How to make server force page refresh?

I want a page where everyone sees the same thing. So if one user does something (types, moves an object, etc...) everyone else sees the changes in (almost) real time. Like if two people were playing tic-tac-toe, they would need to see the opponent's move. (Let's say tictactoe is the app)

I wanted to do it with AJAX, and have the tictactoe board be basically 9 divs. I know I could do something like this: When user clicks a div, send an HTTP request and the server will process it accordingly. Then that content will refresh with AJAX to show their move.

But when you do that, is there a way to trigger the opponent's page to refresh so they also see the move? So that when someone makes a move, it HTTP's the server to do what it needs, then the server gives the updated data to viewers to handle and dispaly?

Any other options?

I'm trying to do this on a webhost, otherwise I'd probably use an applet and a dedicated server.