Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2020-06-23 11:25:13

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 63

### The Hexapawn Algorithm

Hexapawn is a 3x3 variant of chess which was designed by Martin Gardner. Each side has 3 pawns.

Martin Gardner included with the directions how to make a matchbox computer that will learn to play a perfect game. The basic algorithm is:

1. Play a game with a human using the steps below:
a. The human plays a move and takes the matchbox that has his move printed on it.
b. There will be several beads in the box. The human will take a random bead and move the pawn according
to the corresponding move.
c. Repeat with the matchboxes that corresponds to every move
-If the computer wins then put the beads back in the box
-If the computer loses then take the beads out.
2. Keep repeating this, and after some time, the computer will be able to play a perfect game.

The theory behind this is that the computer will "learn" to play a perfect game by eliminating all the possibilities that lead to a loss. This algorithm would not work for things like categorizing images or identifying human faces, but it did work for AlphaZero and AlphaGo, which learned to play the complex games of chess and go by just playing games against itself and learning from its mistakes.

e to the i pi plus 1 is zero -Leonhard Euler | a squared plus b squared equals c squared -Pythagoras | Energy equals mass times the speed of light squared -Albert Einstein | i² = -1 | x^2+1=0 x^2=-1 x=i

Offline

## #2 2020-07-03 01:48:59

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,956
Website

### Re: The Hexapawn Algorithm

What is a matchbox computer?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #3 2020-07-03 02:23:50

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 63

### Re: The Hexapawn Algorithm

Agnishom wrote:

What is a matchbox computer?

pi_cubed wrote:

e to the i pi plus 1 is zero -Leonhard Euler | a squared plus b squared equals c squared -Pythagoras | Energy equals mass times the speed of light squared -Albert Einstein | i² = -1 | x^2+1=0 x^2=-1 x=i

Offline