Diplomatic Go

[antonTobi]

I think the basic idea with the prize pool is ok, but with some better chosen amounts it would allow us to differentiate between more different scenarios. I’ll have to give up on my idea that a 3-way draw is (almost) as bad as 3rd place though, maintaining that preference with a fixed payout seems very unnatural (and maybe impossible).

I thought it felt right when just thinking about rankings, but if we want to think about payouts then draws necessarily become more attractive.

(sorry for making many posts in a row…)

[martin3141]

If you want to hear my opinion, I believe the incentives are already refined enough, and telling people whether a 3-way draw or second place is preferable is not really necessary.

After all you le_4TC pointed out that there is a trade-off between predictability and diplomacy. So I see no need to make the incentives as refined as possible.

[yebellz]

Ultimately, players might also care about who they beat, and how other’s perform. I think it oversimplifies things to think that the outcome only boils down to the individual’s own ranking.

If I’m finishing in a particular rank, and there’s nothing I can do to change that, I’m going to do my best to influence the placement of the other players as I see fit. That would most likely be motivated by the objective of retaliation.

[Maharani]

Quick I love you all for this beautiful discussion. Everyone is putting so much considered thought into it I just love it. Keep going y’all!

[yebellz]

My point here is that Charlie (player C) might have a distinct preference between these outcomes:

1. A > B > C > D > E
2. B > A > C > D > E
3. A > B > C > E > D
4. A > D > C > B > E
5. A = B > C > D > E
6. A > B > C > D = E
7. A = B > C > D = E

It depends on how Charlie feels about Alice, Bob, Dave, and Eve.

[antonTobi]

You’re right, I got a little too caught up in the details and forgot about the bigger picture.

With that in mind, I prefer the original “beat as many other players as possible”. I think that is the simplest to explain and conceptualize.

But I also like the yebellz perspective of multiple head to head games, which would treat a three-way draw and second place on sort of equal footing (of course one might be preferred depending on the players involved).

[antonTobi]

It would be good to discuss some concrete positions before the game starts, to make sure that we haven’t missed some big problems with the rules. Let’s start with a relatively basic one:

The current stone counts are:
21
17
16
12

Blue, red and yellow have enough eyes to avoid capture unless they decide to fill in their own eyes. Black could potentially be captured, but it is not in yellow’s interest to help.

A possible outcome is that everyone waits around until black is eliminated (we should probably have an option to “fast forward” a few turns, without anyone making moves, if everyone agrees). Red, blue and yellow can then safely fill in another one of their own eyes, leaving everyone with 3 eyes exactly. Blue still has fewer stones than red, so their last hope is to fill another eye. This gives yellow the opportunity to kill blue together with red, but yellow doesn’t have to do that to win, so let’s assume that yellow refuses. Then red has to decide between sharing second place with blue, or follow along and also fill in another eye, which will give yellow the opportunity to kill red together with blue (but again yellow has no intrinsic motivation to do so). If yellow doesn’t capture anybody, the game ends with this ranking:

Yellow > Red > Blue > Black

Now go back to the beginning, and consider what happens if black fills in one of their own eyes, allowing blue and red to capture. What happens afterwards is a bit complicated, but it looks like red can easily secure enough area to win. Let’s assume that blue gets exactly 5 more stones, putting them on equal footing with yellow. We are then in a situation similar to earlier, where blue or yellow might fill in their eyes, allowing red the opportunity to capture. If red doesn’t capture anybody, the game ends with the ranking:

Red > Yellow = Blue > Black

With the cooperation of red, either yellow or blue could beat out the other in the final ranking (but capturing looks risky for red, so I think the above is the most likely outcome).

Notice that there are lots of cases where it’s possible to impact the final ranking of other players in a very direct way. It’s not only the players with strong board positions that have this control: In the above example, yellow looks the strongest and black the weakest. But black can choose to deny yellow the victory.

In conclusion, being on good terms with other players is extremely important.

[shinuito]

@le_4TC

Blue, red and yellow have enough eyes to avoid capture unless they decide to fill in their own eyes.

Would they decide to fill in their own eyes?

