A096256 Decimal expansion of the probability of rolling a Yahtzee (5 of a kind) in the dice game Yahtzee.

0, 4, 6, 0, 2, 8, 6, 4, 2, 5, 2, 5, 6, 9, 8, 9, 9, 5, 7, 4, 9, 2, 9, 2, 9, 6, 0, 0, 8, 3, 9, 9, 8, 0, 3, 5, 5, 2, 9, 8, 1, 4, 2, 2, 2, 0, 8, 6, 7, 4, 1, 5, 1, 9, 7, 5, 4, 7, 7, 9, 9, 2, 8, 5, 3, 3, 9, 2, 9, 4, 4, 8, 4, 2, 4, 1, 9, 0, 0, 7, 9, 4, 2, 5, 5, 6, 1, 8, 2, 1, 5, 3, 8, 0, 4, 4, 6, 7, 4, 7, 6, 1, 6, 3, 8

Offset

0,2

Comments

Matt Hudelson's solution at the SMSU link demonstrates the use of a transition matrix to solve this type of problem. This probability is calculated for use of the "obviously best" strategy of directly trying to achieve five matched dice: If a second or third roll is necessary, roll again "keeping only one set of the largest number of matched dice" each time.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Hasbro, Yahtzee Instructions (pdf document), Milton Bradley Company, 1996.

Southwest Missouri State University Challenge Problem Archive, Yahtzee!.

Index entries for linear recurrences with constant coefficients, order 6561.

Formula

Equals 347897/7558272.

Example

0.046028642525698995749292960083998...

Mathematica

First[RealDigits[347897/7558272, 10, 100, -1]] (* Paolo Xausa, Jan 15 2025 *)

Prog

(PARI) 347897/7558272.

Crossrefs

Sequence in context: A203993 A204017 A021960 * A319091 A328227 A059750

Adjacent sequences: A096253 A096254 A096255 * A096257 A096258 A096259

Keyword

nonn,easy,cons

Author

Rick L. Shepherd, Jul 31 2004

Status

approved