Two dice question

That depends on the size of my initial bankroll,
and whether I have Cleopatra hanging on my arm.

Okay, now a serious answer:



No, because the expected pay-out each round is $3.50, which is less than $5.



That doesn't seem like an easy question, but we if agree the player will quit as soon as he's ahead on money, then I know the answer is > 0.5

The probability he wins on the first roll and quits is (1/6).
The probability he doesn't but wins on the second and quits is (5/6)(1/6).
The probability he loses twice, then wins and quits, is (5/6)^2*(1/6).
The probability he loses thrice, then wins and quits, is (5/6)^3*(1/6).

In each of those scenarios, he makes money.
They have a combined probability of about .51775.
There are other ways for him to make money, but after he loses 4 times it gets harder.

This part of the question got my dice rolling lyk two o's in Kolyo.

He wins 21 with one chance in six and loses 5 with each of five chances in six so the probability of making money is 21/46.