Effect of EV on having to bet refund through multiple times?

Is there a basic approximation for the effect of having to bet a refund multiple times before it can be cashed out. For example, if it was only available on slots and lets assume that slot handle is 7%. Can I just ballpark it with (EV)*(handle)^number of times money must be rebet before cashout, like (EV)*(.93)^2, if it had to be bet twice?

Yeah, twice through you would hope to get on average (.93)^2 = 0.8649 = 86.5% of the freeplay back.

simply bet the whole refund at once and EV goes up dramatically.

Quote: MangoJ

simply bet the whole refund at once and EV goes up dramatically.

Now if this was part of a loss rebate and your losses get refunded as freeplay, you are right on the portion of play BEFORE you get your refund, but not after. I'm not sure if the OP was referring to a loss rebate though.

The key for the "after" portion of a loss rebate is to play the minimum amount of coin-in to unlock the freeplay (preferably on higher EV machines).

If you play $100 of freeplay "once through" and either machine is 95% payback, you'll expect 95% back on average even if you bet it a quarter at a time 400 times or bet $100 one time. But if you bet a quarter 800 times instead, then you overplayed by playing "twice through" and would expect $100*(.95)^2 = $90.25 back

Playing "through" the minimum amount necessary is the key for actually grinding the refund. "Once through" is the typical requirement in casinos, so you just stop playing when you played through all your freeplay one time. But if you have to play twice through, then you would have to create coin-in equal to double your freeplay.

Quote: tringlomane

Now if this was part of a loss rebate and your losses get refunded as freeplay, you are right on the portion of play BEFORE you get your refund, but not after. I'm not sure if the OP was referring to a loss rebate though.

Sorry thats a different story with loss rebate.

If you have a 95% payback game, and you need to bet two times the refund amount (say $100, so you need to bet $200 before you can cash out), the grinding strategy gives you $100 * 0.95^2 = $90.25 as EV.

If you bet the whole $100 refund once, and if you win bet the remaining $100 wagering amount again - say on a even paid game, chance of win is 47.5% - you result in:
"Win/Win": $300 (p = 0.475 * 0.475 = 22.5625%)
"Win/Loss": $100 (p = 0.475 * 0.525 = 24.9375%)
"Loss": $0 (p = 52.5%)
resulting in EV = $92.625 which is larger than the $90.25 in the grinding strategy.

Quote: MangoJ

Sorry thats a different story with loss rebate.

If you have a 95% payback game, and you need to bet two times the refund amount (say $100, so you need to bet $200 before you can cash out), the grinding strategy gives you $100 * 0.95^2 = $90.25 as EV.

If you bet the whole $100 refund once, and if you win bet the remaining $100 wagering amount again - say on a even paid game, chance of win is 47.5% - you result in:
"Win/Win": $300 (p = 0.475 * 0.475 = 22.5625%)
"Win/Loss": $100 (p = 0.475 * 0.525 = 24.9375%)
"Loss": $0 (p = 52.5%)
resulting in EV = $92.625 which is larger than the $90.25 in the grinding strategy.

Whoops, I stand corrected. Betting it all is better because there is the chance you initially lose and aren't always subjected to grinding it twice. In practice though, I'm a variance nit and grinding it anyway...haha

Yes, this strategy is of much higher variance. The reward is higher EV. Ultimatively it boils down to personal risk management.