Single Comment

The quantom mathmatical factors would change on every half move and I think
that making the calculations manually might be a bit tedious at times.  To
determine, for example, whether a quantom belonged to white or black, may
detract from the fun of the play. Aside from that, the game should be
enjoyable.  But I imagine in most cases the Bario numeric aspect could be
easily seen to be + or - and so no actual calculation would need to be
made.

A good strategy in this game would be to move (define and identify) the
quantoms that you had marginal control over... thus making them pieces
that your opponent could not control.  Another logical move would be to
capture quantoms whose numeric value favored the opponent.

To make Mr. Smith's proposed game more impressive (perhaps he already has
this in mind) I suggest not using a 'standard' chess set of Black and
White at the start of the game... but rather nuetral pieces (that will/can
become black or white).  This would allow the following, for example: 
Assume an endgame with White having King, 2 Bishops, 2 Knights.  Black
having: King: 1 Knight, 2 Rooks.  Also assume there are 3 unknown quantoms
on the board (ones that in the simple deductive variation would be 2 Black
Bishops and 1 Black Knight) .  With White previously having his Queen and
2 Rooks captured, what could he make of a Bario? [Note: In the
deductive/assigned variant these 3 Barios would already belong to
Black]... Using the nuetral quantom and neutral piece-color concept White
could make a third Knight or third Bishop.  And later a fourth knight or
fourth Bishop.  Thus, we would still be playing with a 32 piece set, but
only the King and Pawn colors would be true White or true Black at the
start of a game.  Of course, the quantoms behind each pawn are so
obviously under each players control there is no danger of the opponent
controlling these during cycle 1.  

It is the first new cycle that the undefined color aspect would really kick
in.  I would not mind playing this tye of game.  But I would not want to do
the math each time.  Of course, for most cases the Bario control would be
obvious and no calculations would be needed except in cases where the
quantom value was near '0.'  When it is at '0' is the Bario up for
grabs or off limits?  I may have missed that answer in an earlier
comment.

I think this has the potential to become a great game.