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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.

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Oct 31, 2006

Some Interesting Puzzles about Changing Games

In November of last year, I wrote a column concerning using 9/6 Jacks or Better strategy to play 8/5 Bonus Poker. (http://www.casinogaming.com/columnists/dancer/2005/1129.html. Some people recently asked me some questions about it, and I thought it useful to delve into it a bit more.

Let's assume you have the hand Jh Th 9h 3c 4d. All players with a pulse quickly play 'JT9' in both 9/6 Jacks and 8/5 Bonus. If I tell you that 'JT9' is worth 19¢ (rounded) more in 9/6 Jacks than it is in 8/5 Bonus, assuming you are playing for dollars and are betting five coins, it sounds reasonable. After all, you probably know that the "6" in 9/6 and the "5" in 8/5 refer to the amount you receive for a flush, so of course hands that can turn into a flush are going to be worth a bit more in the 9/6 game.

So now let's look at the hand Jh Th 9h Ac Kd. This is a closer play, although good players still play 'JT9' in both games. Strong players understand that the value of 'JT9' is lower in this hand that it was in the earlier example for two reasons. The easier-to-understand reason is that the KQJT9 straight is harder to get when you only have three kings remaining in the deck (as is the case in the second hand) than when you have all four kings remaining in the deck. So the Kd is a "straight penalty" to the 'JT9'.

The other reason why 'JT9' is worth less in the second hand is because the Ac and Kd are "high pair penalties," meaning that it's harder to get a pair of aces or a pair of kings when you are throwing one of each away before the draw. High pair penalties aren't any more complicated than straight penalties, but they aren't relevant strategically in most games and fewer people are aware of them. It happens that in this particular hand, the Kd is both a straight penalty and a high pair penalty. That's okay. That happens sometimes.

Now assume I tell you that 'JT9' in the second hand is worth 10¢ (rounded) less in 9/6 Jacks than it is in the first hand.

So far, all of this is background. Now here's your puzzle. In 8/5 Bonus, is the second 'JT9' (i.e from 'JT9'AK) worth 10¢ less than the first 'JT9' (i.e. from 'JT9'34), less than 10¢, or more than 10¢? In other words, does the pay schedule change affect the first hand more or less than the second hand?

Before I answer that question, let me give you another one. Let's go back to the first hand, namely Jh Th 9h 3c 4d. Let's compare it to Jh Th 8h 3c 4d and Jh Th 7h 3c 4d. Good players still hold the hearts in both games. If we know that the value of 'JT9' changed by 19¢ between the games, would we expect that 'JT8' would also change 19¢? Or by more? Or by less?

Neither of these questions is difficult, but most of you haven't thought about them so the answers probably aren't obvious to you. Therefore, I predict that most of you will miss one or both of the questions.

In the first question, the value of 'JT9' changes just as much in both games. In both games, there are 42 ways to get a flush. The number of ways to get a straight and the number of ways to get a high pair change between the two hands, but not the number of ways to get a flush.

In the second question, 'JT9' changes by LESS than 'JT8'. There are 10 hearts remaining in the pack in both games, and the number of (flushes + straight flushes + royal flushes) possible in each game is 45. Since you can't get any royal flushes holding 'JT9', this means that the number of flushes + straight flushes equals 45 in each game.

Since there are three straight flushes possible from 'JT9' (namely 'KQJT9', 'QJT98', and 'JT987') that means there are 42 possible flushes. There are only two straight flushes possible from 'JT8' (namely 'QJT98' and 'JT987'), so that means there are 43 possible flushes. Similarly, from 'JT7', the only straight flush possible is 'JT987', so there are 44 possible flushes.

So with 42 possible flushes, the pay schedule change is worth 19¢ to 'JT9'. With 43 possible flushes, the pay schedule change is worth 19.5¢ to 'JT8'. With 44 possible flushes, the pay schedule change is worth 20¢ to 'JT7'.

Why is this important? A basic understanding of this is helpful if you ever play progressives, or ever play games you haven't mastered and you have to "wing it." Players who have grappled with these kinds of questions have a much better chance of getting the correct play when they come up against progressives or new games than those players who have never tried to figure these things out.