Kibitz for Diplomatic Go: The First Game

[Aumpa]

Assuming that nobody wants to lose (a loss is the worst outcome, according to the rules, and everyone is playing the same game) and everyone is rational so that they will collaborate with anyone to avoid losing, then it follows that they’ll kill a group of the leading player, then the next leading player after that. If white in the above diagram is the sole leader, of course they should kill the group, nonwithstanding that black will appear to have the most to gain. I don’t think black could make a living group in the void left by the white stones versus four players (the other three now have white on their side, with the same motivation to stop black).

So with 5 players on a 9x9, I think the game is likely to be a stalemate.

But I heard that players can be eliminated. I don’t remember seeing that in the rules, but I guess if you have no stones alive on the board you’re “out” with a loss and cannot play any more moves. In that case, I guess it’s possible for a group to make unconditional life after one or more players are eliminated. I think vsotvep realizes this, and may try to eliminate a player or two if it gives them a chance of winning.

[yebellz]

@Aumpa

everyone is rational so that they will collaborate with anyone to avoid losing

It is possible that losing will become unavoidable for some players, that is, they may not have the opportunity to make more points than the other players. Thus, a player may be left with choosing between: 1) losing while opponent A wins, or 2) losing while opponent B wins, or 3) maybe somehow negotiating their way into a draw with the leverage that they have.

@Aumpa

But I heard that players can be eliminated. I don’t remember seeing that in the rules

You can find the full rules in the first post of this thread: Diplomatic Go
See item 7 under “General Order of Play”

@Aumpa

I think vsotvep realizes this, and may try to eliminate a player or two if it gives them a chance of winning.

Yes, he mentions this in his Kibitz log above.

[yebellz]

Private kibitz log from Haze_with_a_Z

---

Sup Spectators! Idk whom you all are but I’ve prob seen you around the forums or on OGS. Actually I’d kinda be surprised if I haven’t seen you before because I’ve seen a lot of people on here but idk. It might be good that I am not in there because I might post too much in the thread(my malko chat already has a bunch of posts because I post each thought(more like each sentence) in there and I manage to go off topic when I am the only one in there. Like I started getting mad at discobot in the first one). That is prob something unnecessary and shouldn’t do but I still do it anyways(stupid me, hahaha). Well I hope you are enjoying yourself throughout your day!

Also for fun I came up with 3 moves to be my 4,5, and 6 moves. They are kinda stupid but like I had to come up with something and I had no clue where to put them. They do fit in with my random strat and that is a good thing. The only way I can beat all of those people is by being unpredictable and not failing on purpose or something stupid like that. Here they are:
4. H3
5. G3
6. D2
Also because pictures are fun, here is a crab:

-Haze with a Z

it won’t let me indent my name D:

[yebellz]

Private kibitz log from Vsotvep

---

Round 6

Haze didn’t play F8, I’m still believing they’re trying to play unpredictably and by doing so end up getting in a worse position, and their chat in the main discussion seemed to elude to that as well, so I have tried reinforcing that strategy by stating that I was indeed clueless where they would play.
Now Haze has three groups, that’s what matters most, in the end.

I think HHG has more benefit trying to creep into the lower left than to come into the top area, especially with F8 in place. Or at least, I hope I can convince HHG of that point. Nevertheless, I’d like to get D8 in at some point, since I’m afraid to be backstabbed any moment now

le_4TC will probably want to make G3 stronger, attacking yellow gives him most value, so I expect G2 / H3 there. 李建澔 on the other hand wants to connect the stones, so might also play G2 / H3.

le_4TC has asked me if I’m planning to play H6, and offers to tell Haze that he wants to get a first move collision on H6 between blue and red, such that black can play their second move on H6.

I’m indeed expecting Haze to play H6, but he’s been indeed very unpredictable so far. H6 will still be a good move for me even if Haze plays somewhere else. The thing I’m afraid of is this, though:

It seems like le_4TC’s offer to Haze is flawed, since Haze needs to reliably set up a first move collision to make sure their second move is at H6. There is however an interesting strategy for Haze & le_4TC if they know reliably that I’ll play H6:

My two stones are in 1-atari, so I’ll practically have to play J6 to defend. There are two scenarios then:

Haze and I collide on J6, which means I should probably capture the G5 stones? Or I should play around G8 / H8 to attack Haze

Haze and I do not collide, which might result in the following situation, where I’ll have to flip a coin for J5 vs. J4 for Haze to capture me.

Both of those scenarios are good for le_4TC: I get split, the two yellow stones might die.

