1. There are 3 reels (like a normal slot machine that you would see in any casino)

2. There are 7 different symbols that you can make combinations with. (combinations of 3 symbols)

3. There are 21 combinations that you win money.

Combo # Payoff

1 2x

2 2x

3 2x

4 2x

5 2x

6 2x

7 2x

8 2x

9 2x

10 2x

11 2x

12 2x

13 2x

14 2x

15 3x

16 4x

17 5x

18 6x

19 7x

20 10x

21 15x

4. Assume that the probability of getting any combination is equal. Each combination is random and independent.

For example, if I put 1 coin into the machine, and I happen to get combo #16, I win 4 coins plus the 1 coin I bet. If I don’t get any of the combinations 1-21, I lose the 1 coin.

What I know how to do

Ok so, since there are 7 different symbols, and 3 different reels, that means there are a total of 343 (7*7*7) combinations. Since the probability of getting each combination is the same, it means that you have a 1/343 chance of getting any combination. This is as far as I know what to do. What are the expected wins/losses if I bet 1 coin? 2 coins? 3 coins?