A couple of people have mentioned that they find what I’m doing here interesting (thanks, by the way, really appreciate the support), but that the math can be hard to follow. So I thought I’d touch on some of the fundamentals.

Most of the math (so far, at least) has revolved around calculating the expected value (EV). You’ll see me use that abbreviation EV a lot. The EV of a play is basically how much you can expect to win in the long run – when the randomness of the cards evens out.

How is this calculated? Suppose the pot already has $3 in it. You need $1 to call. Given the hand, you’re a 85% favorite. What happens if you call? 85% of the time, therefore, you are going to win the $4. The other 15% of the time, you win nothing. And either way, you have to put $1 in the pot. As such, your expected winnings over the long term is 0.85 * 4 – 1 = 2.4. So in the long run, you’ll win $2.40.

That is the basis of the expected value calculation. In poker, however, there are two choices for playing, calling or raising. Things get more complicated when you raise; you have to consider if your opponent will call or fold. Let’s say you’re in a game, and there’s $5 in the pot. You are thinking of betting $2, leaving your opponent with $7 in the pot, and $2 to call. You have a read on this opponent, and believe he’ll fold 20% of the time. If he plays on, you’re a 75% favorite.

What does all this mean for you? When your opponent folds (20% of the time), you’ll win the $7. So the value from this is 0.2 * 7 = 1.4. The other  When he calls, 75% of the time you’ll win $9 (5 in the pot, 2 from your bet, 2 from your opponents call). 25% of the time, you win nothing. So the value you get if he calls is 0.75 * 9 = 6.75. Because he folds 20% of the time, however, he’ll call 80% of the time only, so the value is 0.80 * 6.75 = 5.4. No matter what happens, you’re placing in $2 in the pot.

Combining that all, your expected value from the raise is therefore 0.2 * 7 + 0.8 * (0.75 * 9) – 2 = 4.8. So in the long run, you’ll win $4.80.

In general, here is the formula I use for calculating EV:

EV = f * (p + r) + (1 – f) * s * (p + r + r) – r
where f = probability that opponent will fold; p = pot size before my bet; r = my raise; s = probability of my hand winning in a showdown

If you notice, I don’t consider the scenario when my opponent re-raises me, purely because that makes it too complex and I haven’t figured it out yet (if anyone has an idea on how to do that, let me know).

What practical uses does all of this have? If your EV is positive, you’ll win money in the long run, so the play is a logical one. If your EV is negative, then it’s a misplay, and in the long run you’ll lose money. The higher the EV, the more you’ll win, the better the play.

So yeah, that’s the basis behind the EV calculations that you’ll see me doing a lot. Hope it helps.

Popularity: 6% [?]