相关论文: Tackling the 6/49 Lottery and Debunking Common Myt…

Despite its unusual payout structure, the Canadian 6/49 Lotto is one of the few government sponsored lotteries that has the potential for a favorable strategy we call "buying the pot." By buying the pot we mean that a syndicate buys each…

Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that…

We prove an interesting fact about Lottery: the winning 6 numbers (out of 49) in the game of the Lottery contain two consecutive numbers with a surprisingly high probability (almost 50%).

Lottery is a game in which multiple players take chances in the hope of getting some rewards in cash or kind. In addition, from the time of the early civilizations, lottery has also been considered as an apposite method to allocate scarce…

We use mathematical statistics theory to derive the Compound-Dirichlet-Multinomial (CDM) prediction model. We then use this model to predict winning numbers for the 6-number, 5-number, pick-4 and pick-3 lottery games. We also develop a…

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…

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…

A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been recentlyintroduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain…

Stefan Mandel is said to have won the lottery 14 times. He never disclosed the recipe he called combinatorial condensation, which enabled him to hit the Romanian lottery jackpot in the early phase of his betting career. Combinatorial…

Apportionment is the problem of distributing $h$ indivisible seats across states in proportion to the states' populations. In the context of the US House of Representatives, this problem has a rich history and is a prime example of…

Consumers often face products sold as lotteries rather than fixed outcomes. A prominent case is the loot box in video games, where players pay for randomized rewards. We investigate how presentation formats shape consumer beliefs and…

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

We report a new result on lotteries --- that a well-funded syndicate has a purely mechanical strategy to achieve expected returns of 10\% to 25\% in an equiprobable lottery with no take and no carryover pool. We prove that an optimal…

Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…

We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…

We study a game puzzle that has enjoyed recent popularity among mathematicians, computer scientist, coding theorists and even the mass press. In the game, $n$ players are fitted with randomly assigned colored hats. Individual players can…

There have been long-standing controversies and inconsistencies over the experiment setup and criteria for identifying the "winning ticket" in literature. To reconcile such, we revisit the definition of lottery ticket hypothesis, with…

We introduce a generalization to the lottery ticket hypothesis in which the notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of parameters. We present evidence that the original results reported for the canonical…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost…