# Can anybody explain this extremely basic doubt in Combinatorial Game theory

I have a very basic doubt in Combinatorial Game theory. Whenever I am asked to find a strategy for somebody to win a game or to get the maximum sum or anything as such, what am I exactly supposed to do?

I am asking this because in any question there exist a lot of possibilities for the game to proceed. Moreover, there might exist circumstances in the game when even when the prescribed player does not follow the suggested strategy, he wins.

So what exactly am I supposed to do when I am asked to find a strategy?

PS: This might sound as a very basic doubt, but I am having a lot of difficulty with such questions where I need to find the strategies

• I really think this is too broad. There are a lot of combinatorial games and it can be extremely difficult to sort out strategies (forget Chess, even Checkers is very, very complicated). Best is to go through a lot of the basic cases, like Nim or its many variants. Work by analogy where possible. – lulu Dec 28 '18 at 11:43
• my most basic question is basically define 'strategy' – saisanjeev Dec 28 '18 at 11:45
• An algorithm that dictates a player's move in any possible situation. – lulu Dec 28 '18 at 11:48

For this last, consider chess. A perfect player might never play $$1. e4$$ as white, and may never respond $$1. ... e5$$ as black to this move by white, but a human being using a computer to analyse positions, may well want to analyse positions arising after these moves have been played, even though the computer does not need to play such positions itself.