I was so convinced that the "correct" answers to this excellent question were wrong that I took out a deck of cards to prove it. Then I realised that I was changing one of the rules. So here's the alternate version with Bob's rules:
Alice and Bob are going to have a poker night. They have invented a variant where there are no secrets, and no randomness, called Face-Up Poker. Today, however, the table is full of work and so they're playing on the floor Here's how it works.
A standard 52 card deck is spread face up on the floor.
- Alice picks up any 5 cards from the floor. Bob does the same.
- Alice discards any number of cards, throwing them on the floor. She then picks up the same number of cards from the floor.
- Bob does the same. (He can pick up cards Alice discarded. This is the difference from the other question.)
- They then compare hands, and the best hand wins, with Bob winning ties.
Which player can force a win? What is their winning strategy?
This puzzle assumes familiarity with the rankings of poker hands, but no other knowledge of the rules of poker. For a refresher these rankings, see this helpful page (the hands are listed worst to best from top to bottom).