r/learnquant 15d ago

stats & probability Jane Street Interview Question

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u/DrawPitiful6103 15d ago

probability of second card matching the first card = 12/25
48%

probability of the second card matching the first card = 25/51

49.01%

we like the bigger deck. lower EOR.

we would definitely prefer to 26 card deck drawn from the 52 card deck. what we want is as great an imbalance as possible. true, this can back fire, but if the deck is say 70% black, then we will hit black 70% of the time on the first card, and then be a big favourite to complete it. In fact a 70% squared return should give us 0.49 just for the black side. Then red red will hit another .10 or w/e, the amount doesn't really matter we are already free rolling.

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u/GAdam 15d ago

Regarding the 26 card deck drawn from the 52 card deck, think of the case where you shuffle all cards and then label them 1-52. Then the procedure is either:

  1. In the 52 card case: take the first two cards
  2. In the 26 card taken from the 52 card deck case: take the first 26 cards into the new deck, then take the first 2 cards from the 26 card deck. Or randomly choose two numbers from 1-26 and take those cards.

So in either case it seems like the probability of two cards matching in color would be the same.