High‑performance computing applied to a topic explored by Einstein

In the topological game of Hex, with its extremely few and simple rules (Einstein even kept a board on his desk at Princeton, long before computer science existed), I probably have the best approach ever developed — surpassing, for example, the one proposed by Nobel laureate John Nash, who analyzed the optimal configuration on a board whose four sides are each 14 cells long.

I dream of the proof of my following conjecture, being cited. “Artificial intelligence discovers the winning strategy of Hex on an arbitrarily sized board after first working out the winning strategies on boards of several smaller sizes.” If you do not have powerful enough hardware to demonstrate this conjecture, do you at least use high‑performance computing to fully explore the game tree part (simple theory of games concept) related to a cell on the board with four sides, each nine hexagons long, as depicted at http://webdocs.cs.ualberta.ca/~hayward/hex/?

I need to be informed of the costs.