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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.

Dec. 02, 2003

An NSU Straight Flush Puzzler

Letting a W indicate a wild card in NSU Deuces Wild, which 3-card straight flush combination is more valuable: W56 or W57?

Actually, they are equal to each other. They each have one "inside². The inside for W57 is easy to see. It's missing the 6. But for W56, the inside occurs because it is too close to the deuce. The only straights that either one of these combinations may be a part of are 98765, 87654, and 76543 --- where in each case one or two of the cards may be replaced by a deuce. Using the Dancer / Daily notation, which I've explained in other columns, each combination may be indicated by SF3 -1.

So far, so good. But in our Basic Strategy, which is as good as you can get without using penalty cards, we have the following:

SF3 -1 (W57 W9J) > SF3 -1 (W56)

This is curious. In one paragraph I say the two combinations are equal. In the next paragraph I indicate that they aren't. What gives?

The only time it matters whether one combination is better than another is when they can be in the same five cards. If we actually had W 5h 6h 5c 7c, the correct play is the W55 3-of-a-kind. If you try this on your computer, you'll see W55 in first place and W56 and W57 tied --- and only worth about half as much as the 3-of-a-kind.

To understand why we write the strategy card instruction the way we do, consider:

From W 5h 7h 8s Ts, the correct play is EITHER W8T or W57.
From W 5h 6h 8s Ts, the correct play is W8T.

The strategy rule gives the correct play, whether you understand the following or not. But the question is still WHY?

In the first hand, both W57 and W8T are worth 5.2498 coins. In the second hand, W56 is worth 5.2498 coins (which follows, because we've already shown it has equal value to W57), but W8T is worth 5.2868 coins. Something happens to the value of W8T when it is matched up with 57 that doesn't happen when it is matched up with 56.

The answer is the possibility of JT987 straights --- where again one or two cards will be replaced by deuces. When W8T is matched up with 56, there are 4 jacks still in the deck, four nines, and four sevens. When W8T is matched up with 57, there are still four jacks and four nines, but now only THREE sevens, because we were dealt one and threw it away.

How much is this worth? Obviously, 0.037 coins, which is the difference between 5.2868 coins and 5.2498 coins. For dollar players, this is almost 4¢. For quarter players, this is almost 1¢. How often does it occur? Including the cases where a suited J9 is matched up with a W56 (where the same strategy rule applies), this happens almost once every 27,000 hands. Certainly negligible in the greater scheme of things.

So why spend time on a small-valued difference that happens so rarely? Because there are a LOT of these differences. Players who regularly seek to master the small difference also find they remember the bigger differences too. Players who decide that the little stuff is too small to worry about usually also mess up on quite a bit of the not-so-little stuff too.