HardMarket Making & Games
The Red–Black Card Game
Jane StreetCitadel Securities
Cards from a shuffled standard 52-card deck are revealed one at a time. Your running total gains 1 for every black card. You may stop whenever you like and collect the running total (you may also stop immediately at $0). Playing optimally, what is this game worth?
Approach
Define the state by the cards remaining, not the cards seen.
At each state compare stopping now with the expected value of drawing one more.
Answer
Show the final answer
The answer is 2.62. Sign in free for the full worked solution and to check your own answer.
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