Both are expressions used in informal contexts. When you `psych out’ you become terribly excited about something. You get so excited that in the process you sometimes lose your ability to think clearly.
*When my brother saw the new car I had bought, he psyched out.
When you `psyche someone out’ you get them very excited and make them lose control of their mental ability.
*Watching their children spending money recklessly psyched out the parents.
The expression can also be used to mean `to figure someone out’. When you `psyche someone out’ you begin to understand how his mind works.
*After having been married for twenty years, I still haven’t psyched out my wife.