Assuming that you are not going to be cheating, you can have a deck of cards where you mark the back with a random number. You let the other player know which cards are marked with each number (ideally in a way that won’t let you memorize them).

Then you just handle the cards. You shuffle, you pick the cards, and when you pick for the other player, you do not look at the cards, just at the numbers, that you communicate to them.

This way, they know which cards they have without you knowing them, and you have a simple system.

Obviously it’s very easy for you to cheat, but if it’s just friendly play there’s no reason for you to do so, and therefore for your friend to believe so.