[dmurray]

Why wouldn't it be like human martial arts, where a left-handed fencer or boxer has the advantage of novelty over a right-handed opponent? Even in something like table tennis this has an effect. Baseball too, but for slightly different reasons.

[fwipsy]

This is a good point. Righty fighting righty would mean the large claws are facing smaller claws. Righty fighting lefty means small claw facing large claw. But in either case both crabs are in the same situation so I would expect no advantage to either. Maybe there are other parts of crab behavior or anatomy which are hardwired for a large right claw? Another question is why left clawed crabs haven't died out entirely if they're disadvantaged?

[dmurray]

Maybe the fights are more lethal for both crabs with a righty vs lefty fight, so it's no longer a zero sum game of winner gets the territory, loser gets nothing.

[glompers]

Crabs may not always face each other to fight, since they walk sideways, so there are still opportunities for large claw facing either claw.

[vintermann]

Probably that is limited by how many fights you get into, and how much you manage to learn from them.