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Bubble - +ChipEV, but -$EV

55$ SNG, 4-handed, Blinds 300/600

CO: 5000
BU: 5000
SB: 5000
BB: 5000 (Hero)

2 folds, SB pushes All-In. Hero has AT. Call or Fold?

Here is the biggest difference between tournament and cash games. In a tournament it is often correct to fold even if you have the superior hand. We will examine this special case with ATo.
I put SB into the following range: 22+, A2+, K2+, Q2s+, Q6o+, J7s+, J9o+, T8s+, 98s
(aggressive players will push with more!)

If we call with ATo, we win 58.8% of the time against his range and will score an additional 1200 chips in dead money:
chipEV Call: +7.4% / +1482.9 Chips

Our problem is that we will be out of the bubble in 41.2% of cases and won't make any money at all. For this reason, the $EV is negative for a call:

$EV Call: -0.5% / -$2.25

This is probably the most important realization for every SNG player. A call with a better hand can be -EV. This effect can occur in earlier phases (5-6 handed) of the SNG under certain circumstances, however it is the most important criterion for almost all decisions when 4-handed.

Bubble - Midstack - Call against Bigstack vs Call against Midstack

a) Call against Bigstack

55$ SNG, 4-handed, Blinds 200/400

CO: 7000
BU: 3000
SB: 7000
BB: 3000 (Hero)

2 folds, SB pushesAll-In. Hero ?

b) Call agianst Midstack

55$ SNG, 4-handed, Blinds 200/400

CO: 7000
BU: 7000
SB: 3000
BB: 3000 (Hero)

2 folds, SB pushes All-In. Hero ?

The situations a) and b) differ more than appears at first glance. The reasons are the following:

If Hero calls and loses, he will make no money at all, regardless of whether it's against the big -or midstack. But if he wins, in case a) he will have attained a good position but will not be ITM. In case b), however, victory assures hims a place in the money.

To make clear the consequences of a call from Hero:

Hero has 3000 chips before the hand, which is equivalent to 18.6% or $93.

Call in case a) EV Win = 28.7% / $143, EV Lose = 0.0% / $0

Call in case b) EV Win = 32.2% / $161, EV Lose = 0.0% / $0

A win in case b) pays off by around $18 (!!) more than in a). For us, that means that we can call much less against the bigstack than against the midstack.

Let's try it out. Assuming the big- and midstacks push the same hands against us:

SB: 22+,A2+,KT+,QJ,JT

Then we can call profitably with the following hands:

a) against the bigstack: TT+, AKo, AQs+ (3.8%)

b) against the midstack: 66+, AT+ (8.9%)

As we predicted, our calling range is much looser against the midstack.

Note: In a real scenario our opponents would push a bit looser so we could call looser still against the midstack than we have listed here.

Bubble - Bullying as the Bigstack

55$ SNG, 4-handed, Blinds 200/400

CO: 7000
BU: 7000 (Hero)
SB: 3000
BB: 3000

CO folds, With what hands can Hero push?

As we saw in the last hand, it is hard to call against a bigstack as a midstack. SB and BB will be very tight here and will call Hero with roughly the hands that we called with in case a) of the previous example.

SB: TT+, AKo, AQs+
BB: TT+, AKo, AQs+

Hero can push 100% against these ranges! A push with 32o still has an EV of +1.0% / +$4.86!

Let's assume that SB and BB are good players and know that Hero is pushing with any two cards. Then they can call a bit looser:

SB: 66+, AJo+, A9s+, KQs
BB: 55+, A9o+, A7s+, KJo+, KTs+, QJs

But even against these ranges a push with 32o would be a marginal +EV (+0.1% / +$0.55). So we see: a bigstack can do what he wants on the bubble and shortstacks can't do anything about it, even if they know what he's doing.

You might present the idea that it is even more +EV to push under 100% since you would be more respected and called less, thus reducing the variance. This topic is beyond the scope of the ICM, however, and so will be addressed elsewhere.

Bubble - Bigstack vs Bigstack

55$ SNG, 4-handed, Blinds 400/800 A25

CO: 3000
BU: 3000
SB: 7000
BB: 7000 (Hero)

2 folds, SB is a complete maniac and pushes every hand. With which range should Hero call?

I've chosen such an extreme example on purpose to examine the special relationship between two bigstacks on the bubble Hero knows in this case that SB will push 100%. With what can Hero profitably call in such a situation?

Call-Hands: 99+ (2.7%)

This seems too tight to be true, but it is with just this range that Hero can call +EV. Even with AKs, a call is -EV!! (EV Call AKs = -0.4% / -$2.14) This is because even though Hero will often be ahead (He would win a call 67% of the time with AKs), but calling would still risk loosing his whole stack and then being OOTM. A fold, however, practically assures a spot ITM (there are two stacks with just 4BB left in the tournament!).


