What are you asking about is called smart poker , described in this fascinating article (PDF) of the cryptographic greats Adi Shamir, Ron Rivest and Leonard Adleman. According to their summary of the results:
We present two solutions to the mental poker problem:
- Strict evidence that it is theoretically impossible to card, which at the same time guarantees that both hands are disjoint, and no player knows about (except that the opponent’s hand does not intersect him).
- An elegant protocol for working with cards that allows you to play an honest game at Mental Poker if you wish.
The apparent contradiction between our two results is not related to any tricks or errors in any result. In fact, we will reach the reader - a pleasant task to puzzle the differences in the underlying assumptions that explain our seemingly contradictory Results.
Please note that their result applies only to two poker games. The article Mental Poker with three or more players extends this result to several players.
In short, can this be done? Probably yes. Is it practical? Almost certainly not. Instead, you should install or find a trusted third party.