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.
link to original post

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.