Actually if neither randomness nor skill is a factor, a roll generally isn't called for; the guy with the higher Strength (after all modifiers) wins.
You gotta remember, you only call for a roll if there's a reasonable chance of things not going right (and if the results would have any sort of meaningful impact on the game). I don't have the 20th level PCs roll out attacks or initiative if they want to kill an ordinary rat, and I don't have the PCs roll opposed Intelligence checks or whatever if they're just playing checkers in the bar to kill time.