我国某地区居民购买六合彩活动信息的统计分析

本文主要应用统计学方法对由问卷调查所获得的我国某地区居民购买地下六合彩活动的信息进行分析,分别对购买者的结构,经济状况及收益进行分析,指出地下六合彩的本质及这一现象给我们的警示.同时通过分析一个消费者个体的消费模型给出消费者如何理性消费的建议.     

“Drawings since hit tables in lotteries” and a new multivariate geometric distribution

In number lotteries people choose r numbers out of s. Weekly published “drawings since hit tables” indicate how many drawings have taken place since each of the s numbers was last selected as a winning number. Among many lotto players, they enhance the widespread belief that numbers should be “due” if they have not come up for a long time. Under the assumptions of independence of the drawings and equiprobability of all possible combinations, the random s-vectors Y_n, n 1, of entries in a drawings since hit table after n drawings form a Markov chain. The limit distribution of Y_n as n → ∞ is a new multivariate generalization of the geometric distribution. The determination of the distribution of the maximum entry in a drawings since hit table within the first n draws of a lottery seems to be an open problem.     

Should European gamblers play lotto in the USA?

Any jackpot building game is designed to have a negative expected return for the gambler, but it can be profitable under certain circumstances. Previous studies have shown that the purchase of a single ticket of US-American state lotteries is sometimes a gamble with a positive expected value. Lottery winnings are not taxed in Europe, which suggests that the profitability of European games may be even higher. We present an exact formula for the calculation of the expected value of a single lotto ticket and find European lottery drawings to be far less profitable for the gambler compared to the US-American lotto market. Those US lotteries that generate profitable drawings are not characterized by higher redistribution rates or by their specific rules, but by the purchasing behavior of the gamblers. These gamblers buy far fewer tickets (per capita) and they barely react to increasing jackpots, even though the jackpots are large enough to cause positive expected winnings.     

A note on a symmetrical set covering problem: The lottery problem

In a lottery, n numbers are drawn from a set of m numbers. On a lottery ticket we fill out n numbers. Consider the following problem: what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers? We provide a set-covering formulation for this problem and characterize its LP solution. The existence of many symmetrical alternative solutions, makes this a very difficult problem to solve, as our computational results indicate.     

Discriminatory power and pure strategy Nash equilibrium in the lottery Blotto game

This paper highlights the role of discriminatory power in showing the existence of pure strategy Nash equilibrium in a two-player lottery Blotto game. Precisely, when the discriminatory power of the contest success function in every battle is less than or equal to one, a pure strategy Nash equilibrium always exists for any prizes and budgets. However, we construct examples in which pure strategy Nash equilibrium fails to exist as long as the discriminatory power of only one battle exceeds one.     

Some remarks on indestructibility and Hamkins’ lottery preparation

In this paper, we first prove several general theorems about strongness, supercompactness, and indestructibility, along the way giving some new applications of Hamkins lottery preparation forcing to indestructibility. We then show that it is consistent, relative to the existence of cardinals < so that is supercompact and is inaccessible, for the least strongly compact cardinal to be the least strong cardinal and to have its strongness, but not its strong compactness, indestructible under -strategically closed forcing. Mathematics Subject Classification (2000):03E35, 03E55     

基于非平稳性度量的彩票数据实证分析

非平稳性度量是衡量时间序列平稳程度的方法.利用非平稳度量,给出了C检验,并结合非平稳性度量值,对我国体彩"排列五"、"七星彩"及美国亚利桑那州的博彩"Pick3"的历史数据进行分析,发现博彩各数位上整数"0~9"出现都拥有稳定的概率,但并不是以等概率1/10出现,其分布与i.i.d均匀分布稍有差异,其中"七星彩"均匀性最好,"Pick3"的均匀性次之,"排列五"均匀性稍差.