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Old 02-26-2017, 09:23 PM   #1
RutgersKev
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Full Pay Jacks or Better Risk of Ruin Question

I like Jacks or Better. I've played it for years just about every time I've gone to the casino but I haven't kept any stats to show what my win rate or pace per hour is. I'm pretty sure I can play close perfect strategy in my sleep, and I have no problem putting in long sessions. $ per hour isn't really an issue because I do it for fun.

Casino is offering $1,000 Deposit with a 100% match. 10x clear. Problem is Video Poker (and table games) count as 20%, so I need $50,000 wagered.

Playing quarter full pay (99.54%) Jacks or Better, that is 40,000 hands, with $2,000 available to play. (Deposit plus bonus) What is my risk of ruin? Do I have a decent percent chance of being profitable after the bonus after that many hands?

Thanks for the math!
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Old 03-02-2017, 09:16 PM   #2
Siegmund
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Re: Full Pay Jacks or Better Risk of Ruin Question

Chance of being profitable: each hand has expected value -$.00575 and standard deviation $5.525.
A set of 40,000 hands has expected value -$230 and standard deviation $1105, approximately normally distributed (quality of the approximation depends on this being long enough that you expect to hit the jackpot several times).
So the good news is that your EV is about $770, assuming you make it to the end, and you will come out ahead about 75% of the time.

How often will you not make it to the end?
If you played 40,000 hands no matter what, you'd have about a 6% chance of being down more than $2000 at the end. You have a somewhat greater chance of being down $2000 at some point along the way. A quick simulation had you busting out about 10% of the time.

Assuming you can't afford to risk more than $2000, that means your EV is about -230+900 = $670, instead of -230+1000 = $770, as you'll fail to get the match 10% of the time.
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