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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.

For more details and a schedule of Bob's free classes, visit www.bobdancer.com.

Dec. 10, 2007

A Logical Dilemma

Today's poser concerns strategy differences between two games. Few people, I suspect, know both games cold. Even if you know neither game well, however, you should be able to figure out the poser strictly on logical grounds.

In my column on advanced 10/7 Double Bonus that was published here a last week, I noted that in that game 3-card straight flushes with one inside and no high cards were inferior to 'AJ' in the same hand. There were five such combinations, fitting nicely into two groups, which I'll label (a) and (b):

(a) '234', '235', '245'

(b) '78T', '79T'

In 9/5 Triple Bonus Poker Plus, the combinations in (a) above are also inferior to 'AJ'. Those combinations in (b), however, are not. Please explain. In case you are unfamiliar with the pay schedules involved, I'm including them below:

	9/5	10/7
	TBPP	DB

Royal Flush	800	800
Straight Flush	100	50
Four Aces	240	160
Four 2s thru 4s	120	80
Four 5s thru Ks	50	50
Full House	9	10
Flush	5	7
Straight	4	5
Three of a Kind	3	3
Two Pair	1	1
Jacks or Better	1	1

Before reading my solution to the poser, I invite you to try it yourself. I've presented this problem to a few of my students and many of them were initially stumped, although each eventually got the correct answer when provided with some clues. Learning to think like a strong video poker player requires exercising your brain. This puzzle is a good place to start.

In this particular situation, looking at the pay schedule probably isn't useful. TBPP pays more for the straight flush and four aces, and less for full houses, flushes, and straights. (The fact that TBPP also pays more for four 2s thru 4s is irrelevant in the hands we're talking about.) Figuring out how each of these pay schedule variations affects the combinations in question is a task for a computer program.

If you haven't figured out the answer by now, let me give you a big hint. The straight flush combinations in (a) above have exactly the same value as those in (b). If there is a difference on whether one of these combinations are more or less valuable than 'AJ', the solution must come from the differing values of 'AJ'.

Once you realize that it's the value of 'AJ' that varies, it's easy to figure out that the ten in each of the combinations of (b) above is a straight penalty to the 'AJ', hurting the value of 'AJ' by about 2¢ in 9/5 TBPP and 2.4¢ in 10/7 DB. These numbers are for the 5-coin $1 player.

In our advanced 10/7 DB strategy, we grouped (a) and (b) together because they had the same net effect, namely they were both inferior to 'AJ'. In the strategy, we weren't concerned with "by how much," only with "which one is better."

In 9/5 TBPP we come up with a strategy of (a) > 'AJ' > (b). Technically this is incorrect because in actuality (a) = (b). But since we are only concerned with the relationships of (a) > 'AJ' and 'AJ' > (b) one at a time (because we only have five cards in a hand), it's convenient to put them into one extended relationship.

In other games we have similar relationships. In 8/5 Bonus Poker, for example, '345' and '89T' are the only two 3-card straight flushes with zero insides and zero high cards that are inferior to 'AJ'. The fact that several pay schedule categories are different (e.g. two pair, full houses, four jacks, four aces, and straight flushes) from those in 9/5 TBPP means that the relationship isn't exactly the same, but it's the same type of "straight penalty" situation in both games.

Even if you're not going to memorize all of the penalty card situations in all games, it's good to be generally aware of them.