On card guessing game with one time riffle shuffle and complete feedback
نویسندگان
چکیده
This paper studies the game of guessing riffle-shuffled cards with complete feedback. A deck n labeled 1 to is once and placed on a table. player tries guess from top given feedback after each guess. The goal find strategy maximum reward (expected number correct guesses). We give optimal for this prove that expected n∕2+2∕π⋅n+O(1), partially solving an open problem Bayer Diaconis (Bayer Diaconis, 1992).
منابع مشابه
A Simple Card Guessing Game Revisited
A deck of cards consisting of m red and n black cards is given. A guess is made as to the colour of the top card, after which it is revealed and discarded. To maximise the number of correct guesses one chooses the colour corresponding to the majority of cards remaining in the deck. We determine the expected number of correct guesses with this strategy, as well as the probability of beating an o...
متن کاملNo-feedback Card Guessing for Dovetail Shuffles
We consider the following problem. A deck of 2n cards labeled consecutively from 1 on top to 2n on bottom is face down on the table. The deck is given k dovetail shuues and placed back on the table, face down. A guesser tries to guess at the cards one at a time, starting from top. The identity of the card guessed at is not revealed, nor is the guesser told whether a particular guess was correct...
متن کاملOptimal Guessing Strategies in a Quantum Card Game
Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know better than Alice does on guessing Alice’s card, no matter what Bob chooses to measure his two cards collectively or separately. We also find that Bob’s best st...
متن کامل2 Mixing of Riffle Shuffle via Strong Stationary Times
1.2 Relating the inverse and standard shuffles We now need to relate ∆(t) to ∆(t). We will do this by taking a more general view of shuffles. We will think of a shuffle as a random walk on the symmetric group Sn. The walk is defined by a set of generators G = {g1, . . . , gk} and a probability distribution P over G. (At each step of the walk, we pick a random gi according to P and apply gi to t...
متن کاملA Path Guessing Game with Wagering
We consider a two-player game in which the first player (the Guesser) tries to guess, edgeby-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of her guess, and receives a payoff proportional to her wager if she is correct. We derive optimal strategies for both players for various classes of graphs, and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2020.09.005