A387262 a(n) is the denominator of the winning probability of the starting player to reach n points first in the game "Risk or Safety", assuming optimal play.

3, 7, 11, 4165, 1925, 521145625, 1231278125, 117192622421875, 5225432428125, 10634368774326171875, 64913928515324560546875, 6519012951936493553466796875, 420117998909827688127861328125, 217038092253876925088545128021240234375, 27711032758513212360715995025634765625

Offset: 1

Author

Ruediger Jehn, Aug 24 2025

Keywords

• nonn
• frac
• hard
• new

Comments

For more details see A387260 and A387261.

Examples

			a(2) = 7: For n=2, the optimal strategy is never to stop, but always try to get two consecutive heads. The winning probability is 1/4*(1 + (3/4)^2 + (3/4)^4 + ...) = 4/7.
		

Crossrefs

A387261 are the corresponding numerators.

Cf. A002411, A349697, A349698, A387260.

Extensions

More terms from Jinyuan Wang, Aug 29 2025