VIDEO POKER

A Straight Flush Puzzler

The value of any 3-card straight flush depends on how many insides (or gaps) it has as well as how many high cards. Each strategy-card author uses a slightly different notation, but the first combination above could be listed as something like SF3 2i 1 hi and the second combination as SF3 1i 0hi --- where the number preceding the "i" indicates the number of insides and the number preceding "hi" indicates the number of high cards.

Anyone who has thought about the game at all has noticed that each additional high card is "good" and adds value and that each additional inside is "bad" and subtracts value. Liam W. Daily noticed several years ago that the amount of value added by each "good" high card is very close to the amount of value subtracted by each "bad" inside. From there he came up with a notation system that adds one for each high card and subtracts one for each inside.

Under Daily's notation (which is used on the strategy cards Daily and I co-author, as well as on our Winner's Guides, the first volume of which will be available in two weeks, and in the classes I teach), "A45" contains one high card (adding one) and two insides (subtracting two) for a net rating of -1, so it is indicated as SF3 -1. "245" contains no high card (adding zero) and one inside (subtracting one) so it also has a net rating of SF3 -1. This rating system is used in Jacks or Better, Double Bonus, Pick'em Poker, and Joker Poker. In Deuces Wild, there are no high cards and the deuce is wild, so slightly different notation applies.

So since the two combinations each have the same SF3 -1 notation, that means they each have the same value. Right?

Not really. The notation is a simplification that usually works fine. In dollar 9/6 Jacks or Better, "A45" is worth $2.69 and "245" is worth $2.67". In dollar 9/5 Jacks or Better, "A45" is worth $2.48 and "245" is worth $2.47. Since the value of the flush decreased between "9/6" and "9/5", it's no wonder that the value of 3-card straight flushes decreases too.

That fact that the value of "A45" decreased by 21¢ and the value of "245" decreased by "only" 20¢ is not due to rounding. When you draw two cards to any 3-card flush (or 3-card straight flush or 3-card royal flush), the sum of the number of possible flushes + straight flushes + royal flushes always totals 45 out of a possible 1,081 combinations. In both of these hands, the number of possible royal flushes is zero, but from "A45" there is only one possible straight flush (so the number of possible flushes is 44) and from "245" there are two possible straight flushes (so the number of possible flushes is 43). Since there are more possible flushes with "A45", a change in the value of the flush affects it more.

Even so, whether we're comparing $2.69 to $2.67 or we're comparing $2.48 to $2.47, the difference is small and so using SF3 -1 to indicate both hands is appropriate. How about in 10/7 (or 9/7) Double Bonus? Here flushes pay 7 instead of 5 or 6 and straights pay 5 instead of 4.

When flushes pay 7 and straights pay 5 in Double Bonus, the relative values of "A45" and "235" are $2.88 and $2.83 respectively. Not as close as in Jacks or Better, but still an acceptable shorthand. In the Bally GameMaker version of 10/7 Double Bonus (i.e. where straight flushes pay 80 per coin bet rather than 50), however, the values of the two combinations are $2.97 and $3.16 respectively. This is quite a large difference, and there are a few combinations (a suited QJ for one) which are more valuable than "A45" and not as valuable as "235".

Does this mean our notation system is flawed? I don't think so. It works well most of the time, and the exceptions may be handled with parenthesized information. But the easy-to-confuse notation of SF3 1i 2hi (i.e. a suited QJ9) and SF3 2i 1 hi (i.e., a suited J87) translate to SF3 +1 and SF3 -1, which have very different values. We think the gain from the reduction of confusion more than offsets the occasional exception and the necessary learning curve.