🚀 go-pugleaf

I want to point out that the 'optimal play' as understood in the solvability
problem and 'optimal play' in actual game may be *very* different.

When we try to solve a game, we ask if it is possible for either side to 
force a win against perfect play (i.e. against any reply). The optimal strategy
in this case is minimax strategy: if we can force a draw, but not a win, we 
must not play a move which wins against all but one reply, against which it
loses.

The optimal strategy for *playing* the game is the same *only* if one side
can force a win and we are playing that side. Then we simply play the moves 
which win against all replies.

But what if neither side can force a win from the initial position? (This may
well be true for chess, at least I'd bet on this outcome if the solution were
practically achievable.) Suppose the supercomputer that has solved the game
challenges the World Champion? If it consistently applies minimax strategy,
and the Champion never plays a losing move, all games end in a draw and the
Champion retains the title!

Therefore, the optimal algorithm for winning games is considerably different!

Incidentally, this means that the discovery that the initial position is a 
forced draw would be good news for all the people who fear the loss of
'uncertainty' in chess: it would mean that one must take risks to win!

	Sven

P.S. The last statement is oversimplified. It is true only under some
additional assumptions. Namely, it is possible that the initial position is
a draw with best play, but that (say) white has winning paths in which best
play by black still leads only to a draw, i.e. that white doesn't have to
risk.