heavy cavalry engaging heavy cavalry

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I'm not a rider, but are Polo ponies not trained to pass by other horses rather than ram into them? I've also seen many horses refuse to jump fences, even when they've been trained to do that? Is the anecdote of a horse refusing to step on a man unless specifically battle-trained (very rare mounts I believe), not true?

Polo ponies are trained to ride off their opponent. You can bump (but not too hard...legally) but there are rules about angles of approach, and certainly not head on.

A horse will try to avoid treading on anything which isn't a true surface...so if there is a body in the way, they'll try not to step on it but they can still kick you on the way past as I know to my cost! In a polo match, I fell off and one of my team members rode over me. He was supposed to be behind me as that's how you play polo, but he was WAY out of control. The horse tried to jump me but I was still rolling out of the fall. Only a broken collar bone though mile: