An introduction to the game

The game consists of a set of numbers in neutral territory (yellow area in the center of board).  In the game, the numbers are represented as bags of money (the central theme of the interface). You and the computer take turns choosing numbers. 

If you choose a number, you get the number of points equivilant to that number.  Your opponent (the Taxman) gets the factors of that number. When the Taxman chooses, you get the factors of his choice. Numbers that are chosen go to each player's respective side of the board.  The factors "fly" to the opponent's side of the board.

Whoever has the most points (chosen numbers plus factors) after the last number is chosen, wins.

On the right is the Taxman's side of the board, and you can see his score. 

In the middle is the neutral territory where you can see the quantity of number left in the game

The number will move to your side of the board and the factors will move to the Taxman's side of the board. 

You must then wait while the Taxman makes his choice.

The checkbox sets the person who goes first.  If you want to go first, make sure this checkbox has a check when you press New Game.

The New Game button starts a new game.  The board is refreshed and any options changes take effect.  You may start a new game in the middle of the Taxman's search without causing any harm.  The search will simply stop.

The Options button brings up the game options.  You may view and change the game options at any time; however, option changes do not take effect until the next new game.

The upper bar shows the current difference in scores.  If you are winning, the bar extends toward your side of the board and the number is negative (Taxman is loosing).

The lower bar shows the score difference that the Taxman forsees in the future.  Again, if the bar extends toward your side, you should be winning in the future.  If it extends toward the Taxman, then there is a good chance you will loose (but comebacks are possible). 

The number of moves ahead the Taxman looks before choosing a number is determined in the options.

The other statistics are related to the search technique used.  The program uses the well-known minimax algorithm to find the optimal move at a given depth.   You don't need to know what the statistics mean to play the game, but here is what they represent if you are curious:

	Max Depth displays the maximum levels (look-ahead) the Taxman has searched thus far.
	Moves Tried reports how many individual choices the Taxman has thought of so far.  The reason the Taxman is tough to beat is that he can mentally try as many as 1 million moves (or even more, but it would take longer) before choosing!!
	Cutoffs refers to how many times the Taxman has stopped searching a particular sequence of moves because it was obviously bad.  Cutoffs (alpha/beta cutoffs in AI terms) save ALOT of time in the search.

There are five different options for you to choose from:

	Search Depth: The number of moves ahead the Taxman should think before choosing his number.  The default is 5.  For games of less than 30 numbers this is good.  For games with more than 30 numbers consider using a search depth of 3 if the search takes too long.   For games with 15 or fewer numbers, you can get the Taxman to think to the end of the game by setting a very large search depth.  (There is no limit on the search depth at any time.  Deeper searches just take exponentially more time.  The computer should never run out of memory on a search, so you shouldn't worry about a crash).
	Quantity of Numbers: How many numbers are available to choose at the beginning of the game.   The default is 21.  Hard games usually have 40 or more numbers. (There is no limit on the quantity of numbers, but more than 80 tends to leave the screen cluttered).
	Use Random Numbers: If this checkbox has a check, the game will consist of random numbers from 1 to 2 times the quantity of numbers.  If the box is unchecked, the game will consist of sequential numbers from 1 to the quantity of numbers.  Random numbers bring up special problems.  For example, duplicates often occur in the set of numbers.   If you or the Taxman chooses a number with 1 or more duplicates, the oponent will get all the extra copies of the number (a number is a factor of itself).  A rule of thumb is don't choose numbers with duplicates until the end of the game.
	Use Alpha/Beta Pruning: Normally, the Taxman stops thinking about moves that lead to worse moves.   This saves him (and you) alot of time.  If this box is checked, search time is much faster.  If it is not, search time is slower.  The option is placed here so AI students can take a look at the difference between searching with cutoffs and searching without (keep in mind this was a class project)
	Sound ON/OFF: If you get tired of hearing the Taxman's cranky voice (my Dad!!) then you can turn him (and the sound of the bags moving) using this option.  If the box is checked, the sound is ON. If the box is unchecked, the sound is OFF