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.
