Minimax Card Number Assignment

You have 100 cards and must assign each card a number from 1 to 5. Once you have fixed your assignment, an opponent draws a card uniformly at random and guesses the number written on it. If the guess is correct, you pay the opponent an amount equal to that number; if the guess is wrong, you pay nothing. The opponent knows your full distribution (i.e., how many cards carry each number) and will choose whichever guess maximizes their expected payoff. How should you distribute the numbers across the 100 cards to minimize your expected loss? What is the resulting expected loss per draw?