Game of Sticks

Welcome to the game of sticks!
How many sticks are there on the table initially (10-100)? 10
Options:
 Play against a friend (1)
 Play against the computer (2)
Which option do you take (1-2)? 1

Player 1: Good luck!
Player 2: Good luck!

There are 10 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 3

There are 7 stick(s) on the board.
Player 2: How many sticks do you take (1-3)? 3

There are 4 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 3

There are 1 stick(s) on the board.
Player 2: How many sticks do you take (1-3)? 1

Player 2: You lose.
Player 1: You win!

Welcome to the game of sticks!
How many sticks are there on the table initially (10-100)? 500
Please enter a number between 10 and 100.
How many sticks are there on the table initially (10-100)? 3
Please enter a number between 10 and 100.
How many sticks are there on the table initially (10-100)? 50
Options:
 Play against a friend (1)
 Play against the computer (2)
Which option do you take (1-2)? 1

Player 1: Good luck!
Player 2: Good luck!

There are 50 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 3

There are 47 stick(s) on the board.
Player 2: How many sticks do you take (1-3)? 55
Please enter a number between 1 and 3.
Player 2: How many sticks do you take (1-3)? 3

There are 44 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 3
...

There are 1 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 1

Player 1: You lose.
Player 2: You win!

Welcome to the game of sticks!
How many sticks are there on the table initially (10-100)? 7 
Options:
 Play against a friend (1)
 Play against the computer (2)
Which option do you take (1-2)? 2

Player 1: Good luck!
Player 2 says 'I, the AI, will hope to defeat you!'

There are 7 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 3

There are 4 stick(s) on the board.
Player 2 selects 1 stick(s).

There are 3 stick(s) on the board.
Player 1: How many sticks do you take (1-3)? 2

There are 1 stick(s) on the board.
Player 2 selects 1 stick(s).

Player 2: You lose.
Player 1: You win!

Player 2 says 'That was fun, thank you!'

One of the purposes of this assignment is to practice inheritance, and to see how it can be helpful. To that end, I am giving you some sample code to get started:

• Player.java
• SticksGame.java

To complete this assignment, you will need to make two new classes, Human and AI, each of which subclasses the Player class. You will also need to fill in the details for the method playGameOnce, which you'll find in the SticksGame class. You should not make any changes to the main method, or to the Player class.

One of the amazing things about computers is that they can learn. We're going to develop an AI that can learn to play the game better, with experience. Here's how we're going to do it:

• The AI has a number of hats, one hat for each possible amount of sticks on the table. Initially, each hat contains three balls that are numbered from 1 to 3.
• At every step of the game that the AI plays, the AI selects a random ball from the hat that matches the amount of sticks currently on the board. When the AI chooses a ball from a hat, it leaves it in the hat, but it needs to remember which one it picked, and then takes the amount of sticks that the ball indicates.
• If the AI wins the game, it goes back through its memory of all the balls it picked. Since it won, these all most have been good choices! It then adds a another ball to each hat with the same number on it as the ball that it had selected from that hat. If the AI loses, it will throw away a ball from each hat with the number that it selected from that hat. (Note: A hat must always have at least one ball of each number, hence the last ball of a specific number cannot be thrown away.)
• As more and more games are played, the good moves will be associated with having many more balls in the hats.

For example, suppose there are 10 sticks at the beginning. The hat contents appear as:

hat	1	2	3	4	5	6	7	8	9	10
content	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3

The game may proceed as follows:

1. Player takes 3 sticks, there are 7 sticks remaining.
2. AI randomly picks up ball 2 from the hat 7. This means that the AI takes 2 sticks, and there are 5 sticks remaining.
3. Player takes 1 stick, there are 4 sticks remaining.
4. AI randomly picks up ball 3 from hat 4. This means that AI takes 3 sticks, and there is 1 stick remaining.
5. Player has to take the final stick and loses.

Now, the situation with the AI looks like:

hat	1	2	3	4	5	6	7	8	9	10
content	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3	1,2,3
chosen				3			2

As the AI wins the game, it will add additional balls to match the chosen ones:

hat	1	2	3	4	5	6	7	8	9	10
content	1,2,3	1,2,3	1,2,3	1,2,3,3	1,2,3	1,2,3	1,2,2,3	1,2,3	1,2,3	1,2,3

Next time it plays, when it chooses a ball at random, it will be more likely to pick one that corresponded to a winning play on a previous game.

Note that you shouldn't literally store each one of these balls as a separate number. It would be a massive waste of space to actually store another "2" every time you wanted to record it as a good move. The above description is a conceptual explanation: you should use counts to achieve an efficient approach. It should be something more like:

hat	1	2	3	4	5	6	7	8	9	10
content	1,1,1	1,1,1	1,1,1	1,1,2	1,1,1	1,1,1	1,2,1	1,1,1	1,1,1	1,1,1

… where for each hat above, the position is telling you the move to make (1, 2, or 3), and the number shown is the count of the number of balls in that position. This also means that when you "pick a ball at random," you will need to use arithmetic to pick a number the right fraction of the time.

Your task is to modify the dumb AI from the previous part so that it works as described above. At the end of the game, the AI should print out the contents of all of its hats so you can see if it learned appropriately. At the end of the game, add functionality that asks the human if they want to play again. This way, you can see the AI learning over multiple rounds.

Admittedly, it needs a lot more practice than just a few games, and it wouldn't hurt to have it play both first and second positions. That's what's coming up for the next part of the assignment.

It's ok to make some non-extensive changes to the main method for this part. You'll need to ask the human player to play again, and manage that piece accordingly. You also might want to modify the constructor for the AI player to take the starting number of sticks, so that you know how many hats to make.

We will grade this by running your AI repeatedly, and looking to see if the hats seem to me changing as expected.