vpFREE2 Forums

Bob Dancer's LVA - 19 AUG 2014

#1

I am now ready to tell you the cost of playing Queens or better pays 2 instead of Jacks or better pays 2 DDS. For this discussion order counts because even though the final hand may be the same without order counting in one case you may have doubled and the other case you may not have. For example JJ234 returns 2 bets and J234J returns only 1 so your loss in playing Queens instead of Jacks DDS are 2 bets and 1 bet respectavely. Now instead of 2598960 final hands there are 2598960 times 5! = 311875200 final hands with order counting. Instead of 84480 hands of exactly 1 pair of Jacks there are 84480 times 5! = 10137600 final hands of exactly 1 pair of Jacks. There are (4C2 times 12C2 times 16 times 4!) = 152064 ways that your first 4 cards are exactly 1 pair of Jacks, (you are now doubling your bet) and 40 cards you can catch (any card of the other 10 ranks not in your 1st 4 cards) = 6082560 final hands of 1 pair of jacks where you have a pair of jacks in your first 4 cards. There are (12C4 times 4 times 4!) = 47520 ways that your first 4 cards are a 4 flush that contains a Jack. There are ((4 to the power of 4) times 4! times 3) = 18432 ways that your first 4 cards are KQJ10 or QJ(10)9 or J(10)98. If you subtract out the 288 ways that your first 4 cards are KQJ10 suited or QJ(10)9 suited or J(10)98 suited that leaves (47520+18432-288) = 65664 ways that your first 4 cards are an open ended straight or a 4 flush that contains a Jack, (you are now doubling your bet) and 3 other Jacks you can catch = 196992 final hands of 1 pair of jacks starting with a 4 card opened straight or 4 flush that contains a jack. Combining the 2 cases there are (6082560+196992) = 6279552 ways of ending up with a pair of jacks where you have doubled your original bet for a loss of (6279552 times 2) = 12559104 original bets over "Jacks" DDS. That leaves (10137600-6279552) = 3858048 final hands of exactly 1 pair of jacks that were not doubled. You lose an original bet over "Jacks" DDS in those cases. Your total loss over "Jacks" DDS is therefore (12559104+3858048) = 16417152 original bets. The loss by playing "Queens" DDS over "Jacks" DDS is therefore 16417152/311875200 = 0.05264 or 5.264%.

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#2

I am now ready to tell you the cost of playing Queens or better pays 2 instead of Jacks or better pays 2 DDS. For this discussion order counts because even though the final hand may be the same without order counting in one case you may have doubled and the other case you may not
have. For example JJ234 returns 2 bets and J234J returns only 1 so your
loss in playing Queens instead of Jacks DDS are 2 bets and 1 bet respectavely. Now instead of 2598960 final hands there are 2598960 times
5! = 311875200 final hands with order counting. Instead of 84480 hands of exactly 1 pair of Jacks there are 84480 times 5! = 10137600 final hands of exactly 1 pair of Jacks. There are (4C2 times 12C2 times 16 times 4!) = 152064 ways that your first 4 cards are exactly 1 pair of Jacks, (you are now doubling your bet) and 40 cards you can catch (any card of the other 10 ranks not in your 1st 4 cards) = 6082560 final hands of 1 pair of jacks where you have a pair of jacks in your first 4 cards. There are (12C4 times 4 times 4!) = 47520 ways that your first 4 cards are a 4 flush that contains a Jack. There are ((4 to the power of 4) times 4! times 3) = 18432 ways that your first 4 cards are KQJ10 or QJ(10)9 or J(10)98. If you subtract out the 288 ways that your first 4 cards are KQJ10 suited or QJ(10)9 suited or J(10)98 suited that leaves (47520+18432-288) = 65664 ways that your first 4 cards are an open ended
straight or a 4 flush that contains a Jack, (you are now doubling your bet) and 3 other Jacks you can catch = 196992 final hands of 1 pair of jacks starting with a 4 card opened straight or 4 flush that contains a jack. Combining the 2 cases there are (6082560+196992) = 6279552 ways of
ending up with a pair of jacks where you have doubled your original bet
for a loss of (6279552 times 2) = 12559104 original bets over “Jacks” DDS. That leaves (10137600-6279552) = 3858048 final hands of exactly 1 pair of jacks that were not doubled. You lose an original bet over “Jacks” DDS in those cases. Your total loss over “Jacks” DDS is therefore (12559104+3858048) = 16417152 original bets. The loss by playing “Queens” DDS over “Jacks” DDS is therefore 16417152/311875200 = 0.05264 or 5.264%.

