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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.

For more details and a schedule of Bob's free classes, visit www.bobdancer.com.

June 09, 2009

A Quick Quads Conundrum

I've written a number of articles which present puzzles related to the play of various video poker hands. Today's puzzle is a little different in that I'm not going to tell you the game! It's a Quick Quads game, to be sure, but whether it is Jacks or Better, Bonus Poker, Double Bonus, Double Double Bonus, Triple Double Bonus, or Triple Bonus Poker Plus will remain a mystery, at least for now.

The reason for the mystery is because I want you to try working this one out using logic alone. Too many people would rather just look at a strategy than figure things out themselves. You won't be able to do this if you don't know the game.

Consider the following three hands, where the single quote marks indicate the cards are suited with each other. Further assume you are playing six coins per line so you are eligible to get paid for Quick Quads:

2 'A289'
3 'A389'
4 'K249'

In all three hands, there are three possible ways to play the hand.

4-card flush with one high card
Low pair with lower-card kicker
Low pair by itself
Suppose I tell you that in one of the hands the order of the plays is (b, a, c). (That is, holding the pair with a kicker is the best play, going for the flush is second, and holding the pair without a kicker is third.) In another hand the order is (a, b, c) and in the third hand the order is (a, c, b). Your job is to decide which of the three hands match up with the three rankings. If you understand the basics of Quick Quads this is not a difficult problem.

If this is the first time you've considered a Quick Quad problem, this likely will be beyond you. You might want to download, for free, "A Quick Guide to Quick Quads," by Bob Dancer and Glen Richards, from www.videopoker.com/quickquads That book will give you enough insight into the game for you to figure this out.

First of all, it should be obvious that in all three hands the value of the 4-flush is the same. In each case, if you draw one of the other nine suited cards you'll get a flush and if you draw one of the matching three high cards you get a high pair.

Second, let's compare 22A with 33A. Both hands have identical chances for 3 of a kind and natural 4 of a kinds. They differ in the chances for Quick Quads and full houses. To get a Quick Quad from 33A, you need to draw a 3 and a 2. The key fact to notice is that there are four 2s still in the pack of 47 undealt cards. To get a Quick Quad from 22A, you need to draw a 2 and an A, and the key part of this is that there are only three 2s remaining in the pack. Therefore, you only get three-fourths as many Quick Quads from 22A as you do from 33A.

To get a full house from 33A, you need to draw a 3 (two ways to do this) and an A (three ways to do this) or a pair of aces. We can only get a full house from 22A by drawing a pair of aces. We've already counted drawing a 2 and an A as a Quick Quad. So in addition to getting fewer Quick Quads from 22A compared to 33A, you also get fewer full houses.

If you compare 22A to 442, you find they each get the same number of Quick Quads and full houses --- and are indeed worth exactly the same as each other. At first blush it might appear that 22A > 442 because the ace is a high card, which can be paired to get your money back. This is a mirage. 22AA and 4422 are both two pair and are worth the same.

It is always true in Quick Quads that holding a lower-card kicker that is exactly half-value is less valuable than holding a lower-card kicker that is not exactly half value. If we had compared 44A or 443 with 33A, we would have found them to be worth the same. But in both 442 and 22A, the lower-card kicker makes the combination worth less.

Since we have shown 33A is more valuable than either 22A or 442 and we were told at the beginning that in only one of the three hands is the pair with the kicker preferred to the 4-card flush, clearly we can match up hand II with combination (b, a, c).

So now we're comparing hands I and III. We're told up front that we hold the 4-card flush in both cases, but in one case the pair with the kicker is more valuable than just the pair, and the other case this isn't true.

We earlier said that 22A = 442, so for there to be a difference in the play of these combinations, we must look at 22 versus 44. In games without wild cards, the usual situation is 22 = 33 = 44, but in Quick Quads this isn't the case. The only Quick Quads we can make from 22 are 222AA 44422. From 44, in addition to 44422 and 88844, we can make a Quick Quad with 4443A. This makes 44 > 22.

The answer to our conundrum is the order from I is (a, b, c) and the order from III is (a, c, b), and we've already said that from I the order is (b, a, c). Did you get it right? To get the correct answer you merely needed to apply general Quick Quads principles.

If some of these general principles were foreign to you, I suggest you attend my free 9/6 Double Double Bonus Quick Quads class on Tuesday, June 23 at 1 p.m. at the South Point. Although this class will only discuss the Double Double version of Quick Quads, it will cover the general principles involved in all Quick Quads play. (And, by the way, 9/6 Double Double Bonus Quick Quads is the game that plays the three hands as described in the article.)