Combinatorial Poker

Logic Level 2

Alice and Bob are playing combinatorial poker.

A standard 52 card deck is spread face up on a table.

  1. Alice picks up any 5 cards from the table.
  2. Bob does the same.
  3. Alice trashes any number of cards. She then picks up the same number of cards from the table.
  4. Bob does the same. He is not allowed to pick cards from the trash in this phase.

The one with a better hand wins.

Who has a winning strategy assuming perfect play?

This problem assumes familiarity with the rankings of poker hands, but no other knowledge of the rules of poker. You can review the ideas from here or this problem
Perfect play ends in draw Alice Bob

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Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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1 solution

I found the following solution on puzzling.stackexchange :

Alice goes first and picks...

> 4 tens (and any 1 other card) preventing Bob from making the highest ranked hand the royal flush (A,K,Q,J,10 of the same suit)

Bob must...

> prevent her making a royal flush so he must pick 4 cards each of a different suit in the range Ace to Jack (eg 4 Aces) (and any 1 other card)

Alice can then...

> keep one of the tens and pick 9,8,7,6 of the same suit making a straight flush with 10 as the highest card.

To equal this Bob must...

> also make a straight flush with 10 as the highest card but Alice has already taken all the tens. Oh no Bob has lost.

There is a different variant of the question here

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