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**11**

votes

**5**answers

3k views

### Guess a number with at most one wrong answer

Consider a game where one player picks an integer number between 1 and 1000 and
other has to guess it asking yes/no questions.
If the second player always gives correct answers than it's clear that ...

**49**

votes

**9**answers

7k views

### Does War have infinite expected length?

My question concerns the (completely deterministic) card game known as War, played by seven-year-olds everywhere, such as my son Horatio, and sometimes also by others, such as their fathers.
The ...

**19**

votes

**5**answers

574 views

### $n$-in-a-row game on $\mathbb{R}^2$

For integers $n$ such that $\:3< n\:$,$\:$ what is known about the following 2-player game:
Player_1 and Player_2 take turn choosing points on $\mathbb{R}^2$ that were not previously chosen, with ...

**16**

votes

**1**answer

628 views

### Paul Erdős: Determine or estimate the number of maximal triangle-free graphs on n vertices

Among the collections of the open problems of Paul Erdős on the website of
Professor Fan Chung, there is one called "number of triangle-free graphs".
...

**1**

vote

**0**answers

252 views

### What is known about multiplayer poker with flop?

I am interested in the following simplified version of poker.
Each player gets a card (for example, either A or B).
Then they bet knowing their own cards (for example, the pot initially has 1 euro, ...

**14**

votes

**5**answers

2k views

### Irreversible chess

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...

**7**

votes

**1**answer

222 views

### Optimum Tournament Strategy

Consider a symmetric N-player game in which all players partition one total unit of
energy among individual games. The probability of winning each game is simply proportional to the spent energy ...

**3**

votes

**1**answer

236 views

### Indeterminacy of long games

Hello, all,
Several months ago I sat in on a seminar on AD+, which was incredibly wonderful even though I could barely follow it at all. AD+ is a technical variant of AD, the axiom of determinacy, ...

**2**

votes

**1**answer

96 views

### How to find equilibrium of the following game?

I'm looking at the following game:
2 symmetric players $\{A,B\}$, each choose a number $x_a,x_b\in [0,1]$.
The utility of player $A$ is:
$$U_A = \
\begin{cases} p\cdot x_a &\mbox{if } x_a> ...