adversarial AIs in tic-tac-toe and 2048.nb

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Artificial Intelligences, also known as AIs, are the current coding system on \
the market. They're being used in countless fields for countless purposes, \
but with the emergence of more AIs comes an important question. What would \
happen if two AIs were paired against each other? What strategies would the \
AIs come up with to win against each other? The goal of our project was to \
answer this question. Starting with the simple game of Tic-Tac-Toe, we found \
unique strategies that the AIs developed; we later branched into more complex \
games such as 2048. \
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We first decided to explore adversarial pair AIs with the simple game of \
Tic-Tac-Toe. The game has been studied many times, and is relatively simple \
to code as well, so it was a great choice to begin our project.\
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Before we could build an AI, we had to set up code to play the game. We \
intended to use 0's for spots that weren't filled, 1's for spots that were \
filled by player 1, and 2's for spots that were filled by player 2. We \
started off with a 2D table to keep track of the board's current state. \
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We then set up functions to look at the board and figure out which player \
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Our final win function, called actualWinner, used the column, row, and \
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We then created a function that checked if all the spots on the board were \
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Finally, we wrote code that found a random empty space on the board for the \
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For example, given the starting board, the resulting tic-tac-toe board after \
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To set up our AIs, they needed training sets to learn from. We built these \
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Before we could fill the training sets, however, we needed to have code that \
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Function that simulates a given number of random tic-tac-toe games, and adds \
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Here's some basic info about the training data, including the wins for player \
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Cell["Here's an example of a winning game for player 1:", "Text",
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Cell["\<\
where player 1 wins by taking the diagonal and selecting the center spot.\
\>", "Text",
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Cell["Actively Learning", "Subsection",
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Cell["\<\
So far, we have AI1, a list of winning boards for player 1, and AI2, a list \
of winning boards for player 2. The variable trainingData nicely puts this \
information in an association.\
\>", "Text",
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Cell["\<\
To use this information to play, the AIs check what they have in their \
trainingData. If the tic-tac-toe board exists, the player chooses one of the \
options in its dataset. If the tic-tac-toe board doesn't exist, the player \
just moves randomly.\
\>", "Text",
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Cell["\<\
For a significant number of training games in a player's dataset (these are \
random games), the training data for player 1 looks something like this:\
\>", "Text",
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Cell["\<\
Our next step was to create a function that uses the training data for each \
player to predict the next move. The games that player 1 wins by using its \
dataset are stored in goodgame1, and the games that player 2 wins, using its \
dataset, are stored in goodgame2.\
\>", "Text",
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Cell["Setting up goodgame1 and goodgame2:", "CodeText",
 CellChangeTimes->{{3.846947436820074*^9, 3.846947449781954*^9}},
 CellID->1413525546],

Cell[BoxData[{
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   RowBox[{"{", "}"}]}], ";"}]}], "Code",
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Cell["\<\
The function that uses the training data to play is shown below. Note that \
the training data for each player gets updated after each game, which is how \
the AIs actively learn.\
\>", "Text",
 CellChangeTimes->{{3.846947481187027*^9, 3.8469475280361567`*^9}},
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Cell["\<\
Function that simulates a given amount of games using the AIs training data:\
\>", "CodeText",
 CellChangeTimes->{{3.846947533989311*^9, 3.846947556561635*^9}},
 CellID->83480143],

