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

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• hamza2095
In summary: So the game is a pretty bad bet for the player.In summary, the conversation is about a game designed for a Data class, where the player pays $20 to start and has three rounds with varying chances of winning or losing. The expected profit per play is calculated to be$-17.083333 for the ones running the game, making it a poor bet for the player. The suggestion is made to run a Monte Carlo simulation with a million trials to check the accuracy and labeling the columns for clarity. There is also discussion about potential mistakes in the probabilities and the suggestion to only calculate the expected winnings per game and subtract it from the starting fee.
hamza2095
I designed this game for my Data class but I'm having a lot 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!

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

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.

hamza2095 said:
Here is my attempt at it

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.

hamza2095 said:
I designed this game for my Data class but I'm having a lot 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!

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.

PeroK said:
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.
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.

FactChecker
hamza2095 said:
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.
That's what I got also.

## 1. How do I calculate the expected profit/winning per play of a game?

The expected profit/winning per play of a game is calculated by multiplying the probability of winning by the amount won and subtracting the probability of losing by the amount lost. This can be expressed as (probability of winning x amount won) - (probability of losing x amount lost).

## 2. What is the importance of calculating the expected profit/winning per play?

Calculating the expected profit/winning per play is important because it allows you to make informed decisions about whether or not the game is worth playing. It helps you understand the potential risks and rewards associated with the game.

## 3. What factors should be considered when calculating the expected profit/winning per play?

The factors that should be considered when calculating the expected profit/winning per play include the probability of winning, the amount won, the probability of losing, and the amount lost. These factors can vary depending on the specific game being played.

## 4. Can the expected profit/winning per play change over time?

Yes, the expected profit/winning per play can change over time. This can happen if the odds of winning or losing change, or if the amount won or lost changes. It is important to regularly re-calculate the expected profit/winning per play to stay informed about the potential outcomes of the game.

## 5. How can I use the expected profit/winning per play to make strategic decisions?

The expected profit/winning per play can be used to make strategic decisions by comparing it to the cost of playing the game. If the expected profit/winning per play is higher than the cost of playing, it may be a good decision to play the game. However, if the expected profit/winning per play is lower than the cost of playing, it may be wiser to avoid the game.

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