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Make it HTTPS first of all, research all keywords that relate to sudoku, write a long article about it and have it on the main page. Make sure you on-page SEO is good and keep doing off-page SEO (getting backlinks). If you want to take SEO a bit more seriously, read through a guide like this to start with: https://backlinko.com/seo-this-year. That's what I did to de-mystify SEO in the beginning.
It's intentional. The first 5 games are ad-free. Most of the ad-revenue are from people who stick, so I kind of try to give people the best experience the first 5 games.
Most solitaire games these days have an option of playing a fully random game or a winnable deal. The automatic deal when a user comes to the site is a winnable deal.
I switched from Adsense to Freestar and have been very happy with them. I think you'll have to have a certain amount of volume to get signed with them, but it's difinitely another ballgame than Google Adsense.