# Game Theory

Mathematicians will tell you chess is a two-person zero-sum game. If I win, you lose. If you win, I lose. If you draw, I draw as well. It’s also a game of total information: we both have complete information about what is happening and the location of all the pieces.

It’s a reasonable assumption that if God played God (assuming God is omniscient and plays perfectly at all times) the game would be a draw, and therefore that there is no first move that will give White a winning advantage. In the eyes of God, any position is either a win for White, a win for Black, or a draw: for God there’s no ‘slight advantage’, ‘unclear’ or ‘with compensation’.

In the unlikely event that I find myself sitting opposite Magnus Carlsen in my next Thames Valley League match, God will tell me at the start of the game that I have a drawn position. At some point, probably sooner rather than later, She’ll tell me I have a lost position. This will happen as a result of one of my moves, not as a result of one of Magnus’s moves. The move that swings the game in his favour may be brilliant, spectacular, extremely subtle, or very hard to find, but it will be my mistake, not Magnus’s rejoinder, that decides the game. You see, in mathematical terms, there are no good moves in chess, only acceptable moves and bad moves. Early on in the game each of us will have a choice of some moves which retain the status quo and other moves that lead to a lost position. Once I play a move that tips the balance in Magnus’s favour I will only be able to choose different ways of losing, some more tenacious than others. Magnus, on the other hand, will have some (or all) moves that retain a winning position, some (or no) moves which will turn the game into a draw and some (or no) moves which lose the game.

So how should this affect the way we teach chess? I tell my pupils that I’m not like other teachers. Other teachers will teach you how to play good moves, but I’ll teach you how not to play bad moves. If you never play any bad moves you’ll never lose. Carlsen, Houdini and Stockfish will hold no terrors for you.

Regular readers will be aware that I’m sceptical of the value of demonstrating master games to young children. That, given the way young children process information, this approach will either have no effect or leave your audience confused. What I prefer to do is demonstrate a game in which a clear mistake was made and explain what the mistake was and how to avoid it. I will often use games played by the children themselves: children find it easier to relate to or take an interest in games played by themselves or their friends. You can’t do this with complete beginners who are still playing random moves, but once children understand the underlying logic of chess and can, at least in theory, play a game without making simple oversights, this approach can be very effective. This is one reason why we get children at Richmond Junior Club to record their games and hand in the scoresheets once they’ve reached the appropriate level.

More thoughts about mistakes at chess in a future article, quite possibly next week.

Richard James

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