There's a few things going on. In some cases they make money from the fact they have lots of Bingo players who'll click on their banners and take up paid versions of the games. So they put some of the money they earn from advertising and use to make the free Bingo enticing.
In other cases, you'll see a free bingo site on the .net version. They can advertise that as it's not pay per play. However, most users will figure out that they can change the .net to a .com and end up at the pay version.
Finally, they save a certain amount of money from the profits on the paid side to fund the free version. There's no such thing as really free, there's always an angle somewhere.
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