wiz's word for it when it says you need to shove or call with "x%" of hands. Be sure to go in and adjust all the hand ranges and see how wide or narrow you need to be in certain circumstances. You'll definitely be surprised how wide or tight you need to be - sometimes even folding AK on the bubble!

Keep the bubble going. This is my favorite maneuver. Sometimes you'll have a short stack that will shove, it folds to you and now you are getting 4 to 1 or something crazy to call. Obviously, with these types of odds you can call with 7-2. If I have a large chip lead in these situations, I actually like to fold and keep the short stack in the game. Why? Well, because of my first tip above. You can keep the short stack around and shove into the bigger stacks to whittle them down. By the time the bubble actually pops, you have whittled everyone else down to the point where not getting first place would be crazy.

Summary of the Independent Chip Model

I'm sure at first glance this all seems difficult to understand - and it can be. But with a little bit of practice both on and away from the tables and you'll quickly find that ICM is rather easy to pick up. The more you do it, the more second nature it becomes. Having an understanding of ICM will help you to avoid making terrible bubble mistakes as well as enable you to induce a horrible mistake from someone else - both are +EV in the long run. Good luck!