Suppose you have only two rolls of dice. then your best strategy would be to take the first roll if its outcome is more than its expected value (ie 3.5) and to roll again if it is less. Hence the expected payoff of the game rolling twice is: 16(6+5+4)+123.5=4.25.

## What is the expected payout of the game?

Expected value is a measure of what you should expect to get per game in the long run. The **payoff of a game is the expected value of the game minus the cost**. If you expect to win about $2.20 on average if you play a game repeatedly and it costs only $2 to play, then the expected payoff is $0.20 per game.

## What’s the expected value of throwing a dice up to 3 times?

Hence, the expected payoff of three roll is **4.67**, which is the answer to our problem! Recursively, we can answer this question for n>3. Clearly, as n is getting larger, the expected return will converge to the maximum value which is 6.

## How do you calculate expectation?

The expected value of X is usually written as E(X) or m. So the expected value is the sum of: **[(each of the possible outcomes) ×** (the probability of the outcome occurring)]. In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.

## How do you calculate expected profit?

**Subtract the total cost from the gross income** to determine the expected profit. If your cost of goods sold is $200 for 100 pieces and your total expenses applied to that product are $400 for the month, then the overall cost of your item to you is $600.

## What is fair price of a game?

In general, a game’s fair **price is thought to be its expected value**. If the expected value is $3 , it’s fair to pay $3 to play. If the expected value is −$3 , it’s fair to “pay” −$3 to play—meaning they should pay you $3 to play. Notice that the expected value of paying the fair price is always $0 .