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By the way, regarding spells. I performed the same calculation myself, but for The Eastern Expedition. It seems to be similar.
For probabilities, you need to calculate a sum of this type:
P5 = W(0)/S + sum[i = 1..n][W/S * W(0)/(S - W)] and so on. If anyone understands probability theory, please let me know how to simplify this calculation. I found the probabilities using a computer.