Problem $1.(30$ points$)$

For problem $1,$ you will put answers in your writeup for a $-$ c$.$ Also make alterations to the given python module.

a$.$ Run the ps$3.$py code. You will be prompted to play tic$-$tac$-$toe against a minimax agent. Common wisdom suggests that the best first move is the center square. The agent doesn$$t begin by playing in the center square. Why do you think the agent plays where it does instead of the center? Give an explanation $(4-5$ sentences$)$ in your writeup.

$$ I am not sure.

b$.$ Alter the ps$3.$py code$$s main function so that it calls problem $1$b instead of problem $1$a$.$ You will be prompted to play connect$-4$ against an alpha$-$beta with cutoff agent that is using a silly evaluation function. See if you can defeat the agent in a few games. Describe $(3-4$ sentences$)$ what your plan to defeat it every time. Explain briefly $(2-3$ sentences$)$ why your plan works.

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c$.$ In the function c$4$ good eval, write a new evaluation function. Using this function, write code in problem $1$c that will play an alpha$-$beta agent with depth cutoff $4$ using your evaluation function against a random agent. Play once as X and once as O$.($Note: For this problem and also $1($d$)$ and also $2($b$),$ it may help to write a version of your eval function to evaluate as $$X$$ and another version of your eval function to evaluate as $$O$.$ This is fine.$)$ Have the function return a tuple $($nx$,$ no$),$ where nx is the number of games that your agent wins as X$,$ and no is the number of games that your agent wins as O$.$ So if you win both games, you return $(1,1).$

Describe $(2-3$ sentences$)$ your evaluation function in your writeup and explain $(2-3$ sentences$)$ why you think it should do well. If your agent doesn$$t usually win against a random agent, then you probably did something wrong.

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d$.$ In the function problem $1$d$,$ run $8$ games of an alpha$-$beta$-$cutoff agent using my eval$-$ uation function versus an alpha$-$beta$-$cutoff agent using your evaluation function, with each agent playing $4$ times as X and $4$ times as O$.$ Run four of games at depth limit $2$ for both agents, then four games at depth limit $3$ for both agents. Return a tuple $($nx$,$ no$),$ where nx is the number of games that your agent wins as X$,$ and no is the number of games that your agent wins as O$.$ So if you win all $8$ games, you return $(4,4).$

Problem $2.(20$ points$)$

For problem $2,$ you will put answers in your writeup for a$.$ Also make alterations to the given python module.

a$.$ Find the definition for Gomoku $(5-$in$-$a$-$row$)$ in the aima code. Build an evaluation function for gomoku. In your writeup, briefly explain what your evaluation function is doing.

b$.$ In the function problem $2$b$,$ run $8$ games of a random agent versus an alpha$-$beta$-$cutoff agent using your evaluation function, with each agent playing $4$ times as X and $4$ times as O$.$ Choose a depth cutoff that will allow each game to complete in under $20$ seconds. Have the function return a tuple $($nx$,$ no$),$ where nx is the number of games that your agent wins as X$,$ and no is the number of games that your agent wins as O$.$ So if your agent wins every single game, it will return $(4,4).($Note: As mentioned above, it may help to write a version of your eval function to evaluate as $$X$$ and another version of your eval function to evaluate as $$O$.$ This is fine.$)$