I might play F5 as a first move, and let Haze get H6. Since they’ve been trying to be unpredictable, there is a chance they’ll play somewhere else, it’s not too bad for me, since I gain an attack both on le_4TC’s two stones and on 李建澔’s two stones in the form of 2-atari’s.

If I actually somehow discovered the secret plan by Haze and le_4TC, then F5 is an amazing move:

[Aumpa]

@yebellz

It is possible that losing will become unavoidable for some players.

How can a player not have a chance at a draw if they’re willing to work against the leading player?

[yebellz]

It won’t always be obvious who the leading player is. Who do you think is leading in the game right now? Do you think there is consensus among the players about that?

A leading player might also become unstoppable (i.e., they build unconditional life before others rise to do something about it), so it could become irrelevant that a weak player is willing to try to help against them, when it is already futile.

Further, even if there is a weaker player with a chance to choose the winner, they might not necessarily see the opportunity to use that leverage to coerce the draw. Further, the other players might be willing to take the chances that the weaker player throws the game against them, in order to at least have a chance to outright win rather than settle for a draw. What did you think about the scenario that I discussed above?

Do you think Haze has been playing rationally in this game? What about the other players?

[Aumpa]

Well, there is no single leading player now, but those with more stones (ie, everyone but Haze) is slightly better. But their advantages over Haze are not sufficient to break into a winning lead.

I don’t think Haze has played great so far, but I think others can help them out when it becomes necessary to stop a player from gaining a winning position.

You say a player might be in a losing position if another player becomes unstoppable, but that’s just what I’m saying cannot be achieved by anyone.

@yebellz

What did you think about the scenario that I discussed above?

Do you mean the Alice, Bob, Charlie scenario? I’m not sure what to make of it. It could be written as a game theory matrix chart to see payoffs, but that might be abstractly removed from Five Player Diplomacy Go. So it might not apply.

My suspicion that Five Player Diplomacy Go is a draw with rational play is just my intuition about it. I can’t prove it, but I’m not convinced otherwise, either.

[KAOSkonfused]

@yebellz

It won’t always be obvious who the leading player is. Who do you think is leading in the game right now?

I think that HHG is best off at the moment, because he has the fewest collisions with other players - but that can change anytime.

@yebellz

Do you think there is consensus among the players about that?

No.
Also, I assume that everybody feels too threatened with their own position to be able to focus on destroying the “leading” player. And it’s very unlikely that four of them can agree on a mutual strategy. I don’t see that happen.
9x9 is pure fighting in “normal” Go - and even more so in Diplomatic Go. The players’ strategies would be totally different if this was 13x13. (But it would be hard to realize such a long game without some of the players losing interest, so I’m sure 9x9 is a good choice.)

[quote=“yebellz, post:87, topic:29936”]
Do you think Haze has been playing rationally in this game? What about the other players?[/quote]

Haze’s moves certainly all make sense from their view. I guess, all of them have been playing rationally, more or less. We don’t know about all the alliances and plans the players have/had, and it also makes a difference here how strong someone is as a Go player in general.

[Aumpa]

@KAOSkonfused

And it’s very unlikely that four of them can agree on a mutual strategy.

I think it’s very likely for four players to agree on the necessary tactical moves required to avoid losing. If the alternative to not agreeing is to lose, why wouldn’t they agree?

[shinuito]

@yebellz

However, since the group is made of two distinct chains, in theory , four opponents could cooperate to first capture three stones with plays at A1 and B2, and then fill the remaining eyes in a later turn.

So can you pick a move that’s been played in another turn (already a stone there) to guarantee a collision for you first choice to get a chance to play the second choice?

@yebellz

One of them plays at C8 as their first choice, while the other intentionally collides (with an already placed stone) for their first choice and plays at C8 for their second choice.

I think in that example too, players might be more willing to capture a group in territory scoring since they might be rewarded with the actual capture, even if ultimately it ends up as blacks territory.

[shinuito]

I wonder would Vsotvep consider doing a review afterward since they have such detailed kibitz logs, or maybe le_4TC will make a video, or maybe they could collab on a video review

[yebellz]

@shinuito

So can you pick a move that’s been played in another turn (already a stone there) to guarantee a collision for you first choice to get a chance to play the second choice?

Yes, an intentional collision with a pre-existing stone is allowed. I used that in an example earlier here: Diplomatic Go - #6 by yebellz

@shinuito

players might be more willing to capture a group in territory scoring since they might be rewarded with the actual capture

I’m sure if I fully understood your specific capture counting scheme, since I think there are some details that would need to be ironed out. It’s a bit odd to share captures between multiple players, since it ends up double-counting stones. It also seems that two players could abuse this by feeding stones to each other to boost their scores over the other players, and they could do this at the end of the game, when no other moves are worthwhile.

