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Originally Posted by DankChi
Olaf cannot kill Jax in a one versus one if they are equally fed. His counter strike will make the bonus attack speed from Olaf's passive useless. Very few champs can go against Jax without without being fed compared to Jax. To beat a Jax, you need to shut him down early game.
You are correct, to beat a Jax you need to shut him down early, and Olaf can do that easily, at least in my experience he can. His Reckless Swing goes through Counter Strike, which makes it difficult for Jax to trade with Olaf in lane. Once they are level 6, Jax's Counter Strike will become essentially useless as it won't be able to stun Olaf and Olaf can still do heavy damage to Jax, plus Olaf has innate lifesteal. So yeah, Olaf can shut down Jax early.