# Your question: What are the expected earnings of a simple dice game?

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## What is the expected output of a dice?

When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5.

## How do you find the expected value of a dice?

The expected value of the random variable is (in some sense) its average value. You compute it by multiplying each value x of the random variable by the probability P(X=x), and then adding up the results. So the average sum of dice is: E(X) = 2 . 1/36 + 3 . 2/36 + ….

## 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!

## What is the expected value of two dice?

The expectation of the sum of two (independent) dice is the sum of expectations of each die, which is 3.5 + 3.5 = 7. Similarly, for N dice throws, the expectation of the sum should be N * 3.5. If you’re taking only the maximum value of the two dice throws, then your answer 4.47 is correct.

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## What is the expected value of rolling a dice if you could roll twice?

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 expectation of getting 5 on a roll of a dice?

Two (6-sided) dice roll probability table

Roll a… Probability
4 3/36 (8.333%)
5 4/36 (11.111%)
6 5/36 (13.889%)
7 6/36 (16.667%)

## How do you find the mean of rolling a dice?

To find the mean for a set of numbers, add the numbers together and divide by the number of numbers in the set. For example, if you roll two dice thirteen times and get 9, 4, 7, 6, 11, 9, 10, 7, 9, 7, 11, 5, and 4, add the numbers to produce a sum of 99.

## What is the probability distribution of rolling 2 dice?

Probabilities for the two dice

Total Number of combinations Probability
2 1 2.78%
3 2 5.56%
4 3 8.33%
5 4 11.11%