Based on my rough understanding of your system, if all of the players share credit for the capture, isn’t it effectively like no one getting credit for the captures? Of course in the particular 5-eye case that I gave above, it has to happen in two stages, with only two of the players getting credit for the first part, and only 3 getting credit for the second part. However, one could imagine a simple 4 eye group that all 4 opponents cooperated to capture. If they all get credited for the same number of captures, that provides no additional incentive to capture.

However, I think the above issues are not even the biggest problem with trying to apply territory scoring. A much bigger issue is how to settle life and death disputes at the end of the game. Telling players to play on forces players to lose points (under territory scoring) by filling in territory to capture dead stones.

How do you propose to resolve this issue and deal with life/death disputes under a territory scoring system?

In summary, here are the flaws that I see with territory scoring for this type of game:

1. Needs additional rules (and potential complexity) to determine who gets credit for each capture.
2. Could possible be abused by players feeding stones to each other to arbitrarily inflate their scores (imagine this happening in a quid pro quo setup between two allies at the end of the game).
3. Difficult to settle life and death disputes without distorting the score.

[shinuito]

@yebellz

It also seems that two players could abuse this by feeding stones to each other to boost their scores over the other players, and they could do this at the end of the game, when no other moves are worthwhile.

Actually yeah I didn’t think about that. I’m imagining setting up a ko but with an ally.

@yebellz

if all of the players share credit for the capture, isn’t it effectively like no one getting credit for the captures?

I think that only makes sense when the capturing players = all of the players. Somebody is losing out and not getting points.

@yebellz

How do you propose to resolve this issue and deal with life/death disputes under a territory scoring system?

I don’t even think I understand all the ins and outs of territory scoring in Japanese rules. S Alexander shared a Korean pro game too right where they had to question whether it was necessary to fill in a ko. I guess trying to come up with every possible end case before playing might not be feasible. It could still be fun to play though until something like that arose.

I’m not saying territory would be better, only that if feasible it would possibly incentivise teamwork in captures more than area scoring would.

[yebellz]

@Aumpa

My suspicion that Five Player Diplomacy Go is a draw with rational play is just my intuition about it. I can’t prove it, but I’m not convinced otherwise, either.

I think your intuition may be based on some questionable assumptions:

1. All players will always play rationally, which implies that they need to figure out the best tactics in all situations.
2. The players are so risk-adverse that they prioritize avoiding a loss above all else.

To express my point with rhetorical questions, consider:

1. Why don’t all games of chess end in draws?
2. Why don’t all games of regular diplomacy end in 7-way draws?

@Aumpa

I think it’s very likely for four players to agree on the necessary tactical moves required to avoid losing. If the alternative to not agreeing is to lose, why wouldn’t they agree?

As I mentioned earlier, I think, in Diplomatic Go, it is fundamentally harder to achieve a draw, since the victory condition is plurality rather than majority.

In regular diplomacy, it’s quite common for games to end with 3-way or 4-way draws, since the players will often rally to stop the leader from capturing 18 (of the 34) supply centers (SCs), and these draws can be very stable, since the leader might be holding 15-17 SCs, which forces the coalition to unite around stopping them, since the choice is cleanly between forcing a draw vs allowing the leader to win.

On the other hand, in Diplomatic Go, with the victory condition simply being to have the largest score (i.e., not requiring control of a majority of the area on the board), stopping the leader (say by cooperating to kill one of their groups) doesn’t just prevent that leader from winning, but also shifts the lead to someone else, so it doesn’t always prevent losing. The only way to prevent losing (by the weaker players) is to possibly coerce all of the potential leaders into accepting a draw. However, the potential leaders might not want to just settle for a draw, and might rather just want to force the weaker players to decide which leader gets to win. How people might prefer between these options depends entirely on their risk aversion/tolerance and how much they specifically value winning vs drawing vs losing.

To illustrate this concept, consider a slightly modified version of rock-paper-scissors, where the players have the option of offering/accepting a draw before picking their move, and if a draw is not agreed beforehand, they only throw once with the game ending as either a win/loss or draw.

Now imagine that you are playing this game and your opponent has offered a draw before the moves are thrown. Do you accept? If you do, you are taking the draw with 100% probability, which avoids the possibility of losing, but also avoids the possibility of winning. If you don’t accept the draw, you have 1/3 chance each for winning, losing, drawing (assuming that you know nothing about your opponent’s potential biases for picking any particular move). How you would play in such a game (whether or not you accept the draw) depends entirely upon your risk tolerance/aversion.

