# Tagged Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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:  ...
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### 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 ...