Interestingly, when I keep multiplying the matrix itself many times, the outcome converges to the result below. This implies that over an infinity number of runs, the probability of S wind is 0.625, N wind is 0.3125, and EW wind is 0.0625.
0.625 0.3125 0.0625 0.625 0.3125 0.0625 0.625 0.3125 0.0625
𝑃 =
lim 𝑁→∞
15
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