Help coming up with the right algebra formula to use.

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

 

Could it be as simple as:
(100/X)*Y>1 means bet
(100/X)*Y<1 means don't bet
?

 

Guess I explained it poorly at the beginning. Lemme give it another shot, using a different situation that may be more clear.


There are many slot machine which all pay out either $1 or nothing.

Before each turn, all of the machines display a price-to-play between $0.01 and $1.00. The price is X. Each machine displays different prices at random, but that's unimportant since the price is always known before deciding to play.

What differentiates the machines is that each machine has a different % likelihood that it will pay-out, the % likelihood of a pay-out for a machine is Y.


So what I'm looking for is a formula that will weigh the possibly gain against the risk of actually making it to give some result that will, if followed out enough times to be statistically significant, yield profit. Basically a number that I know "if it's below this, don't bet, if it's above this, bet."

Thanks alot, hope this is more clear,
Jacob

P.S. Would it be as simple only betting when the value of Y/X is one?

 

Y doesn't represent the payout, the payout will only ever be $1 or nothing. Y is the likelihood that you will actually make the $1.