KöMaL 2023 B5323

We are playing the following game: arbitrary real numbers from the interval $[0, 100]$ are written on 2023 cards. Then the cards are dropped in an urn, and one card is pulled out at random. If the number on the card equals 2/3 of the mean of the numbers on all the cards then we will win as much money as the number on the card pulled out. Otherwise we do not win anything. What numbers should be written on the cards so that the expected value of the money gained is a maximum?