5 dice, 1 roll, 1 box

Fives dice, one roll, one box

 
5d1r1b

Okay. Suppose we have five dice and one roll. Only the Ones are taken into account. You can score 1, 2,3,4,5 depending on the number of Ones. What is the outcome of the game if we roll many times and calculate the average of the scores?

The probabilistic value = probabilistic value of rolling 1x1 + probabilistic value of rolling 2x1 + probabilistic value of rolling 3x1 + probabilistic value of rolling 4x1 + probabilistic value of rolling 5x1.

For the exact calculation you need some basic knowledge of combinatorics, thus the result is

0.4+0.16+0.032+0.0032+0.0001286 ≈ 0.59

Let’s stop for a moment here: we want to score Ones. What is the probability - having five dice - to score exactly 1x1, 2x1, 3x1, 4x1, 5x1?

 

Probability

1 x One

0.4

2 x One

0.16

3 x One

0.032

4 x One

0.0032

5 x One

0.0001286

!!! Please note that there is about 0.40 probability at one single roll that you don’t score any Ones or a given number with five dice in one roll!! So please keep this in mind when playing Yahtzee !!!

 

Probability

0 x One

0.4

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