Mathematic-Online problems: Interactive Problem 1356: Yahtzee

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	Mathematics-Online problems:
	Interactive Problem 1356: Yahtzee

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The object of the game ``Yahtzee'' is to make as advantageous scoring combinations as possible by rolling five dice. There are, among others,

Three-of-a-kind (three dice showing the same face and two showing different ones), e.g.

$\includegraphics[width=0.5\textwidth]{TdM_08_A3_bild1.eps}$

$\includegraphics[width=0.5\textwidth]{TdM_08_A3_bild2.eps}$ .

What is the probability of a Three-of-a-kind and a Small Straight, respectively, in the very first roll?

Let us assume that you obtained the combination

$\includegraphics[clip, width=0.5\textwidth]{TdM_08_A3_bild3.eps}$ ,

which you would like to improve by another roll.

Determine the probability that you achieve

Assume that in each case of re-rolling the best possible choice is made among the dice.

Answer:

Probability of

a Three-of-a-kind:

a Small Straight:

$\left. \rule {0pt}{3.5ex} \right\}$ in one roll

Probability of

at least three identical faces:

at least four sequential faces:

$\left. \rule {0pt}{3.5ex} \right\}$ when re-rolling

(The results should be correct to four decimal places.)

automatically generated: 8/11/2017