pizza theory design exactly player randomness simple turn action outcome round unpredictable cook idea good way create pieto set game player take pizza cutter wooden stick die topping counter match player place topping game board space designate xin round player turn place top game board top place adjacent player topping player secretly choose number die player reveal number lie pizza cutter board space match number cutter divide pizza possible outcome create number slice slice player topping opponent replace opponent topping player tie topping topping player remove replace threeway tie change nb player top slice topping remove replace roundwhoever place topping game board winswith player cutter topping color player take turn place topping board topping color board player get topping board player lose

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