Probability Mass Functions for Video Poker Games

Hi, I'm a Math student at Kutztown University and recently my dad got me in to some advantage gambling stuff. I have a good foundation in probability, but I have no idea how to find a probability mass function for any game. Specifically, I'm interested in perfect strategy 9-6 Jacks or Better, because that's the game my dad introduced me too. I'd like to know the probability mass function because I'd like to tinker around with it for fun and maybe my Senior Seminar project. Even just a book recommendation would be good.

Thanks

How are you defining Probability Mass Function in this case? What is the desired domain of the function?

I read the Wikipedia definition of pmf and still don’t know what it says.

The following is from the Video Poker for Winners Software. Does it give you the information you need?

Insofar as a book on how to play the game, the Dancer/Daily Winner’s Guide for Jacks or Better is as complete as exists.

Analyze Jacks or Better

Game Return 99.54%
Standard Dev 4.4175
Variance 19.5147

Pay Frequency %Probability Occurs Every % Return

Royal Flush 4000 64.34575 0.002 40,390.55 1.98
Straight Flush 250 284.08995 0.011 9,148.37 0.55
4 of a KIND 125 6,140.16 0.236 423.27 5.91
Full House 45 29,919.77 1.151 86.86 10.36
Flush 30 28,626.27 1.101 90.79 6.61
Straight 20 29,184.68 1.123 89.05 4.49
3 of a KIND 15 193,489.19 7.445 13.43 22.33
2 Pair 10 335,990.70 12.928 7.74 25.86
Jacks or Better 5 557,697.91 21.459 4.66 21.46
No Win 0 1,417,562.89 54.543 1.83 0

Video Poker for Winners Copyright 2006,2007, Action Gaming Inc.