A player draws the cards from the a 52-card deck one by one, without putting them back in the deck.
Every time before drawing a card he guesses the suit of the card he will draw.
He decides to always guess the suit that occurs most frequently in the remaining deck (if there are
several such suits, he chooses any one of them).
Prove that he will guess the right suit at least 13
(In reply to simulation
My 3 remarks:
1. Gauss would be happy to see the results you've displayed.
2. As we see, it is an excellent bet that the solver will get 16 or
more correct guesses.
3. It would be interesting to find out, what is the average number of "hits" if one is using a random guessing (i.e. ignoring the correct data)-my guess is 13 or slightly lower.