Cards on the table
- Do you play Poker?
- Can’t say that I do.
- I find that strange.
- I have only 2Kb of memory.
- That is not a lot!
- Right! I forget what cards have been played.
- Then I have the game for you.
- As long as it is not a card game I am game.
- It is a card game, but of a different sort.
- Please explain.
- We will put all the cards on the table face up.
- I am beginning to like it already.
- You draw five cards. Any cards you like.
- To build a strong Poker hand?
- Then I will draw any five cards.
- And the best hand wins? I seem to have an advantage!
- Not so fast! Suits have equal value.
- So a flush of spade ties a flush of clubs?
- Correct.
- That is a bit sad.
- After both players have drawn five cards the first player, you, can discard any of his cards and draw from the table to again get five cards on his hand. The second player, me, can then do the same.
- I don’t see how I can win!
- But you can!
Problem source: Martin Gardner via WordPlay.
June 16th, 2010 at 2:02 am
You draw all four 10s and any other card.
Now I can’t draw anything better than a 9-high straight flush. However, I can’t prevent you getting a better straight flush. Proof: To draw at least two cards of each suit entails drawing at least 8 cards. But I may only draw 5 cards. Thus there is at least one suit in which I have not drawn more than one card. If I have drawn the ace or a face card in that suit, you can now win with a 10-high straight flush in that suit; otherwise you can win with a royal flush in that suit.
The most I can limit your final hand is by drawing four jacks and one other card. That prevents you from drawing a straight flush with a jack on your second turn, but you can still draw a 10-high straight flush.
In any case, because of your initial draw, each 10 is unavailable to me because it is either in your hand or among your discards. Therefore I cannot equal or better your hand.