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Poker odds, pot odds and calling with cards to come

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When you have to make a decision to call with more cards to come (like on the flop in Texas Holdem) the problem becomes a little more complicated. More often than not, you know that your hand has to improve in order to become a winner. If your hand doesn’t need to improve and you know you already have the best hand at the table, all you need to do is to pay attention to the board texture that may yet counterfeit your hand before the showdown.

As I said though, you’ll probably be looking to improve your flopped hand. Therefore, you need to find out the odds of your hand improving and you need to compare those odds to the pot odds that you get. As a general rule, if your chances of improving your hand (and thus winning the pot) are better than your pot odds, you should make the call. If they’re not, you should muck your cards.
Here’s an example of the thought process that you should go through in order to determine whether you should call or not. Mind you that poker odds calculators work the same way and they go through the same calculus before telling you what to do.

Suppose you have a 4-card flush on the flop. Two of the cards are in your pocket and two of them are on the table, so your hand is fairly well disguised. The pot is a $50 one and you’re faced with a $10 raise. What do you do?

First, you determine your pot odds. They’re 5-1 (50-10). You’ll need this as a basis for comparison.
Next, you determine the odds of your hand improving to a flush on the turn. There are 52 cards in the deck and you already know 5 of them (2 are in your pocket and 3 are on the table). That leaves 47 cards. Out of those 47, nine cards will help you (because there are 13 cards of the same suit and 4 of them are already in your possession) and 47-9 = 38 won’t.

The odds against you hitting your hand are therefore 38-9 (where 9 is your number of outs), which means they’re basically 4,22-1. Because these are “against” odds, and they’re smaller than your pot odds, it means your chances of improving to a flush are better than the pot odds you get, which means you should go for it and make the $10 call.

This poker odds calculus is only valid for the turn card though. There’s still a river card, and calculating the poker odds for that too is a much more complicated proposition as the pot odds will change through the addition of an unknown number of chips before the river. Thus, if you’re looking to determine the odds you get for the turn and the river card, you’ll only be able to approximate.

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