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Home The Mathematics of Poker The Odds of a Pot Exposed Cards
Exposed Cards

There is one aspect of comparing the odds of making your hand to your pot odds that is frequently overlooked in open-handed games like stud poker and razz: The effect on your play of the cards exposed in other players' hands, which of course includes cards that were folded along with those still out against you. For instance, it would be crazy to play a pair of 5s in seven-card stud with the two other 5s exposed.

Your chances of improving a hand change dramatically according to the number of needed cards that are gone and the total number of cards exposed. The second factor is important. For example, with three spades on your first three cards and no other cards seen, you will make a spade flush in seven cards 18 percent of the time. Now, suppose when you look around the table, you see that exactly one of your seven opponents shows a spade. What does this do to your chances of making a flush? If you say it increases them, you are right. True, one of your needed cards is gone, but so too are six unneeded cards. Therefore, there are more spades proportionally among the unseen cards than you would a5sume if you had seen no cards at all.

Generally, though, it's not so much the total number of exposed cards that people ignore but the number of cards among them that they need. It is very important to pay attention to these cards because their presence can change a playable hand into an unplayable one. Let's say you start with three spades on your first three cards in seven-card stud, and you have seen seven other cards. The following table shows the effect of the other cards on your making a flush.

 Number of Spades Chances For a Flush Besides Your Own % 0 23.6 1 19.6 2 15.8 3 12.3 4 9.1

With no spades out, you have a strong hand. With two out, your hand becomes marginally playable. With four or more out, it becomes a hand not worth a call.

Here are a few more examples from seven-card stud and seven-card razz to demonstrate the effect of exposed cards on the chances of making a hand.

You start with on your first three cards in seven-card stud. You have seen seven other cards.

 Number of 5s and Aces Chances For Aces Up Or Seen Besides Your Own Three-of-a-Kind (%) 0 41.0 1 34.1 2 26.5 3 18.3 4 10.5

You start with on your first four cards in seven-card stud and have seen eight other cards.

 Number of 5s and Chances For a lOs Seen Straight (%) 0 49.8 1 44.8 2 39.4 3 33.8 4 27.8

On your first four cards in seven-card razz. You have seen ten other cards.

 Number of 5s, 6s, 7s, Chances For an 8 Low or Better (%) and 8s Seen 0 81.8 2 76.0 3 72.7 4 69.2 5 65.3 6 61.2 7 56.7 8 51.9

Though you're a favorite to make an 81ow or better with as many as eight of your needed cards among the ten exposed, notice how much harder it is to make a 7 low.

 Number of 5s, 6s, Chances For a 7 and 7s Seen Low or Better (%) 0 69.2 4 51.9 8 29.1

These tables indicate the importance of taking the cards you see in other players' hands into account before you compare the pot odds you are getting to your chances of making your hand.

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