Evaluating returns on hold/draw

May 16, 2005 2:31 AM

By Elliot Frome

A reader recently sent me a question about a deuces wild hand he was dealt. The cards included the following:

4¨ 5¨ 7¨ 2 10¨

There would seemingly be two ways to play this hand. Either draw nothing and take the flush for a 2-unit payout. The other choice would be to discard the 10 of diamonds and go for the straight flush.

Some people might be hesitant to throw away a sure winner to shoot for a hand that might win a little more, a little less or nothing at all. In reality, of course, the proper choice is rooted in our strategy table.

Obviously, the flush has an expected value of 2, based on its 2-for-1 return. What about our 4-card straight flush?

The specific paytable used in this machine included the following payoffs: 1-2-2-3-4-10-15-25-200-800, which is a pretty poor paying machine. The payback of this machine is about 95 percent, which is not very good for deuces wild.

But, one bad choice should not be compounded with another. Once you choose to put money into a machine, you should make sure to make the best possible draw.

If you were to hold the 4-card straight flush, there are six possible draws for the winning hand (3, 6 or 8 of diamonds or one of the other wild deuces).

There are also five possible flush draws (four of the 13 diamonds have been dealt, four additional cards would result in a straight flush). Nine additional draws will result in a straight. Lastly, nine other draws would result in three-of-a-kind.

When we add up the possible coins paid out, we find out that this totals 97. Divided by 47, the number of possible draws, we wind up with an expected value of 2.06.

Thus, the right play is to discard the 10 of diamonds and go for the straight flush. In this particular case, the pat hand is not worth more than the riskier draw, albeit by a slim margin.

Of course, this isn’t always the case, and sometimes it pays to hold the pat hand. Let’s take a look at some more examples.

In full-pay jacks or better, if you are dealt a flush that is also a 4-card royal, there is no doubt that you go for the royal flush. The flush has an expected value of 6, whereas the 4-card royal’s expected value is better than 18.

On the other hand, if the flush is also a 4-card straight flush, then you hold onto the flush since the 4-card straight flush has an expected value below four.

Sometimes, it’s not so easy to tell what the right thing to do is. A 3-card royal has an expected value nearly twice that of a low pair, yet I’m sure there are many who incorrectly keep the low pair, even though it is not even a winning hand.

Conversely, if dealt a high (winning) pair and a 3-card royal, the high pair is worth a smidge more and should be played. Four-card straight flushes, including 4-card inside straight flushes, however, outrank a high pair.

These hands can take an emotional toll on the player. Even though high pairs are really only pushes unless they improve, they are guaranteed to return the original wager, whereas playing for the straight flush will end up with winners only 25 percent to 33 percent of the time, depending on the number of high cards.

The difference is that when you win, you will win considerably more by hitting straights, flushes and, of course, the occasional straight flush. Of course, that’s why they call it gambling.