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So, this may be the simplest question ever asked here, but my brain fails massively and I need help. Here's the situation, any help would be greatly appreciated.

There's a slot machine which randomly charges between $0.01 and $1.00 to play, and will either pay out $1 or nothing. Let's call the price to play X. X is completely random.

The likelihood that the slot machine will pay out $1 on a particular turn can be called Y. Let's assume that one can know Y. The odds for any particular turn are completely random.

So without knowing Y, to make money one would just play the turns priced lower than $0.50, and over time you'd make money.

But knowing Y, you should be able to make bets even on turns that cost close to $1 if you choose only to play those with very favorable odds.

But what is the best way to account for both the potential gain and the risk to come up with the "winning formula"?

Thanks,

Jacob

There's a slot machine which randomly charges between $0.01 and $1.00 to play, and will either pay out $1 or nothing. Let's call the price to play X. X is completely random.

The likelihood that the slot machine will pay out $1 on a particular turn can be called Y. Let's assume that one can know Y. The odds for any particular turn are completely random.

So without knowing Y, to make money one would just play the turns priced lower than $0.50, and over time you'd make money.

But knowing Y, you should be able to make bets even on turns that cost close to $1 if you choose only to play those with very favorable odds.

But what is the best way to account for both the potential gain and the risk to come up with the "winning formula"?

Thanks,

Jacob

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