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    Market-Making & Betting Games · Interview Question

    Cards are revealed one at a time from a shuffled deck; you bet on the next card's color. What's your strategy and edge?

    How to answer

    Bet the majority color remaining: as cards are revealed the unseen deck becomes imbalanced, so betting the majority gives win prob > 0.5 whenever reds ≠ blacks. Greedily guessing every card this way yields ≈30.04 expected correct on 52 cards (versus 26 for blind 50/50). The edge comes entirely from conditioning on cards already seen — the same skill as updating on order flow.

    Key idea: Treating each card as an independent 50/50 flip — cards are drawn without replacement, so the remaining composition is known and exploitable (~30 expected correct, not 26).

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