How to sell a new game, similar to chess
It's important to play test your game A LOT with strangers.  Watch people read your rules.  Things you think are easy to understand people will struggle with!
You may find play test groups local to you.  With global lockdown there are a huge number on online play test groups if you can make a digital version of your game.  Details are here. https://cardboardedison.com/playtest-groups.  I take part in these groups and they are extremely useful.
With regards to trying to find a publisher or self publishing there is an absolute mountain of information online particularly on the Cardboard Edison website.
I will say is there a huge amount of competition out there.  You are describing what is called an abstract game.   There are countless abstracts games on the market already so for it have a chance it would need to stand out.  I'm finding playing in playtest groups lots of game from people who have only played a few games,  if you're going to design a game I recommend playing as many different games as you can to learn what works.
I personally wouldn't bother with a patent, the industry is so interconnected that if anyone was going to steal an idea this would be widely known.  I also don't think you can patent a game mechanic anyway.
My friends who have self published via Kickstarter are doing so because they want to release a game, not because they want to make money.  Kickstarter is also a huge investment in terms of time and money upfront making prototypes, videos, marketing etc.  Self publishing friends have described it as doing a full time job as a hobby.
I'm currently talking with publishers about a game I've spent last 16 months working on and have been play testing online with strangers.  Through online groups I'm fortunate enough to have been able to speak with published designers, My understanding with talking to to them is that designers is that you would get about 5-8% of the wholesale price as a royalty.  So if a game has a retail price of about £50 the designer will get about £1 per copy sold.