Parity, a numbers puzzle game

Suppose the corners and the center are black and the other squares are white. Then every two moves in a row adds one to black and one to white. So an even length sequence keeps the difference between the black sum and the white sum the same. In the end, with all values set to X, this difference equals 5X - 4X = X.

Thus, for an even-length game, we know from the start what X must be: the difference between the black and white sums.

This means there's no room for a wrong move. Any solution has a prescribed number of times to hit each tile. (FWIW, the total number of moves will be 9X - the starting sum = 9(B - W) - (B + W) = 8B - 10W)

So far, we've assumed we'll be playing an even-length game. Might we actually be playing an odd-length game? Sure. In that case, we also know from the start what X should be (since it amounts to making one move, adding 1 to the color not started on, and then playing an even-length game).

Is there an easy way to see from the start whether we play an even- or odd-length game? Is it possible that both are allowed for a given board? It's not yet clear to me. I'll reply with updates. But at any rate, there are at most two different values you can solve with, one for even-length solutions and another for odd-length solutions (and these two values will be next to each other).

[This is all for the version of the game in the early levels. I see from other comments that the game changes at level 51, which I haven't played to yet. I also see that "black" and "white" start actually being used in the game at that point, making this explanation potential confusing.]

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I didn't really think about game theory or anything. I just had an idea and wondered how it would play.

Not so easy anymore

I recollect someone suggesting letting bots(AI) play a number of variations of the game first and then use the outcome to ascertain the difficulty - may be an overkill for a fun game like this?