Folding equity while playing shortstacked

Folding equity is a very important concept in tournament poker. It is important to the way you should play while shortstacked.
In general the more shortstacked you are, the more reason to push all in, even tough you may not have a real hand. The definition of folding equity is as follows:

Folding equity is the concept of adding a higher winning chance (and therefore equity) by playing aggressive enough to make your opponent fold.

Folding equity examples

You are playing a 9-handed tournament and you are sitting on the button. You are the first player to act. You are holding:

You have 10 big blinds left and there are 2 players sitting behind you.  You are not close to the bubble yet. What should you do?

Go all-in ofcourse! You have some folding equity here. Let’s say the three players behing you would call you with the top 15% of hands (hands like AT, TJs, A7s or 77 and better). How big is the chance that all three of them would fold?

The chance of all three players behind you folding to your all in is:  0,85^2= 0,72 , or 72% folding equity.

As you can see you gained a huge edge simply because of folding equity.

Now we will calculate you chances if you get called. According to Equilab you have approximately 35% chance with your 87s against your opponents handrange of 15%.

In this case you have:

72% of your opponents folding 1,5 big blinds plus approximately 1 bb in ante, which gives an expected value of:

0,72*12,5bb= 9bb

You have 25,5% chance of having one caller (0,85*0,15*2).

Inwhich case you will have 35% of doubling up your stack to 21,5-22bb (on average 21,75bb).

0,255 *0,35% *21,75bb= 1,94 BB

in 2,25% of the cases you will be called by two opponents and your winchance is 27,5%.

You will have 27,5% to triple up to 31 BB

=0,0225* 0,275*31bb= 0,19BB

So your expected value will be:

9+1,94+0,19=11,13BB

As you can see Your expected value of 11,13BB is higher then your current stack of 10BB it is therefore correct to make the move.

What happens if your opponents are playing tighter then your assumption?

In case your opponents fold more then 85% of the time, your expectancy gets even better. For instance your opponents fold 90% of their hands against an all in.

0,9^2=0,81

0,81*12,5bb=10,12BB

As you can see you don’t have to make the rest of the calculation to see that you are allready getting a higher expectancy.

Something else happens when you have two loose callers behind you.

Let’s say your two opponents behind you are having a big stack and a loose calling style against small stacks. They call 30% of your all ins with hands like: A5o, A2s, TJo, 55, 98s, K5s etc . You have 37,6% chance against those handranges while holding 87s.

Your expected value therfore becomes:

Both fold: 0,7^2=0,49

0,49*12,5bb= 6,12BB

One player calls: 0,7*0,3*2=0,42

0,42*0,376*21,75BB= 3,43BB

Both players call (inwhich case you have 27,9% chance against both players with their 30% handrange according to equilab):

0,3^2=0,09

0,09*0,279*31bb=0,778BB

The expected value is:

6,12+3,43+0,78= 10,33BB

As you can see regardless of the handranges your opponents call with, you will be having a positive expectancy under these circumstances (87s with two players behind you and a 10bb stack), because of the folding equity.

When is your folding equity not enough to justify going all in?

It depends on:

the amount of players behind you,

on your stacksize  and your opponents stacksizes measured in BB.

on the handranges your opponents call you with.

And with that information you can calculate your expected value.

The Nash equilibrium

There is a heads up chart of which hands you can push all in with, it depends on the quality of your hand and the amount of bigblinds you are holding. It is called the Nash equilibrium chart.

Nash equilibrium

 

 

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