Is infinite bankroll with an infinite lifetime called Zombie video poker? I figured next you're gonna ask about finite bankroll with a finite lifetime, or video poker on the human scale.
For ROR over a particular timespan, I recommend Dunbar's Risk Analyzer.
For Kelly, Kelly actually goes one step at a time, or one hand at a time in the case of video poker, just like the 12 step programs, or Joe Walsh's song if you prefer that image, so Kelly is for humans, not zombies. Use the equation for approximate Kelly CE = EV - Variance/Bankroll/2 . EV, Variance, and Bankroll are in units of bets. Say, for example, you want to play one hand of $5 9-6 double-double at max bet ($25) and your current bankroll is $1000. You know you can't play computer perfect, but you're pretty sure you can play well enough to get the average casino hold down to 1.5% . So, Kelly approximate CE is -0.015 - 42/($1000/$25)/2 = -0.015 - 0.525 = -0.54 = -54%. -54% of $25 is -$13.50 . That's the approximate Kelly average value of playing this one hand, this -$13.50 has to come from somewhere, it either comes from your bankroll or it comes from your day job, or some other source if you have any. Obviously, if you want a fair bet for your bankroll size, assuming you put all the winnings into your bankroll, you would only bet if your CE was zero, or in this case someone else paid you the $13.50 cost to play this hand. If you wanted to grow your bankroll, assuming you put all the winnings into your bankroll, you would only bet if your CE was positive or in this case someone else paid you more than $13.50 to play this hand. CE can only be positive if EV is positive but a positive EV can actually be a negative CE for bankrolls less than infinity. Be careful of your estimate of EV, you could be wrong, so put some work into getting a good estimate or provide some extra margin of safety in your guess. Just assuming your EV is the computer perfect EV value is probably a mistake in most cases. Good luck.
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