Related papers: How to Gamble Against All Odds
We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…
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…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon…
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…
We consider games with two antagonistic players --- \'Elo\"ise (modelling a program) and Ab\'elard (modelling a byzantine environment) --- and a third, unpredictable and uncontrollable player, that we call Nature. Motivated by the fact that…
We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop…
In various situations, decision makers face experts that may provide conflicting advice. This advice may be in the form of probabilistic forecasts over critical future events. We consider a setting where the two forecasters provide their…
There have been several popular reports of various groups exploiting the deterministic nature of the game of roulette for profit. Moreover, through its history the inherent determinism in the game of roulette has attracted the attention of…
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin…
We study the problem of making predictions of an adversarially chosen high-dimensional state that are unbiased subject to an arbitrary collection of conditioning events, with the goal of tailoring these events to downstream decision makers.…
We introduce games with probabilistic uncertainty, a natural model for controller synthesis in which the controller observes the state of the system through imprecise sensors that provide correct information about the current state with a…
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…
We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
Sports betting's recent federal legalisation in the USA coincides with the golden age of machine learning. If bettors can leverage data to reliably predict the probability of an outcome, they can recognise when the bookmaker's odds are in…
A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players uses a finite set of ad hoc strategies to make their decision, based on the past record. The…
What would you do if you were invited to play a game where you were given \$25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61…