🚀 go-pugleaf

In article <xeno.717738632@pv34ad.vincent.iastate.edu> xeno@iastate.edu (Gary L Snethen) writes:
>  The very term "solvable" assumes
>against a player does not make mistakes.

Ah!  I think I see your point.

I had been assuming the players will play consistent with their optimal
strategies in my definition of the solution of the game.  I.e., "best
play" does not go against optimal strategy.  The view I was taking was
that we were "solving the game", rather than actually playing the
game.  Sort of like, working out the best sequence prior to making
the move.

It is very interesting to look at the system that includes that
game plus the two players.  Then lots of questions can come up --
and usually do.  If both players have complete knowledge and can
adjust their strategy based upon their knowledge, then the best
they can do is for each to follow their "optimal strategy" -- a
Nash equilibrium.  (Because if they don't, their opponent will.)

If the players don't have complete knowledge, but can still
calculate the solution to the game (i.e., assuming perfect play by
the opponent), then they also should go for the Nash equilibrium.

If the opponents, don't have perfect knowledge and either can't
calculate the solution to the game (i.e., they will play "inferior"
moves) then there are lots of possibilities depending upon how much
we know about the imperfections in the opponent.  This models the
behaviour of actual chess players who alter their openings to suit
their needs against particular opponents.  There are also some
interesting non-symmetric possibilities, where one player has
complete knowledge, including complete knowledge of the others
imperfections.  As long as the moves played by the "imperfect"
player are deterministic in a known way, an optimal strategy can be
calculated.