I had another idea for how to set up the player incentives, building on this very natural idea by @martin3141 :
I really like the simplicity of this, and would prefer to combine it with stone scoring. For instance, when every (non-eliminated) player passes, the game is over and each player is given 1$ for each stone they have on the board.
If the result of filling out remaining territories is obvious in advance, a player can propose a certain distribution of payouts, and if every non-eliminated player as well as the referee agrees the game can be ended without playing it out.
I think this does for a good game in itself, quite similar to what we’re doing in the first game but in my opinion a bit simpler to explain. I also think it’s better that a player in second place on points can choose to be content with their points, rather than having second place be equivalent to losing. @yebellz seemed to want to avoid this in the original rules:
so this might be up for debate. Personally I don’t see any problems with allowing this. The player in second place still wants to maximize their own points as much as possible.
But let’s now take this a step further to see if we can improve this to incentivize players which expect that they will not surive until the end of the game. What if, in addition to the payout at the end of the game, we made such a payout every time a player was eliminated? Specifically:
If N players are eliminated in a round, all the remaining players get N$ for each stone they have on the board.
This makes it so that, even if you see no way of your stones staying alive until the end of the game, you should try to stay alive until some other player is eliminated. It is directly in your interest to help capture some other players big group, even though this might not open up a chance for you to live, since this makes it more likely that they will be eliminated before you.
Probably the last payout (when everyone passes) should be K$ per stone, where K is the number of remaining players in the game. Then the amount of money paid out during the game is bounded by the number of players times the number of intersections on the board.
Of course I’m not advocating playing for real money, this is just an easy way of talking about incentives. If you want to think about where the money comes from, I think a practical solution is that each player pays 81$ (or whatever the board size is) up front, and then the referee takes what’s left at the end of the game. But again, the money is imaginary.
What do you all think about this idea, any obvious flaws?