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I took advantage of a free slot machine $50$ spin bonus (no deposit required) on a casino site.

I won $£50$ and managed to turn that into $£600$ (so I have $£600$ in my bonus balance).

In order to turn the bonus into cash, you must wager at least $35*$(amount in your bonus balance).

This is the amount in your bonus balance at the time of your first deposit (I haven't deposited).

The wager requirement is to wager only on slot machines so I'm trying to figure out if it is even worth it to deposit money.

The slot payout is about $0.96$ of your wager, so even after an infinitely long playing session with $£600$, I'm expected to wager $£15,000$ (infinite geometric sum) which is not the requirement of $£21,000$.

Do you agree with me or can you see this differently? Thanks :)

Note: $0.96$ is the average payout rate, not constant.

Desmoz
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  • Not sure I understand the rules. Can you make small deposit, then play with that + your bonus, balance going up and down, until you lose everything or can cash out what's left? – Ethan Bolker Dec 22 '16 at 04:30
  • I can make a small deposit, say £10, wager it once then cash it out. Then all I need to do is wager the bonus risk free (the bonus is not affected in anyway by the deposit). – Desmoz Dec 22 '16 at 04:33
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    So your question seems to be about your calculation. I'm not sure where the £15,000 figure comes from. Make the small deposit, play with the bonus until you've wagered £21,000 (or lost all), then cash out. You'll probably win, since 0.96 $\times$ £21,000 is a lot more than the £10 you pay to play. – Ethan Bolker Dec 22 '16 at 04:50
  • I got £15,000 from the expected amount I would wager, summing $600 + 600(0.96) + 600(0.96)^2 + ...$ – Desmoz Dec 22 '16 at 05:22
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    I think there are some subtleties here that make a precise analysis difficult. For example, in the $600 + 600 \cdot 0.96 + \ldots$ calculation, that's them taking a flat $4%$ each time. Which is indeed how it all plays out, in the long run. But I assume you could throw the $600$ down and lose it all right there, also. At any rate, casinos rarely do anything where their expected value is negative, and that's likely the case here (it's not unheard of though, for someone to screw up) [con't]... – pjs36 Dec 22 '16 at 06:18
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    [2/2] Your calculation probably accurately depicts the best case scenario if your luck is "average," and I would safely agree that no, it's not worth it (financially). – pjs36 Dec 22 '16 at 06:18
  • Thanks for the contribution guys :) – Desmoz Dec 22 '16 at 07:05

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