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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!

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    The reasoning on the second guess applies to the third and fourth guess too. If you've drawn $n$ cards with $n<4$ then then some suit still has all $13$ cards in the deck, and you would guess such a suit. So then the chance of a successful guess would be $\frac{13}{52-n}$.2012-01-03
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    Do you mean: As a function of $n$, what is the probability of guessing right on draw $n$, averaged over all $52!$ permutations of the deck, assuming that you guess intelligently based on complete knowledge of the first $n-1$ draws?2012-01-03
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    I considered a very similar question years ago but then I was stuck in its investigation because of my weak techniques. But now, after the deal with complex recurrent sums for a bounty question and the search of a material about semiinvariants for Phani Raj, I noticed such a strategy in a problem from one Russian math olympiad. So I remembered the old problem and felt a power to continue my investigation. :-) And just now, when I already wrote [my results](http://math.stackexchange.com/questions/614468/an-extrasensory-perception-strategy), I found your question.2013-12-21

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