How do I work out fold equity in a hand?

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Amancudno

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Trying to figure out how I work out fold equity in a hand. Obviously factors like read on villain, hand strength and stack sizes play a part, but is there a formulaic way to work this out?
 
Chiefer

Chiefer

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When you make a bet, you are basically absorbing some of your opponent's equity in the hand if there is a chance that they will fold. Fold equity can be expressed by a straightforward equation:

Fold equity = (chance our opponent will fold) * (opponent's equity in the hand).

The % chance that your opponent will fold is based on your knowledge of your opponent. So for example, using your experience you could say that there is a good chance that your opponent will fold 75% of the time when making a bet in a certain situation.

Your opponent's equity in the hand is pretty self explanatory. It's just the % of the pot they expect to win on average by the river. More specifically, it's the % equity their range has, but don't worry about that for now.

Total equity in the hand.

Total equity = our current equity + fold equity.

As you will remember, your total equity in the hand is your current equity plus your fold equity. Fold equity on it's own isn't all that useful, so we add it to our standard equity to give us our overall equity in the hand.

Fold equity example.

Let's say we are on the flop and we know that our opponent is holding Kd Js on the following flop:

Flop: Qs Kh 2s

Our hand: 9s Ts - 42.4% equity.
Opponent's hand: Kd Js - 57.6% equity.

I worked out the equity of each of these hands using PokerStove. Get it already.

Our opponent is first to act and bets in to us. However, we are a little short stacked and believe that if we push all-in there is a 50% chance that our opponent will fold. Without even having to work this out we can already guess that this is going to be a profitable play over the long run, but lets do the math anyway.

Fold equity = (chance our opponent will fold) * (opponent's equity in the hand).
Fold equity = (0.5) * (57.4).
Fold equity = 28.8%.
Now let's find our total equity in the hand.

Total equity = our current equity + fold equity.
Total equity = 42.4% + 28.8%.
Total equity = 71.2%.
So every time we shove all-in with our drawing hand we will have 71.2% equity in the hand on average. Therefore, whereas calling to complete our draw would be unprofitable with our 42.4% equity, the addition of fold equity in the hand makes our shove a profitable play over the long run.

Copy and pasted from Pokerbank.com
 
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