A387261 a(n) is the numerator of the winning probability of the starting player to reach n points first in the game "Risk or Safety", assuming optimal play.

2, 4, 6, 2236, 1026, 275848876, 649346842, 61550866190068, 2737872156886, 5556238701119487884, 33857036312840796476194, 3393041394611453189295265268, 218370486707916654640780231642, 112630244896738642814653528498087299988, 14364898791782224577113184680141626682

Offset: 1

Author

Ruediger Jehn, Aug 24 2025

Keywords

• nonn
• frac
• hard
• new

Comments

The total number of different strategies is given in A387260. See there for more information.

Examples

			a(2) = 4: 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

A387262 are the corresponding denominators.

Cf. A002411, A349697, A349698, A387260.

Extensions

More terms from Jinyuan Wang, Aug 29 2025