Double Double

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This past week, I received an e-mail from a reader asking whether or not you should hold the two pair or only the high pair, when dealt jacks and 2’s in Double Double Bonus Poker.
   
I wonder if the inventor of Double Double knew that this situation would give video poker players headaches and probably be a major cause of  error. My reader knew that the answer lies in which one has the higher expected value, but he didn’t know which of these possible draws actually had the higher value.
   
Let me first explain what “expected value” (or EV for short) is. Expected value is the average number of coins the player can expect to have returned to him when taking into account every possible outcome.
   
There are 47 possible draws to holding a two pair. Four will result in a full house which pays 9 for 36 units (4 times 9). Then there are 43 others resulting in the hand not improving and paying a single unit for 43 units.
   
We add the 36 and 43 to get 79. Divide this by the total number of draws (47) to get 1.68. As you can see, expected value is just an average. The player will get 1 unit back most of the time and will get 9   some of the time, which averages out to the 1.68.
   
Now, if the player chooses to keep just the high pair, it gets a bit more complex, but the concept is still the same. There are 16,215 ways to draw three cards –. 45 resulting in four of a kind paying 50 each (2250 total coins), 169 in a full house paying 9 each for a total of 1,521 coins.
   
Also 1,852 will result in trips for a total of 5,556 more coins, 2,629 in a two pair for 2,629 and lastly, the remaining 11,520 will stay a high pair. In the end, we have a total of 23,476 coins. We divide this by the 16,215 possible draws to get us an expected value of 1.45.
   
As is always the case, we play the hand in the way that provides the highest expected value. So from the calculations above, the proper way to play the hand is to hold the two pair because it only pays 1 unit in Double Double.
   
However, the roughly nine percent chance to hit the full house gives us a much stronger expected value. While we ‘lose’ the chance to go for quads or to hit trips, the probability of hitting the four of a kind is only about 0.3 percent, and the probability of picking up a full house drops to just over 1.
   
By holding only a pair, still 87 percent of our hands will wind up paying just a single unit. We’ll have slightly more winners paying more than 1, but most of them will pay less than the full house would if we hold the two pair.
   
What fun would video poker be if there wasn’t at least one exception to the rule? Some of you may have wondered if it pays to hold the low pair in the example above because four 2’s pays significantly more than four jacks. Get that idea out of your head.
   
Giving up the sure winner for the tiny chance of hitting four of a kind and the even tinier chance of hitting it with an ace, 3 or 4 simply doesn’t add up. However, given that a pair of aces is both a sure winner and pays even more for quad — if you have a two pair with aces and something else, you keep only the pair of aces.
   
The expected value of the pair of aces is about 1.9. Even in the cases where the other pair is 2’s, 3’s or 4’s, you still only hold the pair of aces. The expected value will be slightly diminished in this case, but it is still the proper play.
   
There’s still time to brush up on your strategy tables before the holidays. The stocking stuffer special continues through December. Get both Video Poker: America’s National Game of Chance and Winning Strategies for $15 (includes postage and handling). Additional copies are just $5 each! Send check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.
 

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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