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# Two dice question

Sat 15 Apr, 2017 02:29 pm
There's a game where you are given two fair six-sided dice and asked to roll. If the sum of the values on the dice equals seven, then you win \$21. However, you must pay \$5 to play each time you roll both dice. Do you play this game?

And in follow-up:

What is the probability of making money from this game?
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Kolyo

1
Sun 16 Apr, 2017 05:53 pm
@thatmeow,
thatmeow wrote:

Do you play this game?

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

1
Sun 16 Apr, 2017 08:03 pm
@thatmeow,

thatmeow wrote:

Do you play this game?

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

Quote:

What is the probability of making money from this game?

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.
ekename

1
Sun 16 Apr, 2017 08:43 pm
@Kolyo,
Quote:
What is the probability of making money from this game?

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.

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