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Exact calculation: Call

The following example deals with calculating the EV of a call according to the ICM model.

EXAMPLE

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


CO: 6000
BU: 4000
SB: 4000
BB: 6000 (Hero)

CO folds, BU pushes All-In. SB folds. Hero has A9. Call or Fold?

1.Estimation of the opposing push range

Calculating of a call is much less complicated than the calculation of a push.  The first step is to calculate the opponents range.  Here we will put him on:

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

2.Calculate the EV of different outcomes

If we call, we'll get the following values against the button:

P(Win) = 49.7%

EV(Win) = 38.8% / $194

EV(Lose) = 13.5% / $68

(See previous example for definitions)

Now we weight EV(Win) and EV(Lose) according to their probabilities and obtain the expected value of a call with A9o.

EV(Call) = P(Win) * EV(Win) + (100% - P(Win)) * EV(Lose) = 0.497 * 38.8% + 0.503 * 13.5% = 26.07% / $130.57

The calculation of the expected value of a fold is different here than in the previous example. If we fold here, we don't get to keep our starting stack, rather we lose 600 chips to the big blind. The calculation is:

EV(Fold) = EV(T6000 - T600) = 26.5% / $132.41

3.Comparision of expected values

Now we compare expected values again:

EV Diff = EV(Call) - EV(Fold) = -0.4% / -$1.84

At -0.4% a fold is the correct move.

This is how to calculate the EV of a push or call under the independent chip model. It isn't exactly something you can do in your head. For this reason, I will not focus on the calculation of exact EVs in the following examples. Rather, I will focus on the factors that influence our decision. The calculations will be done with SNG Power Tools.