jkaufman comments on Does Checkers have simpler rules than Go? - Less Wrong
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I've added Hex and it comes in at 377 bytes gzipped (without the swap rule), supporting your impression that it's simpler.
I'd like to point out that without the swap rule it's also very easy to write a program that plays perfectly.
How well does this map to the human experience of the game? Do two experienced players need the swap rule for the game to remain interesting?
It depends on the skill difference and the size of the board, on smaller boards the advantage is probably pretty large: Discussion on LittleGolem