Confused by process

Sorry but I am not getting it right

I want to allow people to have access to various pages, so I will have a group for each page. I create a group (page1). I assign a user to that group. Now on the page I want to secure I check groups_read_post? That won’t limit the page to only one group. So do I create a new capability for each page (groups_read_page1) and then on the page select that capability for that page?
Thanks

http://wordpress.org/extend/plugins/groups/