This is clearly not a sufficient test. You are making up a strawman by assuming that the decision making of the AI is either (i) completely deterministic, or (ii) completely random. This need not be so.
Most likely it is a probabilistic decision making process. Lets say the AI has a certain chance decalring a war on you. Denote it with p (where 0<p<1). Then of course the chance of not declaring a war on you is 1-p. How the program calculates this chance ofc unkown to me, it can depend on many factors. The point is that it is entirely possible that in one turn it throws a dice and gets a number smaller than p, thus declares war on you, yet if you reload the game it throws a number larger than p thus it keeps peace. What you would see is not deterministic but definitely not random either.
The real test would be to run let say 100 of reloads and count the number of DoW. Then compare this sample to a sample generated by random number generator. If you dont get a statistical difference (i.e. the mean of the samples do not differ statistically, i.e roughly speaking the mean probability of getting DoWs is around 0.5) then you could conclude that DoW is random in that given context. Otherwise it is not.
I would bet a large sum of money that it is not.
Also, please take a look at the two lists of DoWs that I posted before and tell me how could you get those list by a purely random process. Thanks.
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