This looks srsly overengineered. There's an easier way. Each player chooses simultaneously an integer from [1, N]. (Like, draw a chit and reveal them simultane

This looks srsly overengineered. There's an easier way. Each player chooses simultaneously an integer from [1, N]. (Like, draw a chit and reveal them simultaneously.) Sum the draws. For a sum of N+1 or more, subtract N.