markus, your third bullet is probably way too harsh.
Maybe make that if you get 3 resignations in a 48-hour period, you may not play 3p in the rest of those 48 hours? It may still be a bad idea altogether. Incidentally, how often are people forced to resign right now? I have all sorts of connection issues but I always manage to reconnect without problems.
Adam, we don't include bots in the leaderboard because there is a big slice of the population playing only bots, and that might skew the ratings. But in principle I wouldn't be against that, but there is the problem of the bot being really bad as it is now.
Then I don't understand what determinism has to do with the issue at hand. Is the problem that the bot becomes predictable? A lot of players are quite predictable as well, at least for better players that know them well. And anyway, a bot need not be necessarily predictable. Most good chess bots are non-deterministic, for example.
Regarding the relative placement of the players and bot, I don't really know how the algorithm works.
But maybe you could secretly rank the bot, and if and only if the bot beats you, count that as a loss relative to the bot. Anyway, when was the last time somebody in contention resigned on you? It won't be very common.
But let me change my stance and argumentate a bit more aggressively instead of defensively. Your proposal of discarding the result of the two players who did not resign will discard a lot of valid results, if resigning stays as common as it is now - and we are not sure we'll be able to do much to reduce it. In a lot of games with two similarily-skilled players and one weaker player, most games won't be able to help ranking the two good players relative to each other.
And for the player in second place the games might even evolve in a game of "stay in contention, screw the third", hoping for him to resign. The player in the losing position always
has an amount of kingmaking (or kingvoiding?) power that is bigger than what can normally happen in any game of 3p Dominion.
In my view this leads to problematic situations being more common than if we allow bot replacement, given that players tend to resign when they are hopelessly losing.
Bot is problematic when it has a good shot at first or second place.
Voiding the result is problematic when the resigning player is hopelessly losing, and has the possibility of voiding half the win for the player who is hopelessly winning.
Since resigning mostly happens when a player is hopelessly losing, bot is less commonly problematic than the alternative.
The voiding system is quick and more fair than what is in place now, so I'm fine with that in the meantime. But I believe it's inferior to having the possibility of playing it out with a bot.
I think the ideal solution would be:
Player A resigns. B and C get a window with three choices:
Resign as second place
Void the remaining game
Play it out with a bot.
If either one resigns, we have a clean result that everybody agrees upon. If both void, we have a clean result that everybody agrees upon. If either player wants to play it out, then they should do so, and that game should be ranked, in the interest of the leading player.
If both resign, uh, they all unlock Saboteur as an easter egg, and you count that as a void.
This way everybody is happy: the leading player is never forced to forfeit by an stubborn opponent, the second place guy can get it over with quickly if they want to, an early resign can safely end in a void if everybody is fine with that, and the bot gets to play a few games and is happy.