Does anyone remember this game from the seventies?
I agree with comment that the question really needs more details but based on what you've said I will assume your describing Guess Who

It fits your description in following ways...

It came out in 1979 and was certainly around when I was a child and I'm only a little older than you.

The game board had plastic slots in which meant you could have cards standing up or face down.

It was a two player game that was really each player playing their own solitaire game until one of them won.