Hearts: Answer to question 2

Q: Can all players tie at the end of a game? Show the scores if they can, or explain why not.

A: No.

Obviously, to have all players tie at the end of a game, the winner must end up with a score of more than 100, so all players pass 100 only on the last hand (which means that no one Shoots the Moon in that hand). Let's work out some possible scores at the end of the second last hand.

The largest multiple of 26 which is less than 400 is 390.

At the end of the second last hand, this total score of 390 must be shared out between the players so that all have an individual score of less than 100. Even if the others are all 99, one player must have a score of at least 93.

In the last hand, someone gets the Queen of Spades, scoring 13. Even if it is the player on 93 who scores 13, she jumps to 106. This cannot be matched by all three players on 99, as they have only the 13 points available between them (for the heart cards).

Note: There can be a 3 way tie for first on 103 (or less), with the last person languishing on 107.