Can someone explain the Wizard's VP risk of ruin tables?

Hello,
I do not understand these Risk of Ruin tables on the Wizard of Odds. What does "cash back" mean in this context, and how come 9/6 JoB doesn't have a column for 0% cash back but the other two games do?

I am not allowed to post links because I am a new member of this forum. The URL is
WizardOfOdds dot com /games/video-poker/appendix/1/

You can also Google "Video Poker: Bankroll Size vs. Risk of Ruin" and it should be the first result from WOO,

Thank you.

Cash back is the amount the casino gives you for each $1 you play.

Risk of ruin for a negative expectation game is 100%. If you play long enough, you will lose all your money.

You need a positive expectation to have a non zero risk of ruin.

The "cash back" is the percentage of coin-in (the amount of money wagered) the casino will refund to the player (using the casino's player's card). E.g., the Plaza advertises $10/point for VP, and points can be redeemed for cash at a rate of 100 pts/$1. Multiplying the two, you get $1000 coin in/1$ cash back, or a rate of 0.1%. Note that the Plaza also awards "Free Slot Play" at the same rate. If the free play can be used on the desired VP machine, then you can consider the cash back rate to be 0.2%.

The reason the JoB table starts at 0.5% cash back is because JoB returns 99.54% to the player. Therefore, you must have a cash back rate higher than 0.46% before it is +EV (positive return for the player) The other two games are already +EV without any cash back. Note that the risk of ruin for any game that is -EV is always going to be 100% for an "indefinite period of play," regardless of bankroll size.

Unfortunately, these days, you'd be hard pressed to find a casino that gives 0.5% cash back without some sort of promotion. Also, I'm not aware of any casino that still has FPDW, and only a handful still have 10/7 DB. And of those that do have 10/7 DB, most will not give points/cash back on it.

ETA: Whoops, 3for3 beat me to it!

Quote: 3for3

Cash back is the amount the casino gives you for each $1 you play.

Risk of ruin for a negative expectation game is 100%. If you play long enough, you will lose all your money.

You need a positive expectation to have a non zero risk of ruin.
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Thank you. So even though the long-term RTP on 9/6 JoB is 99.54%, you still have a 100% chance of ruin in the long run? Is that because we'd essentially be suffering compounded losses? So after n sessions, we have (0.9954)^n * OriginalBankroll ?

Risk of ruin is the probability of busting out your bankroll if you don't achieve a certain win amount. If you make your "desired win amount" infinity, then of course your risk of ruin will be 100% for any game with a -EV.

A more reasonable thing to do would be to set a desired win amount that's something achievable (like one royal flush) and then calculate the risk of ruin.

“So after n sessions, we have (0.9954)^n * OriginalBankroll ?”

Not the right math.

Your EV on each hand is -0.46% of your wager. That number is and always will be negative.

After n hands played, your expectation is: OriginalBankroll - (0.0046 * wager * n)

Interesting 🧐, any way to overcome this disadvantage like 10x point days? (If those still exist for video poker)

Quote: RS

“So after n sessions, we have (0.9954)^n * OriginalBankroll ?”

Not the right math.

Your EV on each hand is -0.46% of your wager. That number is and always will be negative.

After n hands played, your expectation is: OriginalBankroll - (0.0046 * wager * n)
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NO.

(0.9954)^n * OriginalBankroll is the average expected value of your bankroll after n sessions betting 'one bankroll.'

The "risk of ruin is more complicated; it takes into account that a long losing streak can wipe you out. It accounts for the random variance in the game and your odds of eventually being very unlucky.

For example, if you start with a bankroll of $100 and make 10 bets of $10 with a 50% probability there is a risk of ruin of 1/2¹⁰ or 1/1024. So, about one chance in a thousand that you will wipe out your bankroll. If you make 20 bets of $10 each with 50% probability there is a significantly greater risk of ruin.

You might look up "risk of ruin" in Wikipedia or some other online source.

Quote: CeeEnd

Interesting 🧐, any way to overcome this disadvantage like 10x point days? (If those still exist for video poker)
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If the points are worth more than the house edge, then yes. Good luck finding those opportunities.

You never know these days, I appreciate your math focused answer though rs. It's cool there are some smart guys on these forums, that other one, what's it called, Vegas casino talk is full of bottom bell curve Iq individuals.