As you probably know, Quick Quads is a 6-coins-per-line game where, in addition to being paid for "regular" quads, you are paid for quads consisting of 3-of-a-kind where the other two cards add up to the rank of the 3-of-a-kind. For example, 3332A, 99954, and 66633 all get paid as 4-of-a-kinds.
Today's puzzler is specific to 9/6 Double Double Bonus (DDB) Quick Quads (QQ). I understand that you probably don't have the strategy memorized. That's okay. The answer to the puzzler may be inferred logically if you know a little about Quick Quads even if you don't know the strategy for any game.
Consider the following three hands, where each one is followed by two possible correct plays:
1) 8884K
1a) 888
1b) 8884
2) 6663Q
2a) 666
2b) 6663
3) 6662J
3a) 666
3b) 6662
I'm going to tell you from the get go that in exactly two of the hands the b) answer is correct and in the other hand the a) answer is correct. Your job is to figure out which is which.
There are several different ways to attack this problem. I'm going to show you one of them. If you end up with the correct answer, it doesn't really matter what method you used to get it.
Some of you might have a strategy that tells you the correct answer. That's not a bad way to go. I've sold strategies for years (not for this game yet, although I've created one that you can get for free at www.videopoker.com/quickquads ) and they are useful. My personal preference is to figure out why the hands are played a certain way. And strategy cards don't tell you "why." At best they only tell you "what."
I'm going to start out by comparing hands 2) and 3). Because we were told that two out of three of these hands have b) as the correct answer, we know that in at least one of these hands the b) answer is correct—possibly both, but definitely at least one. If we can show that either 2b is more valuable than 3b, or 3b is more valuable than 2b, then we can be sure that we've found one of the hands where the b) answer is correct.
From 2b), there are three cards that will give us a QQ—namely the three 3s still remaining in the deck. There are no cards that will give us a full house simply because we've already counted the 3's as a QQ.
From 3b), there are four cards that will give us a QQ—namely the four 4s, and three cards that will give us a full house—namely the remaining three deuces.
We can conclude, then, that 3b) is clearly more valuable than 2b). Another way to phrase this is that 3b) is definitely the answer to the third hand. This is a standard feature of QQ. Kickers of exactly half as much as the rank of the trips are less valuable than those kickers which are not exactly half the size.
Now let's compare hand 1) with hand 2). It should be obvious that combination 1b) has exactly the same value as 2b). Both combinations have four ways to become full houses, three ways to become QQ, one way to become a natural four-of-a-kind and all of the rest of the time remain a 3-of-a-kind. Therefore, to find a distinction between these two hands, we must see if there's a difference between 1a) and 2a).
In "regular" DDB video poker, 888 and 666 have exactly equal values. In QQ, however, this changes simply due to the number of ways to connect on the QQ. 666 connects on Ace 5, 24, and 33 while 888 connects on Ace 7, 26, 35, and 44. Those extra chances to become a QQ means that 888 is more valuable than 666.
Since it was stipulated that there was only one play where we held the a) combination, it must be the correct plays are 1a), 2b), and 3b).
Were you able to figure it out?
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 his new book, Video Poker for the Intelligent Beginner, Winner's Guides, strategy cards, his autobiography Million Dollar Video Poker, and his two novels, including Sex, Lies, and Video Poker. Dancer's products, may be ordered at www.bobdancer.com or at 1-800-244-2224 Monday through Friday, 9 a.m. to 5 p.m. Pacific Time.
