Oh yeah, forgot to mention the 2-player game I invented that requires no pieces. It's based on haggling.

Designate one player as the seller of an imaginary product and one as a potential buyer. The buyer needs a random secret number B from 50-100 which is the max they can pay, and the seller needs S from 0-50 which is the min they'll sell for. Use an RNG if you have one, otherwise you can do it yourself: Have both think of two random numbers from 0-100. Each says one number but not the other. Add the other person's number to your secret one, mod by 50, then add 50 if you're the buyer.

Negotiate over the price until either a sale is made at P or someone unilaterally kills the deal. Seller wins (P - 50) points, buyer wins (50 - P). If the deal dies, seller loses S points, buyer loses (B - 50). I hope I remembered these right. Then switch sides and repeat.