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After running 10 games with the dataset, here's a look at the stats for each \
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Here's a game where player 1 wins (through the center column):\
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Finally, we can combine all these functions into one final function that has \
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Final tic-tac-toe function for adversarial pair AIs, that first plays a \
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We wrote code to build 2 AIs for tic-tac-toe and have them play against each \
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We started off by analyzing the AIs first moves, to see if it differed from \
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\>", "Text",
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For player 2, it appeared that when player 1 picked the top left corner, it \
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Cell["Clearly, the AI's first moves differ from what we expected. ", "Text",
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To find the AI's winning patterns over time, we ran many random games and \
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To start off, we ran 100 random games for the AIs to learn from, and then \
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We then graphed the wins and losses of the AIs with even more training data\
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Player 1 and 2's win rate similarly started to even out at 50%. We were \
unable to run more random games due to time constraints (our computers aren't \
supercomputers, unfortunately). If we were able to run, let's say up to \
100,000 random games, we would like to see both players' win rate decrease to \
0%, because when two humans play tic-tac-toe logically, it's a draw. \
\>", "Text",
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After making these AIs, we decided to code it so that we could play against \
an AI\[LongDash] just to see who was smarter. We used a Manipulate and \
combined it with our two main functions from earlier: random games and \
training-based games. \
\>", "Text",
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Cell["\<\
We first created an interactive check box, where the humans can select where \
they want to move. The checkbox would influence the startingboard, which then \
would run the AI\[CloseCurlyQuote]s move and display the changes on the \
board. This went on until the game ended, either a draw or a win.\
\>", "Text",
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Cell["\<\
A challenge was timing player's 2 (the AI) moves, because the Manipulate \
updates constantly. We wanted to use something similar to a Wait function, \
where after AI moves, the human is given enough time to select a checkbox. \
For this, we used a Pause function, where the human is given 5 seconds to \
make a move. If the human doesn't make a move in 5 seconds, the AI just makes \
another move. 2 moves in a row, yay!\
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Here is an interactive tic-tac-toe game, where the AI moves RANDOMLY. Note \
that you'll have 5 seconds to make your move, and you'll need to wait a bit \
after your move, to give time for the AI to play.\
\>", "Text",
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Here is the same interactive tic-tac-toe game where the AI uses it's dataset \
and makes logical moves. See the difference?\
\>", "Text",
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2048 is a popular game, where the the goal is to add powers of 2 on a 4 by 4 \
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2048 and tic-tac-toe are massively different games, especially when it comes \
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The overall strategy was to first construct the game, and then generate a \
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Similarly to how we built a model for tic-tac-toe, the first step in testing \
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A simple function to build a starting board by making a 4 by 4 table, and \
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The next step is to build the functionality of the game. This means writing a \
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The first 2 move functions operate similarly, systematically checking for any \
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The game end check just looks to see if there are either no available merges \
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The game driver went through several iterations over the course of this \
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A function that formats the data into a list of rules, as needed by the \
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The final step was to train the Predict function and export it: \
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After exporting the Predict function, we wrote code that combined it with our \
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These games ran more slowly, running over the course of 2 nights. We've \
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But, ultimately, it provides the same result as running this:\
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The next step is to make pairs of the maximum value and the length of each \
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We used this on both datasets\[LongDash] the random games, and the model \
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Cell["\<\
Keep in mind the y-axis log scale! There are 10,000 times more games with \
length 100, than games with a length over 400. \
\>", "Text",
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Cell["\<\
As we can see, the model data (blue) has a longer tail than the random data \
(yellow), showing that games that use the dataset tend to run longer than \
random games. The yellow graph is skewed more to the right than the blue \
graph. \
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Cell["\<\
Here is the histogram of the maximum values with the same color code as the \
previous histogram. The x-axis represents the final value of the game (2, 4, \
8, 16, etc, up to 512). There were no games that actually won (with a maximum \
value of 2048). The y-axis is the amount of games that achieved that final \
value. Most games ended at 64 and 128.  A significant portion of games that \
ended at 8 were a result of the random games. \
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Cell["\<\
In this plot, we can see that although there is some improvement of the \
number of the higher scores using the model,  it doesn\[CloseCurlyQuote]t \
appear to be significant in comparison to the random games. \
\>", "Text",
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Cell["\<\
Here we have the box and whisker plots of the lengths of the games, separated \
into bins based on the high score of the game, and the different datasets, \
using the same color code as above.\
\>", "Text",
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As we can see, each bin of games (e.g. max score of 8, 16, etc...) generally \
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The plot below uses the first occurrence of the max value rather than the \
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Cell["\<\
In this plot, we can see no real difference between the model-played and \
random move games, demonstrating that the model doesn\[CloseCurlyQuote]t lead \
to the games reaching their max value faster, as we had hypothesized.\
\>", "Text",
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Cell["\<\
As we can see from the graphs, the model learned how to increase the length \
of the games rather than bringing them to a higher score faster or more \
efficiently. This was an unforeseen outcome, but was still fascinating to \
observe. \
\>", "Text",
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Cell["\<\
The clear conclusion to this work is that the model using the RandomForest \
distribution made the games run longer, rather than more efficiently, despite \
being trained solely based on the high score of games. This makes sense, \
because as the games go on, the values never decrease, so a longer game will \
have a higher chance of getting a higher score. \
\>", "Text",
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Cell["\<\
We're very proud of our work!

We want to thank Rory for all their help throughout this project. We couldn't \
have accomplished this without them.

While our dataset approach for tic-tac-toe didn't use the Classify or Predict \
functions, it is still a unique approach that functions well in predicting \
the player's next logical move. This approach functions\[LongDash] given a \
good training dataset with a significant amount of winning games. We are \
curious how we could use those functions (Classify, Predict, \
LearnDistribution), however, to see whether the results would change for \
tic-tac-toe. The results of the training data can be seen in the manipulate, \
which makes logical moves most of the time! However, the manipulate was \
tricky to build in regards to giving enough time for the human to make a move. 

With the 2048, we would have liked to train the model directly on the game \
lengths rather than on the high scores, to see if it can more significantly \
increase the length of the played games. It would have also been interesting \
to see if with more data the AI could produce intelligent strategies as a \
human would, rather than just increasing the length of the games to increase \
the probability of getting a higher score (which is still logical!). It would \
also be interesting to see whether different neural net models, as opposed to \
the RandomForest model, would increase the accuracy. As opposed to using the \
Predict function, it may be less time-consuming to run each of the 4 possible \
moves (up, down, left, right), and take the board with the highest resulting \
value (using if-statements) for each move. The reason for including this \
would be as a control, to see if the machine learning model can outperform a \
simpler approach. 

Future work involves running a lot more random training games, so that \
neither player 1 nor player 2 wins (in tic-tac-toe if both players make \
logical moves it\[CloseCurlyQuote]s a draw, and in 2048 you actually reach \
the max value of 2048). It\[CloseCurlyQuote]d be great to apply this approach \
to more complex games as well, such as chess, Nim, or Scrabble. The hardest \
part is setting up the game\[LongDash]running the random training games and \
then using that dataset is shown how to do in this project.

To any intrigued readers, we wish you the best of luck in your future \
endeavours to further develop our work\[LongDash] if you and your computer \
are up to the challenge.

\
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