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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 in practice.

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Pricing a game: EV, re-rolls and when to stop

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Jane Street, Citadel, Hudson River Trading

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A shuffled deck of 26 red and 26 black cards is turned over one card at a time. · QuantMax

A shuffled deck of 262626 red and 262626 black cards is turned over one card at a time. You win $1\$1$1 for each red and lose $1\$1$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.

More games, decision theory and puzzles questions

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.