Calculating the EV is a lot less complicated than the standard video poker game, because you don't have to calculate the EV of 32 possible decisions and pick the best one, plus there are a lot fewer hands to analyze. There are 270,725 possible 4 card combinations, 52!/(48!x4!). I wrote something in Visual FoxPro to generate a table of all possible hands, then get the number of possible cards (out of the 48 remaining) that make each paying hand, multiplied by the payouts. If I bothered to account for equivalent hands with different suits, I'm sure the number of hands would be a lot lower. I took that total payout for each hand and subtracted 48. If the result was positive, I doubled it. I then summed up all the numbers, divided that by 48, and then divided by 270,725.
Assuming that you are supposed to factor in the doubled bets, I get 100.2049% for Jacks or Better, and 96.0082% for Queens or Better. I could have made some mistakes, but my numbers are pretty close. If you don't factor in the additional money bet when you double down, I am getting 100.2573% for Jacks or Better and 95.0171% for Queens or Better.
Bob, can you really play this game at 2,500 hands per hour? I know you are a professional, but that still seems incredible. Playing 9/6 Jacks or Better I normally play 600 but can get up to around 675-700. I've seen people on occasion that looked like they were probably playing 1000. I realize this requires less thought and less buttons to press, but I would think it would be difficult to play this at even double the speed of 9/6 Jacks or Better. Do you mind if I ask your speed at 9/6 Jacks or Better (or any game where you know the strategy well)?
Alan
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