No Feedback Card Guessing for Top to Random Shuffles

Details No Feedback Card Guessing for Top to Random Shuffles No Feedback Card Guessing for Top to Random Shuffles

2010-06-07

arxiv.org/abs/1006.1321v1

Mathematics

Probability

17 pages

Scientific paper

Consider n cards that are labeled 1 through n with n an even integer. The cards are put face down and their ordering starts with card labeled 1 on top through card labeled n at the bottom. The cards are top to random shuffled m times and placed face down on the table. Starting from the top the cards are guessed without feedback (i.e. whether the guess was correct or false and what the guessed card was) one at a time. For m > 4nlog n+cn we find a guessing strategy that maximizes the expected number of correct guesses.

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