so how about something like this: if you play for free (non subscription) how about every so often before you can start a new game you have to click and watch let's say one to three ads all the way through before you can continue.
You're brushing up against a strategy some sites use, that of interstitial ads. Forbes.com (for example) uses those a lot -- a full page ad, with a minimum view timer, that shows before you can see content.
The primary barrier to getting something like that into place is traffic quality. While the demographics of those who visit Forbes.com might be attractive to full-page interstitial advertisers, I can't speak to what it might be here. Also, I suspect Chess.com has a great deal of international traffic -- right now, only US-based traffic is getting decent rates.
how about something that's based on pay as you go: maybe you can buy let's say 10 games for a penny etc