相关论文: Some people have all the luck
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…
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…
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
Humanity has been fascinated by the pursuit of fortune since time immemorial, and many successful outcomes benefit from strokes of luck. But success is subject to complexity, uncertainty, and change - and at times becoming increasingly…
Online gambling sites offer many different gambling games. In this work we analyse the gambling logs of numerous solely probability-based gambling games and extract the wager and odds distributions. We find that the log-normal distribution…
Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases…
Opportunities, such as access to education or family background, shape income inequality by influencing the chances of economic success. Unequal opportunities create uncertainty about whether success is merit- or luck-based. We examine how…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…
We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, we focus on Kelly optimization as a metric, optimizing the…
At a first glance lottery is a form of gambling, a game in which the chances of winning is extremely small. But upon a deeper look, considering that the Jackpot prize of lotteries is a result of the active participation of millions of…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
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…
We consider extensive form win-lose games over a complete binary-tree of depth $n$ where players act in an alternating manner. We study arguably the simplest random structure of payoffs over such games where 0/1 payoffs in the leafs are…
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…
In classic Kelly gambling, bets are chosen to maximize the expected log growth of wealth, under a known probability distribution. Breiman provides rigorous mathematical proofs that Kelly strategy maximizes the rate of asset growth…
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…
There has been much recent work on the revenue-raising properties of truthful mechanisms for selling goods to selfish bidders. Typically the revenue of a mechanism is compared against a benchmark (such as, the maximum revenue obtainable by…
No matter how much some gamblers occasionally win, as long as they continue to gamble, sooner or later they will lose more to the casino, which is the so-called long bet will lose. Our results demonstrate the counter-intuitive phenomenon,…