Now that we know how tight the BB must be here, let's see what a push from the SB looks like if Hero calls only with 99+:

EV Push 32o: +1.9% / +$9.37

(Even if BB would call with a much looser range, such as 66+,AT+, a push with 32o would still be +EV!)

The SB can push profitably without even looking at his cards. This and previous example show just how dominant a bigstack with initiative can be.

Bubble - Calling as Shortstack

55$ SNG, 4-handed, Blinds 300/600

CO: 10000
BU: 4000
SB: 4000
BB: 2000 (Hero)

2 folds, SB pushes. With what hands can Hero call?

Let's say the SB has a range of 70%, which is not unrealistic for this situation. Then Hero can call with 22+, A2+, K2+, Q7o+, Q3s+, J9o+, J7s+, T8s+ (44.5%).

To understand what this means, compare that to Hero's calling range if he had the same number of chips as the SB:

CO: 8000
BU: 4000
SB: 4000
BB: 4000 (Hero)

Assuming SB pushes with the same range as above (70%):

Call-Hands: 66+, A8o+, A7s+, KJo+, KTs+ (14.3%)

The calling range of a shortstack on the bubble is substantially looser than that of a middle stack. The reason is that in that case, Hero cannot hope for another way to get ITM than to win an all-in.

On the other hand, the SB can steal aggressively against a shortstack (even 100% against a tighter big blind), since he's only risking half his stack if he's called but will win a quarter of his stack if the BB folds. (What we said in the example "Ultrashorstack in the BB" about calling with ~3BB in the big blind no longer applies here because we're on the bubble!)

Bubble - Push as Shortstack

55$ SNG, 4-handed, Blinds 300/600

CO: 10000
BU: 2000 (Hero)
SB: 4000
BB: 4000

CO folds. Which hands should Hero push?

First, we must figure out what hands will call us. It must be clear to us that we have little fold equity against the big blind because his odds for a call are too good. The SB will be more careful since the BB is still behind him.

Let's estimate our opponents' calling ranges:

SB: 22+,A2+,KT+,QJ
BB: 22+,A2+,K5+,QT+,JT

According to Power Tools we can push with the following range (min edge .5%):

Push-Hands: 22+, A2+, KTo+, K7s+, QJo, QTs+, JTs, T9s (27.0%)

There is again the question though of whether it's worth retaining the .5% edge. We are the shortstack on the bubble - we won't win by waiting. IN the next hand, the bigstack in the big blind will call almost everything. This means that we're in the last hand in which we will have fold equity. For this reason, it's advisable to forgo the edge and even to make a -EV push.

A 40% range would be even EV; the optimal range is probably between 60% and 70%. Even though our opponents have very loose calling ranges and we're on the bubble (where a coinflip is even -EV!), we can and must push aggressively. The reason is as simple as it is illuminating: we are the shortstack and have next to nothing left to lose. We will not get ITM unless it's through our own initiative so we just have to take risks.

Comparison: Bubble - 3handed

a) Call on the Bubble

55$ SNG, 4-handed, Blinds 400/800 A25

CO: 5000
BU: 5000
SB: 5000
BB: 5000 (Hero)

2 folds, SB pusht All-In. With what hands should Hero call?

b) Call 3handed

55$ SNG, 3-handed, Blinds 400/800 A25

BU: 5000
SB: 5000
BB: 5000 (Hero)

BU folds, SB pushes all-in. With what hands should Hero call?

In both cases, Hero has exactly his share of the total chips (1/4 4handed, 1/3 3handed). What interests us is how his calling range is different from 4handed to 3handed if SB pushes with the same range both times.

Push-Range SB: 22+, A2s+, A3o+, KTs+, KJo+, QJs

a) 4-handed Call-Hands: 99+, AQs+, AKo (4.2%)

b) 3-handed Call-Hands: 66+, AT+ (8.9%)

If we've survived the bubble, we can call much looser again because we no longer risk being OOTM. Once you're ITM, you should focus on winning the tournament instead of trying to weasel your way into second place. This is because the difference between the first and second places is much larger than between second and third.

Summary

Requisite to successful play according to the ICM is the capability for feeling the situation. Whether a push or a call is profitable depends on the opposition and their playing style, the distribution of chips and your own image.

This article as a dozen examples that you should study carefully to understand the mode of thought behind the ICM and the criteria that are pertinent to making decisions. For answers to further questions, you should turn to the forum.

Next article: The Bubble Factor in different SnG formats