# Expected Wins/losses of slot machine

#### godlinx21

##### New Member
Hi guys, I need this for homework. Basically there’s a slot machine and I need to figure out the expected win/loss. Here’s what you need to know:

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?

#### Rounds

##### New Member
Hint: Expectation is not an english word. It is not like having a conversation where we talk about what we expect to happen. Expectation is a term for a very specific mathematical result.

Essentially your issue here is you do not actually know what you are being asked to calculate. If you knew exactly what it meant to calculate expectation, with the set up you have done, you would be home free.

So the question you need to ask yourself is what in carnations does it mean to calculate the expectation?

#### dmmarathe

##### New Member
calculating expectation

My Dear, Since probability of winning is 1/343 , you will win 4 for every \$1 betted 7 win -1 if you lose. Hence for every dollar bet
Expected value= 1/343 *4 + 342/343 *(-1) = -338/343 .
The expected value is independent of money betted.

#### godlinx21

##### New Member
When did I use the word expectation?