@le_4TC

Red, blue and yellow can then safely fill in another one of their own eyes, leaving everyone with 3 eyes exactly.

Is this looking way forward again after black is eliminated and assuming they need to play a new stone or be eliminated?

[antonTobi]

They presumably wouldn’t fill in their own eyes while black is still in the game, since they won’t be close to elimination at that point, so there’s no reason to risk being captured. After black is eliminated, I see no reason not to fill in another eye. Whether they do it right after black is eliminated or right before they themselves are eliminated probably doesn’t make any difference.

[shinuito]

Well I imagine it’s still better to get dame or potential new eyespace points than fill in your own eyespace in terms of getting more stones on the board?

[martin3141]

I believe the current rules are such that blacks stones stay on board even after elimination.

[antonTobi]

Of course, but in this scenario there are no such points on the board. (this is the scenario where black doesn’t fill their own eye, so the black stones will remain on the board even after black is eliminated)

[shinuito]

@martin3141

I believe the current rules are such that blacks stones stay on board even after elimination.

@le_4TC

(this is the scenario where black doesn’t fill their own eye, so the black stones will remain on the board even after black is eliminated)

Ah yes I was forgetting about this. I was probably thinking about the other version where people got eliminated when all their stones were gone.

[antonTobi]

It is a little bit confusing to use the same term to mean something different now compared to the first game, especially given the connotations of the word “elimination”. In the first game, a player was eliminated from the game when all their stones had been eliminated from the board. Now there is no such connection. Does anyone have any ideas for an alternative word to use instead of “elimination”, which fits better with the current rule?

[Vsotvep]

Next board to discuss:

We have:

Blue	12
Yellow	11
Red	10
White	5
Black	5

It is round 12. Players need at least 13/2 - 3 = 3.5 points on the board to not be eliminated, hence every player needs 4 stones remaining at the start of next round.

Let’s think about what players could have for incentives here. Does every player have a meaningful goal?

[martin3141]

In my opinion if depends on what happened earlier in the game, but considering the position in a vacuum, here’s what I’d be thinking:

Black and White are the closest to being eliminated, so perhaps they fight for second to last place. Black’s obvious attempt to capture four White stones is J8. White might try to block this by playing J8 themselves, setting up a collision, and play J5 on their second move. If Black anticipates this choice, they could also submit J9, which would capture White in this scenario. So It’s somewhat of a 50/50 if Black manages to capture White.

The other players are not close to elimination yet. Yellow and Red are entangeled in a big fight, and it seems c4 is an important next move. Yellow may also play H3 to escape the “3-atari”, or fill a liberty of the three red stones at F2.

Looks like Blue has the best position, especially since the other players are fighting against each other.

[Vsotvep]

Here are my thoughts for each player.

White

White has the largest problem: any other player getting J8 would mean elimination, since getting those stones captured would mean the elimination of White. White also has the problem that any player can play J9 in anticipation to White playing J8, so this move is risky in any way.
Blue can be an ally to White, since J8 + H9 will mean that the H8 stone gets captured before White’s last liberty is removed.

Black

Black needs to survive longer than White. Apart from capturing the White stones, Black has another survival strategy: playing anywhere on the board, hoping not to be captured, creating more groups and hoping White will remain capturable for another round. Unless three of Black’s stones are captured, this will ensure Black’s survival.
Another interesting deal that Black can offer to all other players is to capture the Red stones. With smart collisions it may be possible to capture as many as 8 of Red’s stones (ensuring that Red would be eliminated). Since Black is no threat to Blue nor Yellow, they’ll likely agree, and White will likely agree, since it would ensure their survival for another round. Of course, Black could betray White, so this is a tricky decision.

Red

Red really needs to get C4 in before the groups are disconnected. However, Red may be aware of their impending doom if all four other players work together, and choose to eliminate White by playing J8. This would ensure that Red is eliminated simultaneously with White. A strategy could be to block C4, and then move to J8 to prevent ending last.

