BIVERSI

On a 10x10 toroidal board, with two reversi start patterns (one crossed and one parallel) set up antipodal to each other. Play mechanics and game object as at Reversi, but 1222 transformer. The two moves per turn must be played one in each section as long as they remain disjoint; after which moves may be played anywhere legal.

a b c d e f g h i j        O's      X's
                         ================
o o . . x . . . . .   1.  .  c4    d4  g9
. o x x . . . . . .   2. d3  f10   i8  d2
o o o x . . . . . .   3. a1  g6    e1J b4
. o o x . . . . . .   4. b4  i7    j7  a5
x x x x o . . . x x   5. a7  e5    f6  j0
. o . . . o o . o o   6. j8  i9    b6  b1
o . . . . . o o o o   7. b3  b0    j6  i0
. . . . . . o o o o   8. j5  c5    d5  i5
. . . . . . x o x .   9. h9  i6    
. o . . . x . . x o   0.

Rules and other rules

There is a difference between "rules of the game" vs "rules about playing the game". "Rules of the game" are purely logical ones - all that is needed to play (or referee) by a computer. i.e. The board and piece powers, the actual moves, prohibitions and priorities. "Rules about playing the game" are specifically for humans; they are physical rather than logical. i.e. playing time, what to do about irregularities or illegal moves, whether things like "check" have to be said out loud, fast scoring methods, blowing smoke in your opponent's face, etc.

In three player games, it seems a good rule to say "it is illegal to leave a next-player immediate win, if preventable". Also, if player A wants to make sure the next opponent plays to block the 3rd opponent from an immediate win, he must say, "B, C is about to win, please stop him which you can do by playing this". Then B is physically obliged to stop C, and A gets the proper reward for his forethought. But if both A and B overlook that C has a win coming up, A will say nothing, B will fail to prevent it, and C will duly win, without (a legally required) takeback, and profit from HIS own alertness. This is a good compromise that does not affect the purity of the rules of the game and makes it the responsibility of the previous previous player to warn that danger is at hand. This is fair since it's the previous previous player who benefits from all this anyway.

The PIE rule

The more long-term the goal is, the smaller the relevance of the PIE rule. There is a strong temptation to think this way, but I am in some doubt. For example in Go, it turns out that once the board size is past a small minimum, the komi is remarkably constant. It seems to be about 7 for all board sizes greater than 5x5. This suggests that the long-termness of the goal (at least of some games) is irrelevant - the PIEness is always about the same; though of course it diminishes in PROPORTIONAL importance to the other moves.

Another reason is that the initial advantage can be built up with good play to its final conclusion. The PIE rule is a tool for the placing player to reduce it to a value very near zero. Ideally, a perfect use of PI implies that only a perfect player can use that setup to achieve victory

p.s. For some reason I'm reminded of a pair of comments about playing against GOD (Game Optimization Device) and the DEVIL (DEVice of ILegitimacy)

* GOD always makes the optimal game-theoretic move; but
* DEVIL always makes the best move given what your overwhelmingly likely response is to be.

If GOD plays a perfect game; DEVIL may play even better (!) because it exploits your weaknesses.