##Tic-Tac-Toe console game

This is my implementation of the well-know game. You can specify the size of the grid and choose to play "reverse" Tic-Tac-Toe in which you lose if you get three-in-a-row.

To implement the game I used TTTBoard class skeleton (only class methods and their description was provided, I had to write all the logic) from Principle of Computing Coursera course.

The interesting bit was to implement the Machine Player, which was the homework for the above mentioned course.

The machine player will use a Monte Carlo simulation to choose the next move from a given Tic-Tac-Toe position.

An outline of the simulation:

1. Start with the current board.
2. Repeat for the desired number of trials:
3. Play an entire game by just randomly choosing a move for each player.
4. Score the resulting board.
5. Add the scores to a running total across all trials.
6. To select a move, randomly choose one of the empty squares on the board that has the maximum score.

2.ii in more detail

Scores are kept for each square on the board. The way you assign a score to a square depends on who won the game. If the game was a tie, then all squares should receive a score of 0, since that game will not help you determine a winning strategy. If you won the game, each square that matches your player should get a positive score (corresponding MCMATCH in the template) and each square that matches the other player should get a negative score (corresponding to -MCOTHER in the template). Conversely, if you lost the game, each square that matches your player should get a negative score (-MCMATCH) and and each square that matches the other player should get a positive score (MCOTHER). All empty squares should get a score of 0.

In Monte Carlo methods, you perform a bunch of random trials in order to figure out the expectation that some event, or multiple events, will actually occur.

Why would you do that? Well, usually you do this in situations where it is difficult or impossible to directly compute the answer, or perhaps directly computing the answer would take far too long.

Why is this called the Monte Carlo methods? Well, it's, because of the similarity to going to a casino and basically playing and recording the result of a bunch of, of gambling games, and in that situation you're basically randomly sampling,the probabilities of winning and losing those games. And perhaps such casinos appear in Monte Carlo.

In the real world what kind of of situations do we use this in? Generally Monte Carlo methods are used for you know, sort of physical or mathematical problems and the the major classes of problems are optimisation problems, figuring out probability, distributions and numerical integration.