Related papers: The Hollyfeld Gambit in Astrophysics
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
A gambler walks into a hypothetical fair casino with a very real dollar bill, but by the time he leaves he's exchanged the dollar for a random amount of money. What is lost in the process? It may be that the gambler walks out at the end of…
The allocation of resources plays an important role in the completion of system objectives and tasks, especially in the presence of strategic adversaries. Optimal allocation strategies are becoming increasingly more complex, given that…
We investigate the most popular approaches to the problem of sports betting investment based on modern portfolio theory and the Kelly criterion. We define the problem setting, the formal investment strategies, and review their common…
We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state…
We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending string consists of at most four maximal runs of heads or…
There are at least two ways to interpret numerical degrees of belief in terms of betting: (1) you can offer to bet at the odds defined by the degrees of belief, or (2) you can judge that a strategy for taking advantage of such betting…
In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. \textbf{184} 661--670 (2013)] for making predictions instead of only performing a successful…
It is well known that in games with imperfect information, such as poker, bluffing with some probability can be a component of the optimal strategy. However, as far as we know, nobody has ever exhibited a Scrabble position in which the…
We introduce General Lotto games with Scouts: a General Lotto game with asymmetric information. There are two players, Red and Blue, who both allocate resources to a field. However, scouting capabilities afford Blue to gain information,…
The Colonel Blotto game, introduced by Borel in the 1920s, is often used for modeling various real-life settings, such as elections, lobbying, etc. The game is based on the allocation of limited resources by players to a set of fields. Each…
Consider a card guessing game with complete feedback in which a deck of $n$ cards ordered $1,\dots, n$ is riffle-shuffled once. With the goal to maximize the number of correct guesses, a player guesses cards from the top of the deck one at…
Heavy-tailed impact distributions, intrinsic uncertainty, and the high costs of proposal-based peer review increasingly challenge research funding decisions. Using large-scale bibliometric data, we show that past scientific performance…
Is flipping a coin a deterministic process or a random one? We do not allow bounces. If we know the initial velocity and the spin given to the coin, mechanics should predict the face it lands on. However, the coin toss has been everyone's…
The Labouchere gambling system is hypothesized to increase the probability of winning a predetermined arbitrary profit in a gambling system such as a coin flip or a roulette game in which both payouts and odds are 1:1. However, use of the…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
We consider a setting where in a known future time, a certain continuous random variable will be realized. There is a public prediction that gradually converges to its realized value, and an expert that has access to a more accurate…
Recent research has proposed the lottery ticket hypothesis, suggesting that for a deep neural network, there exist trainable sub-networks performing equally or better than the original model with commensurate training steps. While this…
Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not…
Parrondo's coin-tossing games comprise two games, $A$ and $B$. The result of game $A$ is determined by the toss of a fair coin. The result of game $B$ is determined by the toss of a $p_0$-coin if capital is a multiple of $r$, and by the…