Page 8 - December 2003 • Southern California Gaming Guide

SOUTHERN CALIFORNIA GAMING GUIDE
Which Two-Pair Hand is More Frequent?
Tby Bob Dancer
wo pair as a nal hand isn’t very exciting. Strangely, not all two-pair hands are equally
likely, and today’s column is meant to be a fun exploration of why.
Every game has a slightly di erent pattern of two-pair hands, so we are limiting this to 9/6 Jacks or
Better (that is, where the full house returns 9 for 1 and the ush returns 6 for 1) and we assume you are playing according to computer-perfect strategy. Take this as a quiz and see how you do.
f. AA553 is more common than KK553 because you sometimes draw two cards to (A53), but you should never draw two cards to (K53).
g. 55443 is more common than 44332. is might be the toughest one to work out. e 3-card straight ush (543) is more powerful than the 3-card straight ush (432) so you hold it more. Compare, for example, [KQ](543) where you hold (543) with [KQ](432) where you should hold [KQ]. Because (432) is so close to the ace, (432) and (532) have exactly the same value, and that value is lower than that of (543).
How’d you do? I suspect that only 9/6 Jacks or Better experts would get these all correct as you needed to know correct strategy pretty well to get some of the answers. Is the information in this column immediately useful? Absolutely not! I hadn’t even considered these things until recently and it hasn’t slowed me down too much. But one of the secrets to my personal success is that puzzles like this fascinate me and so I’m better able to gure out new puzzles (such as how to take advantage of a particular promotion) easier than many others can. I suggest the more you work at these puzzles, the better your gambling results will be too.
Bob Dancer is America’s best-known video poker writer and teacher. He has a variety of “how to play better video poker” products, including Winner’s Guides, strategy cards, videos, and the award- winning computer software, “Bob Dancer Presents WinPoker,” and a brand-new book Million Dollar Video Poker. Dancer’s products may be ordered at www.bobdancer.com
Column: Video Poker With Bob Dancer
Page 8
DECEMBER 2003
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Available
Which is more common? And there are no ties. With every choice, there is an easily understood reason why one nal hand occurs more frequently
than the other.
a. KK553 or 99553?
b. KKQQ3 or KK883?
c. 99887 or 99447?
d. TT66A or TT66J?
Below are my answers.
a. KK553 is more common than 99553 by a big
margin simply because it is correct to start a hand with KK far more often than you start a hand with 99. Letting parentheses indicate same suit, from (AQJ)KK you should hold the kings, but from (AQJ)99 you should hold the 3-card royal. And from (K973)K you should hold the high pair, but from (K973)9 you should hold the 4-card ush. In addition, often you hold a single K and draw four cards — but you never hold a single 9 and draw four.
b. KKQQ3 is more common than KK883 for a couple of reasons. First of all, we have exactly the same logic as in the previous paragraph. e second
reason is that there are many hands where it is proper to draw three cards to either (KQ) or KQ, but it is never correct to draw three cards to K8.
c. 99887 is more common than 99447 because there are 3-card straight ush draws including a 9, 8, and 7. For example, from KQ(987) it is correct to hold (987). But from the equally likely KQ(974) it is correct to hold KQ.
d. TT66J is more common than TT66A. Why? Because there are many hands where holding ( JT) is correct [such as ( JT) 872] but there are no hands in this game where holding AT is the correct play.
e. JJTT5 is more common than KKTT5. It is correct to draw three cards to (JT) more frequently than it is to draw three cards to (KT). Compare the equally likely ( JT)A37 with (KT)A37. In the rst hand you should hold ( JT), but in the second AK. Or maybe compare (JT5)93 with the equally likely (KT5)93. Good players play ( JT) in the rst hand and K by itself in the second. Finally, compare the equally likely (JT)K53 with (KT)J53 and you’ll hold (JT) in the rst hand and JK in the second.
e. JJTT5 or KKTT5? f. AA553 or KK553? g. 55443 or 44332?
December 1, 2003