What is the maximum possible number of legal moves from
a Hive board position? I know of a position where the
number is 131. I believe that is close to the maxumum.

I'm offering a prize of 1GG for each qualitative improvement.
Ie; for a position with 133 possible moves, I pay 2GG, 135=4GG
and so on.

Fine print: positions which are visually identical are the same,
so for example ant moving left to a position and ant moving
right to the same position are not different moves. It is only
one player's move at any time, so count the moves available
to either black or white, but not both. No mosquitos - just
the standard set.

Send a picture of your positions, and your count of moves,
to me privately (so as to not reveal your strategy to the
general public). I will periodically post news of the
current best, and when I think the contest has probably
reached the limit, I will post the winning entries.

The most convenient way to generate positions is to use
a review room at boardspace.net to set up your position,
and when you have a winner, take a screen shot of the result.
You can also use the "show text" menu item to capture
a replayable text record of the position.

RESULTS:
This has proved to be too much fun to keep the images secret, so visit this page: http://boardspace.net/hive/hive-move-challenge.html
The current best result is 214 moves.

I'd guess he means any possible position that can be reached without breaking the rules.

Conceptually, I mean any position that can actually be reached
in a game; but not necessarily an adversarial game. Black
and white might have to collude to reach the position.

I am willing to assume that any valid hive where the queens
are not captured is reachable.

131? Felt like an eternity...

Yeah, I think you are. The point is not to count the number of positions that can exist in the game, the point is to count the number of possible moves a player has from a given position. You fabricate the position so as to maximize the number of possible moves. The current goal is to set up a position such that one player has more than 156 possible moves. Hopefully that makes more sense.

The unexpected success of this challenge has depleted
my slush fund of GG, so I'm now reduced to soliciting
donations to pay my debts. Please donate GG to this
thread to help fund this important research! Otherwise
I'll be uploading images and reviewing games for weeks.