If I ever design an FPGA, it'll have hexagonal tiles. So you can play Settlers of Catan on it for competitive PnR.
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Okay how about this: Each player draws a secret number. You start with a small rectangular board and take turns drawing tiles with logic gates that you form into a circuit to produce your number, or disrupt your opponent's circuit.
Routing as a trading game. Each player has to route all their nets before any other player can finish theirs. "I'll trade you a span 4 wire in tile B7 against two route-through LUTs."
