VIDEO POKER
 Bob Dancer writes a video poker column for beginners to experts. He also writes a column each week with Jeffrey Compton titled Player's Edge, which features information on promotions at various Las Vegas Hotel. Player's Edge is published each Friday in the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.
May 07, 2002
An Unusual Way of Thinking About a Deuces Wild Hand
In standard Deuces Wild (i.e. the game where 4-of-a-kinds pay 5 and 5-of-a-kinds pay 15) consider the following two hands:
Qh Jh Th 8h 5c hold QJT
Kd Qd Jd 9d 5s hold KQJ9
In both hands the choice is between a 3-card royal flush and a 4-card straight flush --- and notice that in the first hand it is correct to go for the royal and in the second it is correct to go for the straight flush. (If you are not familiar with this particular game, just take the information presented so far as gospel truth and go on with the column. There is a useful lesson to consider even if this is not your main game.)
Let's assume I tell you the max-coin value of the QJT8 is 6.9 coins --- which it is, with rounding. Here's my question. Is the value of KQJ9 higher than 6.9 coins, lower than 6.9, coins or equal to 6.9 coins? Keep in mind that we hold KQJ9 but we do not hold QJT8.
The correct answer is that KQJ9 is also worth 6.9 coins. In both hands, there are 47 different cards we could draw. 5 of those cards give us a straight flush (including the four deuces), 7 cards give us a regular flush, 3 cards give us a regular straight and the other 32 cards give us nothing at all. Count them up on your fingers and you'll see that I am correct. So if the QJT8 is worth 6.9 coins, so must be KQJ9.
So now the question becomes: If the two combinations are both worth exactly the same amount (which they are), then how come we hold one of them and do not hold the other? A combination worth 6.9 coins should either be worth holding, or not worth holding. How can the answer sometimes be "hold" and sometimes be "don't hold"?
The answer is that there are more cards in the hand. In the first hand, the value of QJT is 7.0 coins. And since 7.0 is greater than 6.9, we go for the royal. In the second hand, KQJ is worth 6.6 coins, which is less than 6.9, so now we go for the straight flush. In both cases, we hold the highest combination. And in both hands, keeping EITHER the 3-card royal or the 4-card straight flush is much better than drawing five new cards (which is worth about 1.6 coins).
To some beginning players, it is not at all obvious why the QJT combination is worth more than KQJ. After all, in both cases you need to draw two perfect cards to connect on the royal. The answer to this deals with the number of straight flushes and straights. KQJ can be part of a royal and an A-high straight (as can QJT), and also a K-high straight or straight flush (as can QJT). But QJT can be part of a Q-high straight or straight flush and KQJ cannot. That is why QJT is worth more than KQJ.
In games which give you your money back for "jacks or better", sometimes KQJ is worth more than QJT and sometimes not. After all, KQJ has three high cards but only one straight flush possibility and QJT has only two high cards, but two straight flush possibilities. So depending on how much straight flushes are worth, either one could be worth more than the other. But in Deuces Wild, where high cards are meaningless because you need 3-of-a-kind to get your money back, the extra straight and straight flush possibilities with QJT make it a clear choice.
That's it for this week. Until next time, go out and hit a royal flush.
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