Related papers: Comparing dealing methods with repeating cards
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear…
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.
We consider a novel setting where a set of items are matched to the same set of agents repeatedly over multiple rounds. Each agent gets exactly one item per round, which brings interesting challenges to finding efficient and/or fair {\em…
In the compulsive gambler process there is a finite set of agents who meet pairwise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the…
We construct a diffusion approximation of a repeated game in which agents make bets on outcomes of i.i.d. random vectors and their strategies are close to an asymptotically optimal strategy. This model can be interpreted as trading in an…
We study the following repeated non-atomic routing game. In every round, nature chooses a state in an i.i.d. manner according to a publicly known distribution, which influences link latency functions. The system planner makes private route…
In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…
This paper studies a sequential decision problem where payoff distributions are known and where the riskiness of payoffs matters. Equivalently, it studies sequential choice from a repeated set of independent lotteries. The decision-maker is…
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…
We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for $n$-sided dice with pairwise ordering induced by the probability, relative to $1/2$, that a throw from one die is…
We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a random walk on the symmetric…
This paper is about the following question: How many riffle shuffles mix a deck of card for games such as blackjack and bridge? An object that comes up in answering this question is the descent polynomial associated with pairs of decks,…
The strategies adopted by individuals to select relevant information to pass on are central to understanding problem solving by groups. Here we use agent-based simulations to revisit a cooperative problem-solving scenario where the task is…
Single-elimination tournaments are the standard paradigm both for the main tennis professional associations. Schedules are generated by allocating first seeded and then unseeded players with seeds prevented from encountering each other…
Alice and Bob take turns (with Alice playing first) in declaring numbers from the set $[1,2N]$. If a player declares a number that was previously declared, that player looses and the other player wins. If all numbers are declared without…
In a well-shuffled deck of cards, what is the probability that somewhere in the deck there are adjacent cards of the same rank? What is the average number of adjacent matches? What is the probability distribution for the number of matches?…
Repetition-based draw rules in deterministic games like chess ensure termination but introduce strategic artifacts, allowing players to enforce draws independent of positional value. We propose an asymmetric modification: threefold…
We consider iterative voting models and position them within the general framework of acyclic games and game forms. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of…
We consider a card guessing strategy for a stack of cards with two different types of cards, say $m_1$ cards of type red (heart or diamond) and $m_2$ cards of type black (clubs or spades). Given a deck of $M=m_1+m_2$ cards, we propose a…