-4
votes
0answers
33 views

What are the odds in the card game war that the game will start and finish on the first battle? [on hold]

What are the odds? My 6 year old daughter and I played war. On the first card we both played sevens and the battle bagan. We played three face down and one up and they matched again. Again, we ...
15
votes
6answers
1k views

Is a fair lottery possible?

I'm trying to come up with a scheme for a lottery where each individual has roughly the same chance of becoming the winner, regardless of the number of tickets one holds. So no individual should have ...
15
votes
1answer
429 views

The Chow & Robbins game ≈ 0.79295350640: improvements could come from simple statistics, or from a continuous version of the game

This question seeks help with improving a numerical estimate of the value of the Chow and Robbins game. Much about this game is unknown, such as whether its value is rational, but there are two routes ...
4
votes
1answer
539 views

Conditioning on one term of a sum of random variables

Let $\theta$ be normally distributed with mean $\bar \theta$ and variance $s^2$. Let $Z$ be normally distributed with mean $0$ and variance $\sigma^2$, and chosen independently of $\theta$. Define ...
1
vote
2answers
243 views

How to assign a score to items based on a set of partial rankings

I have the following setup: There is a collection of items I and a collection of partial rankings V. That is, an element of V is a total ordering on a subset of I. There is no expectation of ...