Tic Tac Toe - A Deterministic Game

A Deterministic Game

What is a deterministic game?
A deterministic game is a game where the outcome of the game can be determined right from the start of the game. That means, there is a strategy that a player can use to obtain an outcome favourable to him (however it does not always mean he will end up in a win).

In the example of Tic-Tac-Toe:

We can find a strategy for the player who starts first to either win or draw (which means the worst outcome is a draw for him, but he will never lose if he use this strategy).

For many of you, you might know that the strategy is to always placed at the corner, but how do we explain this?

You can draw a game tree to find all the possible game plays between 2 player.

Please view http://en.wikipedia.org/wiki/Tic-Tac-Toe for the first 2 step of the game tree and continue from there.

Or you can view the explanation at

http://www.chessandpoker.com/tic_tac_toe_strategy.html

http://www.wikihow.com/Win-at-Tic-Tac-Toe

Just for interest, these are the variation of Tic Tac Toe

3D tic tac toe

What is a Game?

It sounds dumb, but not a lot of people know the proper idea of a game or have misconception of how a game should be.

A game is an event played by 2 or more players. A "game" with only 1 player is strictly speaking not a game, it could be just a puzzle.

Some definitions which you should know:

A turn:
A turn of a player is when the player needs to make a move. Most games have players alternating turns, but it might not be for some. Occassionally, when it is a player's turn, he/she cannot make a move and the turn is pass to the other player.

Outcome:
The most straight forward outcomes of a game is win, lose or draw, which is determine by the rules of the game. Sometimes, an outcome requires a numerical value, i.e. a score 6 - 5 or player A wins player B by 5 points etc.

Misconception: A game need not have to have a clear winner, i.e. Player A wins. An outcome when both player win is possible, this is what we call a win-win situation (this does not mean a draw) .

Other important concepts of a game are whether a game
i) is deterministic
ii) involves probability

These concepts will be explored when we talk about some simple games.