Puzzle of the month

One hard problem a month, the same for everyone. No clock: take as long as you like until it closes at the end of 31 October 2026 (UTC). Get it right to go on the board; the worked solution is published when the month ends.

Puzzle #1 · October 2026

Games, decision theory and puzzlesExpert

A shuffled deck of $26$ red and $26$ black cards is turned over one card at a time. You win $\$1$ for each red and lose $\$1$ for each black, and you may stop whenever you like. What is the game worth with optimal stopping? Give a decimal to three places.

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly.

Solver board

Nobody has solved it yet.

In order of first right answer, timed from the month opening. Players show by name when their profile is public.

Past puzzles

This is the first. When a month closes, its puzzle moves here with its final board and the worked solution.