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## What is the expected value of rolling 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.

## How much would you pay if you were allowed to roll twice and take the higher of the two?

If you can reroll twice, then on the first roll, you should stop only if you roll a value higher than the expected value of the two remaining rolls, which we found above to be 4.25. so you would pay a **maximum of $4.66**.

## How do you find the expected value?

In statistics and probability analysis, the expected value is **calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values**. By calculating expected values, investors can choose the scenario most likely to give the desired outcome.

## How do you calculate expectation?

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens: **(P(x) * n)**. The formula changes slightly according to what kinds of events are happening.

## What is the expected value of the roll of a 12 sided die?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

9 | 30/36 (83.333%) |

10 | 33/36 (91.667%) |

11 | 35/36 (97.222%) |

12 | 36/36 (100%) |

## What is the expected value when rolling a fair 12 sided die?

If you are trying to maximise the expected score, then since the expected value of the 12-sided die is **6.5**, it makes sense to stop when the 8-sided die shows greater than 6.5, i.e. when it shows 7 or 8, each with probability 18.

## What is the probability of 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% |

## 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!