MathDB

Two players in turn play a game. First Player has cards with numbers

2, 4, \ldots, 2000

while Second Player has cards with numbers

1, 3, \ldots, 2001

. In each his turn, a player chooses one of his cards and puts it on a table; the opponent sees it and puts his card next to the first one. Player, who put the card with a larger number, scores 1 point. Then both cards are discarded. First Player starts. After

1000

turns the game is over; First Player has used all his cards and Second Player used all but one. What are the maximal scores, that players could guarantee for themselves, no matter how the opponent would play?

Problem Statement