I've been playing 5x5 Go with a lot of people new to the game, and have been using some simplified rules for faster teaching:

  1. You can play on any empty intersection, unless it would make the board look like it did previously.

  2. If you take away the last liberty ("line leading away") from a group of pieces, they're lifted, opponent's ones before your own.

  3. The winner is the only one with pieces left on the board.

I'll start them with a number of their pieces already on the board ("handicaps") that I'm guessing will be about balanced. Over time they'll need fewer and fewer.

After playing a bit, often in the first game if they're picking things up quickly, we introduce the idea that if it's clear you're not going to win you resign.

At some point you likely get to a game where both have pieces that can't be lifted. After declaring that a tie, I'll explain territory scoring and passing. If they're the kind of mathy person I think will enjoy it I'll show them the Tromp-Taylor version, and with that we're ready to move on to larger boards.

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People reading this may be interested that 5x5 Go is solved. 7x7 Go is probably out of reach.

Probably out of reach for solving rigorously. A strong engine equipped with something like the opening books at https://katagobooks.org/ might well "solve" the game in the sense of always winning won positions and at least drawing drawn positions (if the komi value used makes draws possible). I suspect that always getting the best possible score (but without rigorous proof that that's so) might be in reach.

It's worth noting that although this teaches the rules in a intuitive fashion, I think this may encourage people to form a two eye stronghold - and then sit back happy with a tie. Though perhaps this is hard to get on such a small board. Or even this is the concept you want to teach!

Another scoring option could be to use the Stone Counting variant, where whoever has most stones on the board at the end is the winner.

More general comments about teaching go: I would encourage skipping 9x9 for teaching, I found that this doesn't really give a sense of territory and instead making one mistake often costs you the game.

Sensei's Library also has some collated thoughts from people on board sizes, and some other different variants for teaching

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