Suppose on a board you have several stacks each containing several sticks. You and your opponent are picking up sticks, one stack at a time in a turn. One who finishes the board is the winner.
This is known as the Game Of Nim. It is a solved game. At any position you may calculate out the best move.
Suppose you have 3 stacks containing 3, 4 and 5 sticks. To find the best move we need the concept of Nim Sum of 3, 4 and 5 and the strategy is to take out sticks from a stack to make the next Nim Sum 0.
To find the Nim Sum we need to convert 3, 4 and 5 to their binary expressions and find their Nim Sum which is their original binary sum while setting the only rule 1+1 = 0.
3 = 011
4 = 100
5 = 101
Nim Sum = 010
Now if we take out 2 sticks from the first stack then there Nim Sum becomes 0.
1 = 001
4 = 100
5 = 101
Nim Sum = 000
We have mathematical proofs showing if Nim Sum of stacks is non-zero we may turn it to zero by taking out sticks from a stack and if Nim Sum is zero then whatever one does with the stacks the Nim Sum becomes non-zero.
Variants of Nim have been played since ancient times. The game is said to have originated in China—it closely resembles the Chinese game of "picking stones" but the origin is uncertain. The earliest European references to Nim are from the beginning of the 16th century. Its current name was coined by Charles L. Bouton of Harvard University, who also developed the complete theory of the game in 1901, but the origins of the name were never fully explained.
At the 1940 New York World's Fair Westinghouse displayed a machine, the Nimatron, that played Nim. From May 11, 1940, to October 27, 1940, only a few people were able to beat the machine in that six-week period; if they did, they were presented with a coin that said Nim Champ. It was also one of the first-ever electronic computerized games. Ferranti built a Nim playing computer which was displayed at the Festival of Britain in 1951. In 1952 Herbert Koppel, Eugene Grant and Howard Bailer, engineers from the W. L. Maxon Corporation, developed a machine weighing 23 kilograms (50 lb) which played Nim against a human opponent and regularly won. A Nim Playing Machine has been described made from TinkerToy.
The game of Nim was the subject of Martin Gardner's February 1958 Mathematical Games column in Scientific American. A version of Nim is played—and has symbolic importance—in the French New Wave film Last Year at Marienbad (1961).
QUESTION I: Could we have the proofs of the Theorems mentioned above?QUESTION II: Has Alpha Zero solved the game of chess?REFERENCE: Wikipedia, Play to Win with Nim Article