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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. 11, 2003

An Interesting 3-card Straight Flush Observation

Using parentheses to signify suited cards, today we're going to look at (KQ9), (KJ9) and (QJ8) in the myriad of games where you get your money back for a pair of jacks or better. Each of these combinations has two high cards and two insides and, generally speaking, has the same value as each other. In the notation used on Dancer / Daily strategy cards and Winner's Guides, we call these a SF3 +0 because we add 1 unit for each high card (in this case two) and subtract 1 unit for each inside (in this case two). These combinations are grouped in our strategies with those combinations that have one inside and one high card, such as (J98) or (QT9), and those with no high cards and no insides, such as (789) or (345). If you prefer notation such as SF3 2i 2hi, SF3 1i 1hi, and SF3 0i 0hi, be my guest.

In games where flushes return 6 for 1 (such as 9/6 Jacks or Better, 10/6 or 9/6 Double Double Bonus, plus others), when these combinations are matched up with AKQJ in the same five cards, you usually hold the SF3.

In games where flushes return 5 for 1 (such as 8/5 Bonus Poker, 9/5 Double Double Bonus, plus others), the lower value of the flush reduces the value of these combinations. In a dollar game, assuming no other elements of the pay schedule changed (for example going from 9/6 Jacks or Better to 9/5 Jacks or Better), these combinations are reduced by 20¢.

The unsuited AKQJ combination, since no flush is possible, is completely unaffected by the return on the flush. It so happens that usually the strategy now becomes (QJ8) > AKQJ > (KQ9, KJ9).

How can this be? We said earlier that (QJ8) has the same value as both (KQ9) and (KJ9), so how can one be more valuable than AKQJ and the other two less valuable? The answer is due to the way the individual members of the SF3 interact with the cards in AKQJ.

For example, when you look at AK(QJ8), you have the full number of chances to get the QJT98 straight. All four Ts and all four 9s are still in the deck. When you look at AQ(KJ9), on the other hand, there are fewer chances for the KQJT9 straight because there are now only three Qs still in the deck, along with the four Ts. This is an example of a "straight penalty", which we abbreviate "sp". The reduced chance for a straight is worth 7.4¢, assuming straights return 4 for 1.

As a strategy creators, Liam W. Daily have two totally different choices for how to present this information.

a. (QJ8) > AKQJ > (KQ9, KJ9)
b. SF3 +0
AKQJ (> SF3 +0 with sp)

The first way gives the WHAT, but it doesn't tell WHY. The second way (which provides equivalent strategy) gives both the WHAT and WHY, but expresses it in terms of penalty card considerations. Which is better?

In our Level 3 strategy (which is defined as being as close to perfect as possible without mentioning penalty cards), we are forced to go with the first choice. In our Level 4 strategy (which is defined as being perfect, although sometimes extremely rare, complicated and small-valued differences are left to the appendixes of the Winner's Guides rather than placed in the strategies), we use the latter definition.

Which is better? For me personally, I'd rather know WHAT and WHY. Daily would rather know WHY, and then he can figure out the WHAT. Other players have their own preferences.

Some players have a philosophy to ignore penalty card considerations as being too complicated. This is one of the few cases where the correct play can be accurately stated with or without penalty cards.