Yes, capturing appears to be pretty anecdotal with the rules weāre currently using. The black stones in the large white territory will die, but theyāre pretty much the only ones.
This game is almost-exactly Amazons, I think. The possibility to occasionally capture stones doesnāt feel like itās worth the extra complexity and visual clutter of using black and white stones instead of immortal arrows.
Also, the 11x11 board was a bit ambitious!
As for the infinite cycle due to suicide: if we forbid suicide, then itās possible that a player can move an Amazon, but cannot shoot a stone. This is especially true because Amazons can move diagonally, whereas stones only have orthogonal liberties. What happens then? Does this player lose?
It seems reasonable to define such a case as an illegal move.
Even with banning suicidal moves, it could still be possible that the players endlessly cycle the game position in a manner analogous to triple ko.
Even though there havenāt been any captures on the board, thereās been a few times where they affected how I played. Nothing too major, but Iāve enjoyed that little sprinkle of go mechanics on top of amazons!
Good point. Yes, with illegal suicides and the āif you have no legal move, you loseā, that would be a loss. But itās a bit unsatisfying to break that beautiful part of Amazons (that an Amazons can always shoot if it can move). All the more reason to keep suicide legal and switch to stone scoring! 
Of course my go-to rule here would be positional superkoā¦ although draw by 3-fold repetition also feels kind of appropriate, given that Amazons draws some inspiration from chess
What kind of repeating positions are there? I think a regular ko shape would be easy to construct, but it seems like it would be super rare in actual play. If we have some more examples of repeating positions, that may help decide which repetition-handling rule feels most fair.
You could also go for much weirder versions of Go x Amazons like each move youāve the choice to play a Go stone normally, or move a go stone like and Amazon and shoot another stone.
I imagine that would be weird but maybe you could do area or stone scoring or whatever.
Positional superko would be a nightmare to play correctly. In standard go with positional superko, itās relatively easy to figure out which player will have to play a ko threat. In Amazons+Go+Positional superko, you can change the position by moving an Amazon. So the question becomes: how many different intersections can you move your Amazon to, while making sure that itās still in line of sight of the ko? If I have 3 different intersections to move my Amazon, and you have 2, thatās already 6 different positions for one ko. If there are three kos on the board, then the number of possible positions before we reach a cycle can be a very large number.
I think this might be one of the reasons why chess ends in a draw in case of a cycle, rather than having a ko rule like in go where the players keep playing but one of them has a forbidden move. The ko rule is too āpreciseā: you have to figure out which player will repeat the position first. In chess, pieces move around a lot, so repeating the position in a cycle is a lot less clean than a ko in go, and a ko rule would be a nightmare too.
C7-D6, D5
Re: Repetitions, it sounds like a simple ādraw by agreementā rule would work pretty well for our purposes? No need to track repeated board states, but the players would realize pretty soon if theyāre not making progress in the position.
Actually, even constructing a forced cycle is a bit tricky under the new rulesā¦ This was my first attempt:
The issue is that black can just play B6-D4, E4! (capturing and winning the ko at once)
This is of course assuming the rules are phrased such that E4 is captured immediately after the Amazon is moved.
There was a fun example of why a three fold repetition rule was supposedly changed in shogi. My source being Hidetchi of course:
tldr; an example from a game showed you could avoid threefold consecutive repetition and people could do a thue morse type sequence also to avoid threefold consecutive repetition of moves, so instead it became 4 time situational repetition.
This is one example of a position where the captures already matter quite a bit in the current rules: I need to respond here if I want to keep L8 and L9 dead.
K9-L10, K11
(Edit: although actually, I donāt think I will get to claim the territory left after capturing them, so keeping them dead isnāt worth that much after all!)
Yup. Similarly, it might not be interesting for me to capture D11.
It seems that with the new rules, it would more often be possible for the capturing Amazon to gain access to the empty area left behind.
F5-G4, F5 (first capture of the game!)
I can capture too!
D6-B8, D6
C10-D11, C10:
