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I completely agree with Ment regarding the issue of increasing damage! Let's introduce a standard for builds in our build space: damage per 100 turns. The norm of a vector (second order ||•||2), for example, is equal to its length, but in our case, the norm will be the maximum possible damage that can be inflicted by a fixed army (the choice of army is up to the person establishing the norm!) in a given build. Of course, the game isn't that simple, but our Euclidean space can always be modified to the necessary precision. So, in this space, let's introduce a measure: the expected value of the norm of this build across all possible fixed armies. In simpler terms, we take an army of 100 peasants, try all possible ways to defeat 100 dragons (in this build), find the maximum possible damage with different combat tactics, and do the same for each possible army. Of course, in our stochastic experiment, the sample will not be in the hundreds of thousands, or even millions, but that's what mathematical statistics are for! However, we only need it to find the expected value, and given the sample size, it's not advisable to calculate the sample mean, so I recommend using other unbiased estimates.
Since we have now strictly introduced a measure in our space, let's start measuring! Returning to Ment's statement, let's formulate it in light of our space with a norm and a measure: the measure of a build with doubled initiative and luck equal to five is greater than the measure of a build with true luck. This is not proven because there are many counter-builds (such fixed armies) that won't allow us to have 5 luck in combat, but only 2 that will "lock" true luck (or more?).
Without getting into mathematics, there are enough ways to increase damage without true luck by increasing the corresponding characteristic, so that one of them can be combined with doubled initiative, but there are fewer ways to double initiative!