2
votes
1answer
51 views

Deriving statistical distributions from games

The normal distribution can be derived from basic principles and calculus The Normal Distribution: A derivation from basic principles. Are there other distributions that can be derived like this from ...
12
votes
3answers
551 views

Formula for picking time closest to (but after) target

Let's say you have an arbitrary length of time. You are playing a game in which you want to push a button during this time span after a light comes on. If you do so, you win ($+1$), if not, you lose ...
0
votes
0answers
57 views

Optimizing a population to maximize probability of achieving certain samples.

Preface: I'm reasonably comfortable with mathematics on the whole, but I don't know too terribly much about probability theory, or optimization. I play Magic: The Gathering, and am trying to apply a ...
0
votes
0answers
42 views

Extended Probabilities in Risk

I'm working on a paper furthering some research into probabilities in the RISK game. The paper my research is based from is Osborne's paper on the use of Markov Chains, ...
3
votes
2answers
109 views

probable squares in a square cake

There is a probability density function defined on the square [0,1]x[0,1]. The pdf is finite, i.e., the cumulative density is positive only for pieces with positive area. Now Alice and Bob play a ...
0
votes
1answer
60 views

Which distributions should be used to model the winning & 2nd bids in second price auctions?

With second price auction which distributions should I use to model the winning bids and 2nd bids (separately)? I'm thinking of using Gaussian. However for the winning bids r.v, it has to satisfy: $$ ...
2
votes
1answer
121 views

Nash equilibria in games with infinitely many strategies

As a simple example, suppose two players A and B play a game wherein each picks a positive integer, and if they both pick the same integer $N$ then B pays $f(N)$ dollars to A, for some given payoff ...
0
votes
2answers
216 views

Given a victory condition and a set strategy, what are the chances of winning on a given turn in a game of Magic: The Gathering?

Tl;DR: You have winning cards. To win, you must be able to play those cards, and have them in your hand. Your hand is randomly drawn. When might you win? How could find the answer to this (very ...
0
votes
1answer
225 views

Measuring Roulette sequence probability

Statistics has always been my weakest point in math, so please bear with me. I'm not asking how to win, just analyzing the game. Assuming an American Roulette with two zero slots, the greens, or ...