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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.

Jan. 5, 2010

An Interesting Logical Inference in Double Double Bonus

It'll be a cold day in hell before you'll see me playing 9/6 Double Double Bonus, which only returns 98.98% when played perfectly. At least that was the case before M casino periodically started having 4x point days. Since then they seem to have removed the 4x and 3x point days and have eliminated several machines from being eligible for the point multipliers, but for a few months this game was the most lucrative in the casino, so long as you were willing to play $10 or $25 single line on 4x point days.

As is my custom, I attempted to learn the game perfectly before I sat down in the casino. There aren't a lot of penalty cards in this game so I found mastering this game easier than mastering several other games (including any version of Deuces Wild or game where flushes return 5 for 1).

The normal strategy for an unsuited AKQ or AKJ in this game is to just to hold the ace. One of the strategy rule exceptions in the Dancer/Daily strategy reads as follows:

A with fp plus sfkp < KH with no sp

If you're new to penalty cards, the notation might seem a bit strange. Most players, however, find that after the notation is explained find the rule not particularly difficult.

KH means KQ and/or KJ. This same notation is used on Video Poker for Winners. The "H" means a high card (i.e. a card where you get your money back if you pair it up) lower than the first card indicated.

fp means a flush penalty to the ace --- which simply means a card in the same suit as the ace.

sfkp means "straight flush kicker penalty" to the ace, which is specifically a 2, 3, or 4. A 5 would be a straight flush penalty, but not a straight flush kicker penalty. (I assume you know that in Double Double Bonus you receive 2,000 coins with four aces and a 2, 3, or 4. With four aces and a 5-K, you "only" earn 800 coins.)

sp means straight penalty to the KH, which means close enough so that you can complete a straight that includes a KQ. In this instance it means a 9 or higher.

When you add together the "fp plus sfkp" penalties plus look at the strategy as a whole, there are some restrictions. The fp cannot be a nine or higher as that would give the KH a straight penalty. Also, the fp cannot also be a sfp (i.e. 5 or lower) because when added to the sfkp it would give you a 3-card A-low straight flush. Therefore, the fp must be in the range 6-8.

As examples, where quote marks mean the cards are suited with each other, examine the following:

a.'A83' KJHold KJ
b.'A93' KQHold A. The 9 is a sp to KQ
c.'A75' KJHold A. There is no sfkp
d.'AT3' KQHold ATKQ
e.'A52' KJHold 'A52'. This is a 3-card straight flush draw.

Okay, that wasn't so tough. One question about this would be why is this rule limited to KQ and KJ? Why not QJ? After all, QJ is more valuable than either KQ or KJ because of the number of possible straights. Surely if you hold KQ from 'A83' KQ you would also hold QJ from 'A83' QJ because QJ is worth about 3¢ more to the 5-coin dollar player than KJ is. So why isn't QJ mentioned in the strategy rule?

Even if this isn't a game you regularly play, this is a logical inference that isn't that difficult to players who are familiar with strategy cards. Can you figure it out? I encourage you to at least try to figure out this conundrum before reading on. I don't mind waiting until you do.

The key reason why QJ isn't included in this rule is that this rule lists an exception to the normal A > KH ranking. QJ is superior in value to the ace (i.e., from an unsuited AQJ, the standard play is to hold QJ). Penalties to the ace do not change the play because even without penalties, QJ > A. There are some situations where the QJ is penalized with an 8 or 9 where we hold the ace from AQJ, but those aren't the rules we're talking about today.