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Of course Paypal won't help, you sent a 'gift' of money to someone.
A friends / family (or gift payment) is intended as a transfer of funds from family or friends to one another. For this reason, there is no processing fee when payment is made with bank or PayPal balance.
However as it is a “gift” payment, there is also no Buyer protection as no goods or services should have been exchanged.
If he was not a close mate or family member you should never use that option as it enables the seller to evade his paypal fees and negates your buyer protection at the same time.
You also risk having your account limited for using this option when you are purchasing goods as its against Paypal rules.
Your only hope is if you funded your paypal payment via a credit card then contact your card issuer and see if they will help you but unfortunately again as it was a 'gift' of money they may decline as well.