Odds of guessing suit from a deck of cards, with perfect memory While teaching my daughter why drawing to an inside straight is almost always a bad idea, we stumbled upon what I think is a far more difficult problem:
You have a standard 52-card deck with 4 suits and I ask you to guess the suit of the top card. The odds of guessing the correct suit are obviously 1 in 4. You then guess again, but the first card is not returned to the deck. You guess a suit other than the first drawn and the odds are 13/51, somewhat better than 1 in 4.
Continuing through the deck your odds continually change (never worse than 1 in 4, definitely 100% for the last card) what are your overall odds for any given draw over the course of 52 picks?
Can this be calculated? Or do you need to devise a strategy and write a computer program to determine the answer? Do these type of problems have a name?
Dad and to a much less extent daughter, await your thoughts!


overall odds for any given draw over the course of 52 picks

If I rephrased your question as "how much should you be willing to pay to play the game where I will show you $n$ cards out of 52 and if you guess the next remaining card then I give you a dollar" would an answer to this question be suitable?  Just to be clear, in this game you would have to pay up front before you see any cards (although you know the number $n$ beforehand), and you should be willing to pay up to a quarter when $n=0$ and up to a dollar when $n=52-1$.  This is not really an  answer, I just wanted to understand the question.
Alternatively, would you allow the player to see the $n$ cards (rather than just the number $n$) before deciding how much to pay?  Or on the other hand would you not even allow $n$ to be known, but you would require the player to decide how much to pay and then $n$ is chosen uniformly at random between 0 and 51 at the beginning of the game?
