Reply #29: isn't the player who goes second assured (potential) victory?

[foo_bar]

Maybe under "real world conditions" the player who knows what he's doing will win regardless, barring a lucky guess by an unschooled second mover (statistically unlikely, mathematically possible). Similar but opposite in that respect to Tic-Tac-Toe: in TTT, the first mover A can't lose when he makes all "correct" moves (although he can be drawn), whereas the second mover B can't win against all-correct mover A even when B makes all correct moves (although he'll draw).

Expressing your example in binary to simplify (?) the almighty XOR, the "board" begins in this state:

001 (1)
011 (3=1+2)
101 (5=1+4)
111 (7=1+2+4)
^^^ XOR
000 (0)

That already looks not so simple. Oh well. So it begins in an even-parity state, meaning the first mover A inherits a losing position on the first move (where odd-parity means the final straw), and second mover B is obliged to keep his opponent on the losing end of eenie-miney-moe. Therein lies the illusion: mover B has all the free will, and A has none of it, since A tautologically spends his first move flipping the desired state into the undesirable one.

So your point is well taken, although it applies as well to statistical fraud as the electoral kind.

On edit: does Marienbad have the loser with the last straw or the winner? I found contradictory accounts on the wicked web, although it's unfair either way. Guess I'll have to rent it:

Last straw loses:
In Marienbad, two players alternately draw counters from one of four nim-heaps formed by 1, 3, 5 and 7 counters. The player making the last move is the loser. Since the nim-value of this game is zero, the second player can always win, which makes Marienbad a distinctly unfair game.
http://mathworld.wolfram.com/Marienbad.html

Last straw wins:
In the movie, M politely lets X make the first move. Unfortunately, X always loses...In the normal convention, the player who removes the last object wins, in the mis`ere convention the player to move last loses.
http://64.233.161.104/search?q=cache:FrBNhQC8sl0J:www-mgi.informatik.rwth-aachen.de/Teaching/Games-SS02/ch1.ps+marienbad+politely&hl=en