Bob Dancer and Liam W. Daily have just released the second edition of Winner's Guide Volume 1 -- Jacks or Better. This new edition has been expanded to 128 pages and features the following enhancements: 1) A complete discussion of the differences between Jacks or Better and other popular games, including Double Bonus, Double Double Bonus and Deuces Wild. 2) Enhanced (more user-friendly) notations --- done in conjunction with the latest Dancer/Daily Strategy Cards. 3) An updated strategy for Level 4 Flush-5
With these improvements, Winner's Guide Volume 1 presents the most comprehensive discussion of Jacks or Better ever published.
In 9/6 Jacks, for instance, 'QJ8', 'KQ9' and 'KJ9' are preferred to AKQJ. These are all 3-card straight flushes with two high cards and two gaps. In 8/5 Jacks (whether the quads return 25 or 35), 'QJ8' is preferred to AKQJ, but 'KQ9' and 'KJ9' are not.
The easy part of this, discussed last week, is that the 3-card straight flushes decrease in value by about 20¢ (for the 5-coin dollar player) when flushes pay 5 instead of 6. Since the value of the flush doesn't affect the value of AKQJ, it's no wonder that strategy isn't identical between the games.
The harder question is why is 'QJ8' higher than AKQJ and 'KQ9' lower. Both combinations are 3-card straight flushes with two high cards and two gaps. Why should they have different values?
If the other two cards in the hand were lower than an 8, 'QJ8' and 'KQ9' would have identical values. But when the other two cards are such that the hand includes AKQJ, things change. This is an example of a 'straight penalty'.
When we look at 'QJ8' (and the other two cards are AK), there are four 9s in the deck and four Ts which can be used to get straights. When we look at 'KQ9' (and the other two cards are AJ), there are three Js and four Ts to create straights. The reason we have few cards to make a straight is because we were dealt a J and threw it away.
This straight penalty is worth 7.4¢. Whether this is a major or trivial amount depends on your perspective. To me, every 7.4¢ counts.
Let's look closer at 3-card straight flushes when we go from 9/6 to 8/5. All 2-gap straight flushes (such as 'KT9', 'A35', or '357') change in value by 20.35¢. One-gap straight flushes (such as 'QJ9' or '457') change in value by 19.89¢, and the no-gappers (such as 'JT9' or '345') change by 19.43¢. Does this strike you as strange? Only the value of the flush changed. Why would this affect these straight flush draws differently?
When we draw two cards to any combination in a 52-card deck, there are exactly 1,081 different 2-card combinations we could draw. Drawing to any three spades, for example, there will be exactly 45 out of 1,081 combinations that will give us five spades. These 45 5-spade combinations may include a royal flush, one or more straight flushes and the rest will be regular flushes.
On the combinations we are considering, a royal flush is not possible, so the number of straight flushes and regular flushes must add up to 45. To a 2-gap straight flush (such as '347'), there is exactly one combination that will complete a straight flush (namely '56' in this case), so that means 44 regular flushes are possible. To a 1-gap straight flush (such as 'JT8'), there are exactly two combinations that complete the straight flush (namely 'Q9' and '97' in this case), so that means 43 regular flushes are possible. Starting with a no-gap straight flush (such as '678') there are three combinations to complete the straight flush (namely '45', '59' and '9T'), which means there will be 42 regular flushes.
One extra flush opportunity out of 1,081 chances on a dollar game amounts to 0.46¢ when we change the value of a flush by one unit. This is not a number worth memorizing, but understanding why different 3-card straight flush combinations are affected differently by a change in the value of a flush helps you memorize strategies. The more you understand about video poker, the more strategies 'make sense' rather than are just a jumble of unrelated rules.
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