Winning with a worse deck

Discrete Mathematics Level 5

You and a friend are playing poker together. After soundly defeating your friend for several rounds in a row, you offer your friend the following handicap:

You will play with part of a standard poker deck consisting of only the cards 2 through 6 (20 cards), while your friend will play with the remaining cards (32 cards). You will play a game of poker in which each player is dealt 5 cards and there is no 'discard and replace' phase. The normal rules for poker hand superiority apply.

If the probability that you win a round of this version of poker is \(P\), then what is \(\lfloor1000P\rfloor\)?

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Andy Hayes by Andy Hayes
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