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Poker math: Pot odds and hand equity

Poker is a game based on both math and psychology. While high-level poker is more and more psychology based, it never hurts to know your mathematical odds to perfection. These odds will tell you what the mathematically correct decision is, and making mathematically correct decisions is a must when going for the EV+. How you use this mathematical data depends on the reads you have on your opponents and, at the end of the day, on what you think is right under the given circumstances, but it is there and it does point you to the right direction.

Your mathematical odds in any given situation hinge on two factors: the pot odds that you get and your hand equity.

The pot odds represent a relation between the amount of money that's already in the pot (the money you stand to win) and the amount of money you have to call (the cost of staying in the pot). Generally speaking, the more money there is in the pot, and the less it takes you to call, the better your pot odds are. If the amount of money in the pot is truly huge compared to the size of the call you have to make, you should make the call on just about any two cards, but I'm getting ahead of the matters here …

Suppose you have a $10 pot and your opponent makes a $2 bet. You now have $12 to win, and it'll cost you $2 to stay in contention. Your pot odds are 12-2, which means 6-1. To find out your pot odds under any circumstance, just divide the pot with the amount of money you have to call.

As I said above, in theory, you can get good-enough pot odds to commit on just about any two cards. In reality though, your pot odds will always be much worse than that. You'll need to add another variable to the equation to make heads and tails of it: your hand equity.

In order to determine your odds of hitting a hand that will most likely turn out to be a winner, you need to start with your outs. The outs are the cards that you need to make your hand. Finding out the number of your outs should be simple, but sometimes it can be tricky too. You start from the premise that there are 52 cards in the deck, out of which there are 4 groups of 13 suited cards and 13 groups of 4 similar value cards. From the total of 52, you always need to subtract your own two pocket cards and the cards that are already on the board. In the case of a flush draw on the flop, you have 9 outs. There are 13 cards in the deck of the same suit, and you have 2 in your hand and 2 on the board: that translates to 13-4=9 outs.

You need to be careful not to count outs twice (in case you have a flush and a straight draw) and not to count anti-outs. There are cards for instance which would fill up your straight draw, but which would also fill up your opponent's flush draw. By definition, an out is a card which gives you a winning hand. If it gives your opponent a stronger hand, then it's obviously not an out for you.

After you calculate your number of outs, you need to find out the actual odds so you can compare them to your pot odds. In the above described case, you have 9 cards out of the remaining 52-5=47 cards that help you, but 47-9=38 don't. the odds against your making your hand are 38-9, or 4.22-1. These odds are way smaller than your 6-1 pot odds, which means it makes sense to call.

Poker rakeback or poker propping deals alter your odds a little, because they give you money back on the dough you stuff into the pot, but their impact is not that significant (though at high stakes, it may well be). Just sign up for rakeback and go about your business as usual then pocket the extra dough at the end of the week/month and you're done.

Sport Allstar

Posted at 5:40 AM

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Poker math: Pot odds and hand equity

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