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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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Aug 20, 2007

An Interesting Strategy Twist in Super Double Double Bonus

Super Double Double Bonus is a rather obscure game, but it can be found at times. The 8/5 version returns 99.69% and is relatively easy to play.

For those not familiar with the game, there are a lot of 4-of-a-kind bonuses in this game

	1-coin	5-coins

Four A with 2,3,4	400	2,000
Four A with J,Q,K	320	1,600
Four J-K with A, J, Q, K	160	800
Four 2-4 with A, 2, 3, 4	160	800
Four aces	160	800
Four 2-4	80	400
Four 5-K	50	250

The interesting hands I want to compare today, with suits irrelevant, are 2229A and JJJ9A. The correct play on the first hand is 222 and the correct play on the second is JJJA.

Holding the ace "kicker" to JJJ is an unusual play. It's not unheard of to hold kickers, but it's rare. What is more unusual is why you should hold the kicker to JJJ (where you'll collect 800 coins if you collect the fourth jack) but not to hold the kicker with 222 (where you'd collect the same 800 coins for snaring the fourth deuce.)

See if you can figure out why there's this difference. I don't mind waiting for you to figure it out.

When you see the answer, or read it below, it'll be obvious and not seem like much of a puzzle. But many people have blinders on and can't see the answer until it's pointed out to them.

In both hands, holding the kicker is worth $33.30 for the 5-coin dollar player. In the 47 possible draws, you'll collect the correct card one time for $800, three times you'll collect a full house for $40, and the other 43 times you'll end up with the $15 set of trips. Take the average of these events and you'll arrive at $33.30. Doing it yourself isn't very tough, but using good software to do it (Video Poker for Winners is my recommendation) for you is easier.

So if holding the kicker is worth the same amount, why is it sometimes the correct play and sometimes not? The answer, obviously, is how much the trips are worth when you don't hold the kicker.

When you draw two cards to trips, there are always 1,081 combinations to consider in a 52-card game. On these particular hands, you'll end up with the original trips 969 times, full houses 66 times, quads-without-a-kicker 35 times and quads-with-a-kicker 11 times. These numbers remain the same in both hands.

So again, if the numbers are the same, why is there a difference in the correct play?

The answer is simply how much you get for the quads-without-a-kicker. For four deuces you get $400 and for four jacks you get "only" $250. This makes holding the three deuces by themselves worth $36.98, which is higher than the $33.30 benchmark for holding the deuces with the kicker. Holding the three jacks by themselves is worth $32.12, which is less than the benchmark.

If there are two kickers in the hand (not a full house), the numbers vary a little. That is, from 2223A the value of holding just the three deuces is reduced by 37¢ to $36.60 (rounded). This is still above $33.30 (which isn't affected by the second kicker), so the play remains unchanged. From JJJQA the value of holding just the three deuces is reduced by 51¢ to $31.61. This makes holding the kicker more important. It doesn't matter whether you hold the ace or queen kicker.

As a bonus question, you might want to consider why losing the extra chance at the kicker is worth 37¢ in the first case and 51¢ in the second. Why is it different?

The answer is much the same as before. With 2223A, one of the $800 kicker quads is reduced to a regular quad worth $400. A net change of $400 over 1,081 hands averages out to 37¢ each time. With JJJQA, one of the $800 kicker quads is reduced to a regular quad worth $250. A net change of $550 over 1,081 hands now averages 51¢.

Video poker math isn't particularly difficult once you immerse yourself in it. The more times you work out these problems, the better you'll be able to analyze promotions and other new situations in the future. If you wait for someone to figure it out for you and post the answer on the Internet, you'll likely miss a lot of the benefits. If you can figure it out for yourself before everyone else knows about it, you're that much ahead.