# B How do I go about calculating the expected profit/winning per play of this game

1. Nov 21, 2016

### hamza2095

I designed this game for my Data class but I'm having alot of trouble calculating the expected profit per play of this game. We have taken up examples involving lottery tickets in which you have to calculate the profit and winning per ticket bought but I can't seem to apply the same concepts to my game due to the various stages and rules.

This is how the games goes

You pay $20 to start and there are three rounds Round 1: There is a 1/2 chance you win and move on, and a 1/2 chance you lose Round 2: There is a 2/6 chance you move on to the next round, and 1/6 chance you win$10 AND move on. (3/6 chance you lose and get nothing)

Round 3: There is 1/12 chance you win $100, and if you lose you get nothing Here is my attempt at it After multiplying every correlating x and y value i get E(X) = -18.5, meaning the profit the ones running the game make is$18.5

Help is greatly appreciated!!!

2. Nov 21, 2016

### Staff: Mentor

He best way to check something like this is to run a Monte Carlo simulation with a million trials or so.

3. Nov 22, 2016

### FactChecker

It would help if you labeled the columns so that it is clear what series of results each represents. I am not sure what the 3'rd column ( -10, 1/12 ) represents. They should all be labeled so you can check that all the possibilities are accounted for exactly once.

4. Nov 22, 2016

### Stephen Tashi

You should do an analysis where the probabilities of the possible outcomes add up to 1.

List all the different experiences a player may have and the probability of each of those experiences. Those probabilities should add up to 1 if you have made a complete list.

5. Nov 22, 2016

### PeroK

There an obvious mistake, in that the probability of winning $100 should be twice that of winning$110. You have it as three times.

I also think you may be double counting the $10 win. It's better to keep the losses out of it. Just calculate the expected winnings per game. Then subtract this from the$20 stake.

6. Nov 22, 2016

### hamza2095

Thank you. I made a chart saying there is a (1/2)(1/6) = 1/12 chance to win $10, and that there is a (1/2)(3/6)(1/12) = 1/48 chance to win$100

after multiplying the prizes and subtracting the starting fees ($20) I got$-17.083333 per play.

7. Nov 22, 2016

### FactChecker

That's what I got also.