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Bob Dancer writes a video poker column for beginners to experts. He also writes a column with Jeffrey Compton, "Player's Edge", featuring information on promotions at various Las Vegas casinos. Player's Edge is published each Friday in the Neon section of the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.

Nov. 04, 2003

A Puzzler from Double Bonus

In last week's 10/7 Double Bonus class at Fiesta Rancho, I posed a "mind stretcher." This is a puzzle whose answer is not readily apparent, but at the same time, easily within the knowledge grasp of the students. I have some "tried and true" mind stretchers, but last week I asked one that I hadn't discussed in a while. Since nobody in class could figure out the answer, perhaps it's good to repeat it here.

Consider the two best 3-card royal flushes in this game --- namely KQJ and QJT. KQJ is the only combination which has three high cards and the potential for a straight flush. QJT has only two high cards but is the only combination that has the potential for TWO different straight flushes. So is it more valuable to have the extra high card, or the extra straight flush potential? We'll see.

Here's the question: Consider the following two hands, where the parentheses mean "suited". (KQJ4)3 and (QJT4)3. In each case, one of the best two 3-card royals was joined with two low cards, each too far away to be part of a straight with the 3-card royals, and one of added cards is suited with the royal. The choice in both cases is between a 4-card flush and a 3-card royal.

From (KQJ4)3, the correct play is the 4-card flush --- (KQJ4). From (QJT4)3, the correct play is the 3-card royal --- (QJT). [If you are a Double Bonus player and didn't know this, it will be money-in-the-bank for you to study some more.]

Here's the question: In the above scenario, what can we conclude about the relative value between KQJ and QJT? Can we say that KQJ is more valuable than QJT? Or perhaps QJT is more valuable than KQJ? Or is there not enough information to decide?

Since QJT is more valuable than a 4-card flush and KQJ is less valuable than a 4-card flush, it appears to be obvious that QJT MUST BE more valuable than KQJ. And yet that conclusion doesn't follow. Can you see why not?

The reason that conclusion doesn't follow is that the 4-card flushes aren't comparable. (QJT4) is a 4-card flush with TWO high cards (worth 7.34 coins) and (KQJ4) is a 4-card flush with THREE high cards (worth 7.66 coins). Just because we know that QJT is worth more than 7.34 coins and KQJ is worth less than 7.66 coins, we still don't know whether KQJ or QJT is worth more.

It turns out in the above hands, QJT is worth 7.63 coins and KQJ is worth 7.59, so, indeed, QJT > KQJ. But I couldn't know that until I looked it up on WinPoker. There was no way to logically infer which was worth more from the information presented.

Note that which is the more valuable combination is irrelevant to every decision you make in Double Bonus. Why is it irrelevant? Because you never have to choose between them. You cannot get a KQJ in hearts and a QJT in spades in the same five cards. If you have both KQJ of spades and QJT of spades, you hold the 4-card royal KQJT.

So now the question becomes: If it's totally irrelevant which is more valuable, why am I wasting your time with it in a puzzle? Because the more you understand about video poker, the better your results will be. See my July 1, 2003 article in this series for a longer explanation of these benefits --- although that particular column contained a different puzzle.