Yellow

The most immediate concern for Yellow is being disconnected. None of the groups are really in much danger though, with only B3 being in 2-atari. Yellow could ask the assistance of another player to get C4 in. Collaborating could also open up E6 being played simultaneously, which would be a big leap towards connection.

Blue

Blue has no dangers at all of being captured, and can pretty much choose whatever they wish to do. They’ll have to be careful not to allow Yellow to grow too strong, since Yellow is their biggest rival at this point. Blue may for instance insist on playing E6, instead of having Yellow do that. Blue also has no incentive to play C4 to help Yellow.

[martin3141]

It appears to me that the newly defined elimination rule and objective motivates players to work against other players who are close to them in terms of points / board position.

In the latest example I would rank

Blue > Yellow > Red > Black ~= White

in terms of board presence.

Let’s consider the perspective of player Yellow. I imagine they would be interested in preventing player Red from overtaking them, and potentially hope to eventually prevail longer than player Blue. On the other hand the players Black and White currently don’t pose a big threat to Yellow.

I’m assuming other players would make similar arguments, and as a result, all players are somewhat motivated to work against whoever is close to them in terms of board presence. Of course the exact position needs to be taken inco consideration too, as players would naturally want to capture chains next to their own chains.

All of this makes me think that player Blue, in addition to having a clear lead, also has the ability to cooperate with or even manipulate players White and Black, who probably don’t mind helping player Blue, who they can’t realistically overtake, and they might hope to survive longer by cooperating with Blue.

Here’s how player Blue might try to leverage this to their advantage: They play 1.H5 and hope for their best-case scenario, which is that White plays 1.J5 and Black plays 1.J8. This would result in both Black and White being simultaneously captured and eliminated, giving Blue control over the upper-right corner and pretty much ensure their win. How could Blue try to manipulate White and Black in a way that this best-case scenario happens? For example by convincing White that Black will play 1.J9. At the same time they tell Black that White will not play 1.J8.

Whether such a ploy would work or not is unsure of course. Regardless I believe the new incentives make it difficult to justify teaming up against the leading player (except for the “second place player”). Instead players might rather sabotage opponents who they hope to overtake in the final ranking.

I’m undecided whether this is a good or a bad thing.

[Vsotvep]

I think I agree, I had a hard time coming up with any reason for any of the players to attack Blue on this board. And I had a hard time finding incentive for Blue to play. On the other hand, with this board Blue is disproportionally far ahead of the rest (which was more or less on purpuse: I wanted one safe strong player, two fighting strong players and two desperate weak players).

---

I think due to similar unbalance HHG got very strong in the first game we played, because Haze and I were keeping each other busy, as did le_4TC and 李建澔, but due to a ceasefire between Haze and I, we were able to limit HHG by capturing the lower left and disabling a potential move creating eyes.

Probably the incentive should remain the same in the example board above: although Blue is too strong to really be harmed by any of the players, Red is also pretty strong, but can be eliminated in one move by all other players working together. Clearly this is good for every of the other players (since they’d not be first to be eliminated).

[yebellz]

Suppose in a five player game, would a hypothetical player, Dave, ever prefer the latter outcome over the former?

1. A > B > C > D > E
2. B > C > E > A > D

Of course, the latter case offers a strictly worse personal ranking, so preferring it directly contradicts the stated objective and perhaps one might even call Dave irrational for playing to prefer such an outcome over the former.

However, let’s imagine that Dave was actually in a much stronger position a few rounds ago, and thought that he had a pretty good shot at winning, except that a vicious betrayal by what was a sworn ally in Alice knocked him out of his golden position. Suppose his position was so wrecked by Alice’s aggression that he now sees only two possible strategic paths that roughly correspond to influencing the game toward one of the above outcomes or the other.

Is taking 4th place (instead of 5th) really such a great consolation prize? Or would he find more satisfaction in saying that he managed to ruin Alice’s game as well?

Perhaps, if Dave had thought carefully, he might have instead even anticipated the attack by Alice earlier, and although Dave might not have been able to mitigate the attack with board plays, he could have threatened such retaliation in attempt to prevent Alice’s betrayal.

Honestly, in a losing position, I would care more about settling grudges than optimizing my own rank.