Looking a bit closer at Wythoff

 This is the Wythoff game, and the goal is to remove the last chip from the two piles. So the counter goal is to never leave a last chip, and so on working backwards.  The solutions are those radial lines converging to the corner. Ity is a relative game, the move you make always counters the opponents move.

When the game is changed to allow adding and removing chips, and the pit boss extinguishes nearly equal ask/bid pairs, with bit error. The goal becomes different.  I will speculate, then I think prove, that we get a dual goal, co-estimate both Pi and Phi, such that the players remain in some region, near a bound 'radius'.  This is where I am at.  I go here because I remember a relationship on the hyperbolic curve where Phi and Pi meet, very closely. In the continuous model, it was where tanh'' was peeking.

How did humans get cloghed up with their math algorithms?

That is the puzzle.  Why do  certain transcendentals and primes show up in unusual spots on both number and physics theory? The connections has to be network analysis, or paths along semi-directed graphs.  That is most of what number algorithms do, run a graph.  So, that model might include queueing up bit error,  That includes re-quantizing the graph, as if both physics and mah ate in a constant battle to get actual computing quants that utilize he x axis efficiently enough so Ito blesses the yheory of operation.. We arer almost everywhere correct.

In physics that becomes no empty space and bubbles overlap with some semi-styable dimensionality. Round off error becomes channels of bubbles exchanging over lap states, moving a bit error round the loop.