Related papers: Testing for dice control at craps
A variation on Janowski's cubeful equity model is proposed for cube handling in backgammon money games. Instead of approximating the cubeful take point as an interpolation between the dead and live cube limits, a new model is developed…
Two different controlling methods are proposed to stabilize unstable continuous-sliding states of a dry-friction oscillator. Both methods are based on a delayed-feedback mechanism well-known for stabilizing periodic orbits in deterministic…
We consider a class of zero-sum stopper vs. singular-controller games in which the controller can only act on a subset $d_0<d$ of the $d$ coordinates of a controlled diffusion. Due to the constraint on the control directions these games…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
When shuffling a deck of cards, one probably wants to make sure it is thoroughly shuffled. A way to do this is by sifting through the cards to ensure that no adjacent cards are the same number, because surely this is a poorly shuffled deck.…
Game dynamics structure (e.g., endogenous cycle motion) in human subjects game experiments can be predicted by game dynamics theory. However, whether the structure can be controlled by mechanism design to a desired goal is not known. Here,…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
This study applies complexity sciences to analyze the game of Padel. Data from 18 professional matches were collected, and the probability distributions of the total number of shots and the probability distribution of rallies' duration were…
Selecting the combination of security controls that will most effectively protect a system's assets is a difficult task. If the wrong controls are selected, the system may be left vulnerable to cyber-attacks that can impact the…
We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…
We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…
Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to…
Poker is a family of card games that includes many variations. We hypothesize that most poker games can be solved as a pattern matching problem, and propose creating a strong poker playing system based on a unified poker representation. Our…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
In the sport of cricket, the side that wins the toss and has the first choice to bat or bowl can have an unfair or a critical advantage. The issue has been discussed by International Cricket Council committees, as well as several cricket…