Same rules nearly. Two piles, bid and ask. Three exchanges, add to the ask pile, the bid pile, or extinguish an equal amount from both piles. But change the first part only subtract equally a pile and the rules are exact. So the players migrate up and down the sequence, using essentially the golden ratio. But, deeper, the players are using an estimate of the golden ratio, and the real game is to have the better estimate then anyone else. But the path to a better estimate requires a bit of constant motion or uncertainty.
The golden ratio appears because of divisibility, somehow, in a way I do not get, the golden ratio is the optimum allocation of prime numbers for grouping such that we get an algebraic ring, it is the quickest path to meeting Ito Years it has been since I noticed this connection between charts analysis and maximum entropy channel betting.
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