Thanks Harry. The Wizard has the following on his site.
http://wizardofodds.com/ask-the-wizard/video-poker/probability/
To get back to the problem at hand, it will obviously only take one four of a kind to cross the first one off the list. The probability the next four of a kind will be one that you need is 12/13. So, on average, it will take 13/12=1.0833 trials to get it. Once you have two crossed off the list, the probability the next one will be one that you need is 11/13, so that will take 13/11=1.1818 more trials to get the third one.
Following this pattern the total expected number of four of a kinds to get at least one of each kind is
1 + (13/12) + (13/11) + (13/10) + ... + (13/1) = 41.34173882.
---In vpFREE@yahoogroups.com, <harry.porter@...> wrote :
Not looking to step on anyone else's toes, the 17,499 is a straightforward calculation:
The value assumes play of standard 9/6 Jacks strategy, without strategy modification to accelerate quad hits.
Mean time to the first quad hit is 423.3 hands. After hitting your first quad, there are 12 remaining quads to hit, out of 13 possibilities; mean time to hitting the next target quad is (13/12)*423.3 = 458.6 hands.
Calculation of the subsequent "mean time to hit" proceeds similarly, with values of (13/11)*423.3, (13/10)*423.3, etc. Adding the results for all 13 quads yields the suggested cycle of 17,499.
My guess is that with an ER-optimized strategy, the cycle would drop into the range of 15000-15500 hands.
---In vpFREE@yahoogroups.com, <jeff-cole@...> wrote :
The value assumes play of standard 9/6 Jacks strategy, without strategy modification to accelerate quad hits.
Mean time to the first quad hit is 423.3 hands. After hitting your first quad, there are 12 remaining quads to hit, out of 13 possibilities; mean time to hitting the next target quad is (13/12)*423.3 = 458.6 hands.
Calculation of the subsequent "mean time to hit" proceeds similarly, with values of (13/11)*423.3, (13/10)*423.3, etc. Adding the results for all 13 quads yields the suggested cycle of 17,499.
My guess is that with an ER-optimized strategy, the cycle would drop into the range of 15000-15500 hands.
---In vpFREE@yahoogroups.com, <jeff-cole@...> wrote :
Can you tell us how you calculated the 17,499? Or share your source?
---In vpFREE@yahoogroups.com, <tringlomane@...> wrote :
---In vpFREE@yahoogroups.com, <tringlomane@...> wrote :
Actually it's easier than a regular royal. If all quads were equally likely (they aren't but it's close), then collecting all 13 quads should take about 1 in 17,499 hands. Since succeeding pays the equivalent of half a royal, this adds over 2% to the base game. So games like 8/5 JoB can be considered "playable". The only risk is if the casino yanks the game while you're almost done collecting the quads, you are likely "out of luck" then.
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