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Interesting analysis. One error I think I found was when you started with a pair of jacks, say JJ234, you said there were 40 cards you could draw that wouldn’t give you two pair. I think there are only 36 that wouldn’t give you two pair or trips.

FWIW, I passed the problem by J.B., the programmer behind much of the Wizard of Odds website. His models say the game is worth 100.19% if it’s Jacks or Better and 95.99% if it’s Queens or Better. That comes out to a 4.20% difference. I do trust J.B.'s numbers. Nordo is clearly more competent with these calculations than I am — but if I were forced to choose between trusting one or the other, I’m siding with J.B. with absolutely no offense intended.

I’m not going to try to reconcile the two different numbers. For my purposes, whether the game is 95% or 96% is 100% irrelevant. I’m not going to play it.

Bob

#3

I’m shooting blood from my eyes after reading this.
"Mother PLEASE make it stop"

CF

Age & treachery will overcome youth & skill.

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-----Original Message-----

From: Nordo…@…com [vpFREE] <vpF…@…com>

To: vpFREE <vpF…@…com>

Sent: Fri, Aug 22, 2014 10:54 am

Subject: Re: [vpFREE] Bob Dancer’s LVA - 19 AUG 2014

` I am now ready to tell you the cost of playing Queens or better pays 2 instead of Jacks or better pays 2 DDS. For this discussion order counts because even though the final hand may be the same without order counting in one case you may have doubled and the other case you may not have. For example JJ234 returns 2 bets and J234J returns only 1 so your loss in playing Queens instead of Jacks DDS are 2 bets and 1 bet respectavely. Now instead of 2598960 final hands there are 2598960 times 5! = 311875200 final hands with order counting. Instead of 84480 hands of exactly 1 pair of Jacks there are 84480 times 5! = 10137600 final hands of exactly 1 pair of Jacks. There are (4C2 times 12C2 times 16 times 4!) = 152064 ways that your first 4 cards are exactly 1 pair of Jacks, (you are now doubling your bet) and 40 cards you can catch (any card of the other 10 ranks not in your 1st 4 cards) = 6082560 final hands of 1 pair of jacks where you have a pair of jacks in your first 4 cards. Th
ere are (12C4 times 4 times 4!) = 47520 ways that your first 4 cards are a 4 flush that contains a Jack. There are ((4 to the power of 4) times 4! times 3) = 18432 ways that your first 4 cards are KQJ10 or QJ(10)9 or J(10)98. If you subtract out the 288 ways that your first 4 cards are KQJ10 suited or QJ(10)9 suited or J(10)98 suited that leaves (47520+18432-288) = 65664 ways that your first 4 cards are an open ended straight or a 4 flush that contains a Jack, (you are now doubling your bet) and 3 other Jacks you can catch = 196992 final hands of 1 pair of jacks starting with a 4 card opened straight or 4 flush that contains a jack. Combining the 2 cases there are (6082560+196992) = 6279552 ways of ending up with a pair of jacks where you have doubled your original bet for a loss of (6279552 times 2) = 12559104 original bets over "Jacks" DDS. That leaves (10137600-6279552) = 3858048 final hands of exactly 1 pair of jacks that were not doubled. You lose an original bet over "
Jacks" DDS in those cases. Your total loss over "Jacks" DDS is therefore (12559104+3858048) = 16417152 original bets. The loss by playing "Queens" DDS over "Jacks" DDS is therefore 16417152/311875200 = 0.05264 or 5.264%.
Sent from my iPhone
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#4

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

#5

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)?

···

This is a stud game. 9/6 Jacks is a draw game. Stud games are MUCH faster.

My actual speed on this game was an estimate. I didn’t play it because the pay schedule sucked.

Bob