In this article we are talking about the following example:



The hand has been played in a 6-max SNG with a typical pay out structure (65%, 35%). We assumed that your opponent is pushing the top 33.6% of his hands (22+, Ax+, K4s+, K9o+, Q8s+, QTo+, J8s+, JTo, T7s+, 97s+, 87s, 76s).

To understand situations like this, we should first of all calculate the chip equity for a call. In this lesson "Playing Preflop: Calling ans Isolating All-ins" you will find more information about that process. The following calculation shows the equity for a +cEV-call:

Required equity for a +cEV-call (chip equity) = 3725 / (4425+3725) = 45.71%

For a call with a positive cEV you would need 45.7% against your opponents range. The following hands got this equity:



AQo has an equity of 60.82% against villains pushing range. That means, that a call will show a long term profit of 1232 chips.

As we are talking about a SNG, you have to take care of the risk premium as well (also known as bubble factor or ICM-effect). The theories behind this concept can be found here: "Chip Value: The Risk Premium Concept".

To calculate the risk premium, you simulate the two decisions (call and fold) and compare the changed stack values. The value of your stack can be calculated with an ICM-calculator like this one. To do all the math yourself, we assume, that the SNG got a buy-in of $11. Further information about stack values can be found in this lesson: "Chip Value: The Independent Chip Model (ICM)".

$EV of your stack after a fold: $25.45
$EV of your stack after a successful call: $37.30
$EV of your stack after an unsuccessful call: $0
Probability for a successful call: 60.82%
$EV of your stack after a call: $37.30 * 60.82% + $0 * 39.18% = ~$22.69

You can see that the value of your stack is higher after a fold then after a call, so the fold is the better decision here. A call might bring you 1232 chips, but costs you - $2.76.

Required equity for a +$EV-call = $37.30 * %equity > $25.54 = 68.47%
Required equity for a +cEV-call = 45.71%
Risk premium = 68.47% - 45.71% = 22.76%

Summary: The equity of your hand in this spot has to be 22.76% higher then your chip equity, to make this call profitable.

This result gives us some important information, because now we know about the hands we could make a profitable call with. In our example the call would just be profitable with the following range:



That shows us, that AQ is a clear fold in that spot.

Ih you use the PokerStrategy.com Equilab to compare these hand to your opponents pushing range you will find out, that they have an equity higher than 68.47%. For example:



In the article about this exercise we also asked, in what kind of SNGs you would call an all-in. We want to answer this question referring to two other very popular formats of SNGs: 9-player and 180s. To not make it to complicated we assume that our opponents are pushing the same ranges as in the example above (which is not unrealistic).

The pay out structure of a 9-player-SNGs:

First: 50%
Second: 30%
Third: 20%

In the same spot as abovementioned you could find a call with a positive $EV with the following hands:



The pay out structure of a 180-player-SNGs:

First: 30%
Second: 20%
Third: 11.4%

A call would be profitable with these hands:



The examples show us, how important it is to make a good assumption about the value of your stack when calling an all-in. It not just helps you to understand the hand ranges, but also the "magic of the ICM" :) .

You have learned now, how to analyse such situations. If you like, do the math for the 9er- and 180s-SNGs! How big is the risk premium here? What about the other SNG-formats? What happens if your stack sizes change or the number of players? Just imagine all the possible situations and play with them!

Please post your answers, questions and calculations in this thread. Have fun! :)