I’m certainly no math expert – not even a talented amateur – but it seems to me that two different concepts are being confuzzled here.
On the one hand, there’s the following question: what is the correct percentage number which accurately expresses a particular power’s chances of winning on either the Europe or the Pacific side of the board? I think it’s a fair question, and that the forum’s rule experts and math experts will have an interesting discussion about how these figures ought to be calculated.
On the other hand, there’s the question raised by Garg’s original post; in generic terms, it could be expressed as: If Power A has an X% change of winning on the Europe side of the board, and if Power B has a Y% chance of winning on the Pacific side of the board, how does this translate into a Z% chance of victory by the team (Axis or Allied) to which Power A and Power B both belong? I find the question problematic in several respects.
First, Garg’s post (if I read it correctly) uses Germany as Power A, 50 as X, Japan as Power B, 50 as Y, and 75 as Z; assuming for the sake of argument that 50 is an accurate figure for both X and Y, how does that figure get translated into Z = 75? Is it by adding 100 and 50, and then dividing by two? If so, what’s the rationale behind that equation?
Second, the calculations (whatever their basis is) seem to assume that X and Y are static and unrelated figures. But is that necessarily the case? Let’s say, for the sake of argument, that we’re dealing with a standard game in which all the players follow the standard models for playing their respective powers as effectively as possible, and let’s say that this situation does indeed result in X being 50 for Germany and Y being 50 for Japan. Now let’s assume that the US player throws all of his resources into the European theatre. Wouldn’t that result in the value of X decreasing and the value of Y increasing? Would the two changes precisely offset each other, leaving the calculated value of Z unchanged, or would the situation be more complicated?
Third, and most fundamentally, I’m wondering about the concept of adding together two “individual power winning on one side of the board” situations and translating them into the result of “one particular team winning on the entire board”. Global 1940 is played between two coalitions, the Axis and the Allies, on a map representing the entire world, not just between five major powers and several smaller ones on two halves of the global map. To give an exaggerated example: if, let’s say, the Axis has a 100% chance of winning on the Europe side of the board and the Allies have a 100% change of winning on the Pacific side of the board, what does that work out to mathematically for the global game as a whole? A draw? A half-win and a half-loss by both sides? This sounds a bit like the Schrodinger’s cat paradox in quantum physics, in which a cat is mathematically described as simultaneously being both dead and alive.
