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Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a…
In a competitive sport, every little thing matters. Yet, many sports leave some large levers out of the reach of the teams, and in the hands of fate. In cricket, world's second most popular sport by some measures, one such lever---the…
We study, in various special cases, total distributions on the product of a finite collection of finite probability spaces and, in particular, the question of when the probability distribution of each factor space is determined by the total…
We identify a new type of paradoxical behavior in dice, where the sum of independent rolls produces a deceptive sequence of dominance relations. We call these ``anti-inductive dice". Consider a game with two players and two non-identical…
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…
Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth $W_t$ quantifies the evidence against the null hypothesis after $t$ rounds, and the null…
A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to…
Controlling a dynamical system is the ability of changing its configuration arbitrarily through a suitable choice of inputs. It is a very well studied concept in control theory, with wide ranging applications in medicine, biology, social…
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…
Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an…
Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded…
Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation.…
A flourishing empirical literature investigates the prevalence of $p$-hacking based on the distribution of $p$-values across studies. Interpreting results in this literature requires a careful understanding of the power of methods for…
The standard paradigm for confirmatory clinical trials is to compare experimental treatments with a control, for example the standard of care or a placebo. However, it is not always the case that a suitable control exists. Efficient…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
A novel model for dynamical traps in intermittent human control is proposed. It describes probabilistic, step-wise transitions between two modes of a subject's behavior - active and passive phases in controlling an object's dynamics - using…
Dice odds in the board game RISK were first investigated by Tan, fixed by Osbourne, and extended by Blatt. We generalized dice odds further, varying the number of sides and the number of dice used in a single battle. We show that the…
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…
We introduce a compact probabilistic model for two-player and two-team (four-player) squash matches, along with a practical skill-comparison rule derived from point-scoring probabilities. Using recorded shot types and court locations, we…
Consistently checking the statistical significance of experimental results is one of the mandatory methodological steps to address the so-called "reproducibility crisis" in deep reinforcement learning. In this tutorial paper, we explain how…