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What is Expected Value in poker?

The term EV in poker, short for expected value, is about using probability mathematics to describe the average long-term average outcome for a situation. In order to calculate expected value in poker you need to consider every possible outcome, multiply each by the probability of each happening and then add those numbers together. You can therefore compare different EV of different lines such as working out whether shoving is +EV  (positive expected value). The purpose of which is to choose the line with the highest EV, i.e. is it best to call, fold or shove and a poker equity calculator does this for you.

Fold Equity Calculator

Fold equity is about working out how often an opponent has to fold for our ship to be +EV. It is about combining the EV of our opponent folding, our opponent calling and we win and our opponent calling and they win.

To work out whether a shove is a +EV play you need the following seven pieces of data:

1) Effective stack (how much you’re pushing)

2) Current pot size

3) Size of opponent’s bet (which you are shoving over)

4) Size of opponent’s remaining stack

5) Opponent’s betting range

6) Opponent’s calling range

7) Estimated equity (when called)

Let’s assume we are playing 6 max £1/2 NLHE and our LAG opponent raised in the hijack position £7 pre-flop and it’s folded around to us in the BB and we decide to call with Jd9d bringing the pot to £15. Both us and the villain started with exactly £200 (100BB). We check and our opponent continuation bets £9 on a 8sTh2d board and we decide to check shove on their ass.

Is this a +EV play?! The first four components above are easy to see – we are pushing £193, the pot is currently £24, our opponent has bet £9 and has £184 left. The final three are tricker. First we need to work out (best guess on table dynamics and what we’ve seen) our opponents betting range for this flop. A LAG will be opening in the hijack with a wide range of hands as far down as say 65s or J9o but will only be continuation betting on this flop with something.

A fair assumption for c’bet range is 27% as shown in the second image), basically any pair, draw or overcards. That works out to be 354 card combinations (13 pairs x 6, 21 suited hands x 4 and 16 off-suit hands x 12) or 27% of the total of 1326 card combinations. Now we need to work out the opponent’s calling range which we assume to be sets, overpairs and top top pair for 52 card combinations (image 3).

This means they will fold 85% (only calling 52/354) of the time and vs this calling range we have 35% equity (image 1). Therefore the FE calc looks like this: Opponent folds 85% time – we win £24 x 85% = £20.40 Opponent calls 15% time and wins – we lose £193 x 15% x 65% = £18.82 Opponent calls 15% time and loses – we wins £184 x 15% x 35% = £9.66 Total EV = £20.40 – £18.82 + £9.66 = £11.24 meaning we win £11 every time we shove and do this dumb play!