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Case A has a more exponential-shaped buying power curve and VP curve.

Case C has a more linear buying power curve, and VP point curve.

Case B is in the middle.

If you actually model Dominion with a differential equation and solve said differential equation, buying curves (meaning the amount of $ you have, on average to spend that turn) are, at best t^{2/3}- which is not only not exponential and sublinear, but concave down.

The winner in these games will be determined by the length of the game.

This is, with no doubt, the key to unlocking Harem's power.

What I'm trying to articulate here is that without a doubt, trading buying power for current VP is what is going on here, and if you graphed these two curves, the linear curve starts out ahead, but the exponential curve surpasses it. When? I'm not sure. It may pass it too late, and thus never win (in province games).

So maybe for province games, there may not exist paper-rock scissors, maybe it does. But, if paper rock scissors doesn't exist for Province games, simply due to the length of the game being short enough that perhaps Case C always wins. But I'm fairly certain that Paper/Rock/Scissors will exist for Colony games.

I believe that one of the fundamental flaws in many player's analysis is that they are assuming that the optimal Harem/Gold buying ratio exists. And I am not so sure one does. As superdad points out the power of a Harem strategy will depend upon the length of the game, but a large part of that "length" is determined by the parody of the piles.

In my longer analysis, which I will post once I fix all the mathematical errors (which, as mentioned above includes differential equations), it turns out that,

**on an average basis Harem performs equally with Gold**. Specifically, given a fixed amount of time, if you were to draw an "average" hand every turn, then the Gold and Harem strategies can yield the same number of points in that period of time. The key, however, is that Dominion is not a fixed time game, and that a player buying a Harem (instead of a Gold, say), is lengthing the game. A Gold player can then lengthen the game buy buying a Gold (instead of a first Province). In turn, this gives the Gold player more power buy more provinces later in the game. If the Gold player buys 5 provinces, with high likely hood, that would be enough to overcome the Harem player's bonus.

**In particular, lengthening the game by buying treasures over Provinces may not benefit either player in general, and may be determined by the exact situation- including the "oddness" and "evenness" of each pile.** Specifically, I think Harem is way too chaotic than it seems- especially if both players may have strategies regarding the Harem.