There’s no limit to the number of games you can analyze. You can analyze as many games as you want, either your own or from other players, using the games observed in the playing area, or from the game history available on the website.
However, in order to distribute resources fairly among all member, a priority system is used. Players who request game analyses for the first time that day have priority over those who have already requested several analyses. This priority is then readjusted. Players in their trial period are limited to analyzing 3 games per day. Still, we have allocated sufficient resources so that the wait time is as short as possible.