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

1,1

Comments

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

Links

Table of n, a(n) for n=1..15.

Rüdiger Jehn, Optimal strategy in the game Risk or Safety, arXiv:2603.01002 [math.CO], 2026. See p. 10.

Example

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, A394776.

Sequence in context: A033319 A185151 A218087 * A090315 A083753 A170807

Adjacent sequences: A387258 A387259 A387260 * A387262 A387263 A387264

Keyword

nonn,frac,hard

Author

Ruediger Jehn, Aug 24 2025

Extensions

More terms from Jinyuan Wang, Aug 29 2025

Status

approved