A366996 a(n) is the denominator of the expected end time of a game with three gamblers, one of which starts with capital n, the others with capital 1 each, conditional on the event that one of the two poor players wins.

1, 7, 41, 197, 7025, 68761, 1663251, 178945525, 132150155017, 16077043550231, 4833128874789907, 250487901809049775, 6590569678028479808009, 30288529373611329886681, 111694000110134843095617996833, 2161868815213291879136716036071, 7842015457241561891262053489240216057

Offset: 1

Author

Pontus von Brömssen, Oct 31 2023

Keywords

• nonn
• frac

Comments

In each round of the game, 1 unit is transferred from one randomly chosen player to another. Players play until they are out of money, so when the first player is out the other two continue to play. The winner is the player who ends up with all n+2 units of money.

See A366995 for references and programs.

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..53

Crossrefs

Cf. A366566 (A366995(n)/a(n) rounded to nearest integer), A366995 (numerators).