There is such a game with chips or cards. There are an even number of chips, and there are N different types of chips among them. Chips are randomly shuffled and divided equally between two players. The winner is the one with the most different types of chips. And we need to find the probability of a draw in the game, with a certain number of different chips.

For example:
black - 3;
white - 2;
red - 1;

Permutations:
rww vs bbb : probability - 1/10 (not draw)
rwb vs wbb : probability - 3/5 (not draw)
rbb vs wwb : prabability - 3/10 (DRAW!)

So we need to find out the number of permutations with a draw.
I'd be appreciated for any ideas. Thanks.

P.S. (the problem is practical)

The number of chips of the same color <= 10
The number of colors <= 50