In game theory (GT), the fundamental basis for understanding such decision-making is that each player will have preferences between different probability distributions over the definite outcomes (aka “lotteries” to use the typical GT phrase). Under mild and reasonable assumptions that these preferences are self-consistent, in theory, a utility (payoff) function does exist, however, in practice, the specific utility function is not obvious and not even feasible to determine without a very precise understanding of each player’s risk tolerance/aversion.

Diplomatic Go (and regular diplomacy) are not only imperfect information games (due to the unknown actions from simultaneous moves and private chat), but also incomplete information games, since every player’s utility function and risk tolerance are not necessarily common knowledge.

[shinuito]

@yebellz

Why don’t all games of chess end in draws?

There’s a valid (by making moves) way to play a draw in chess where you repeat the board position or play enough moves without capture. I think offering a draw there is just cutting that process short. I mean a lot of games of chess seem to be draws.

I know it was rhetorical, but I guess it depends on your mentality. Do you consider a draw as better than a loss. Is a draw by perpetual check when you were clearly about to be check mated a better outcome say than just losing outright. Pointswise in a tournament probably.

I kind of assume on the 9x9 board with 5 players somebody probably gets eliminated because space runs out fast. Then you have to re-ask the question if Diplo Go on 9x9 with 4,3 players should be a draw.

@yebellz

The only way to prevent losing (by the weaker players) is to possibly coerce all of the potential leaders into accepting a draw. However, the potential leaders might not want to just settle for a draw, and might rather just want to force the weaker players to decide which leader gets to win. How people might prefer between these options depends entirely on their risk aversion/tolerance and how much they specifically value winning vs drawing vs losing.

I think we might need to come up with some 3-4 player 9x9 seki’s like the hanezeki - where it’s not really a seki only in the sense that it’s not worth capturing because the outcome is worse that not playing - hence draw offerings

[yebellz]

@shinuito

There’s a valid (by making moves) way to play a draw in chess where you repeat the board position or play enough moves without capture.

There are also a lot of other ways to draw the game, via stalemate (i.e., having no legal moves that do no result in self-check) or both players having too little material to achieve checkmate. In regards to the latter, it is well-known which combinations should be insufficient, so players will simply offer a draw should such a material deficiency be reached, rather than wasting more time to trigger the no capture rule.

@shinuito

I mean a lot of games of chess seem to be draws.

Yes, of course I know that a lot of high-level chess games are draws, and it is widely believed that perfect play in chess should lead to a draw. Given that assumption, the point of my rhetoric was to consider why aren’t ALL chess games draws? Obviously, one reason is that human players cannot achieve perfect play, and hence fall short of the ideal rational agent that makes perfectly rational (and hence strategically flawless) moves. Further, humans generally choose to actually play the game, rather than offer and accept a draw immediately (before the first move is even played). This indicates that people are willing to accept some risk of losing, for the sake of having some chance of winning. Of course, externalities (like the requirement to decisively beat the title holder in order to mount a successful challenge) will also motivate going for wins, rather than settling for only draws.

@shinuito

Do you consider a draw as better than a loss.

Yes, I consider a draw to be better than a loss, but my point is to say that it is not enough to just consider a model for player preferences that only specifies “Win > Draw > Loss”. To really begin to model what rational behavior may be in a game, one must also consider player’s risk tolerance/aversion. For example, what may be a player’s preference between a strategic choice that they believe leads to 30% win, 30% draw, 40% loss versus another strategic choice that they believe leads to 10% win, 75% draw, 15% loss?

In my previous post, my last point ultimately says that is a naive assumption that payoffs (utility function) for win, draw, loss could be quantified with a simple choice of numbers (like +1, 0, -1). Even though this payoff assignment satisfies the inequality “win > draw > loss”, they do not necessarily capture the actual risk aversion/tolerance of a particular human player.

@shinuito

I think we might need to come up with some 3-4 player 9x9 seki’s like the hanezeki - where it’s not really a seki only in the sense that it’s not worth capturing because the outcome is worse that not playing - hence draw offerings

I think it’s interesting to call such positions hanezeki, but ultimately, if players are compelled to stop capturing and pass to end the game, they still have to score, which may produce a decisive winner. One would have to threaten to change that outcome, in order to compel the presumptive winner to settle for a draw instead.

[shinuito]

I was just thinking of the hanezeki examples https://senseis.xmp.net/?Hanezeki

Where it’s a seki even though in theory the stones can be killed. Like this one on that page
I guess I was thinking of cases where a draw was offered but maybe the board was tied anyway, or a least a tie between a few players.

I guess I’m not sure in what situations you’d offer a draw instead of going to scoring.

[yebellz]

I love that circular hanezeki by Harry Fearnley.

I even created a topic in the past about it:

Life and Death Problem

Status? [position] Spoilers below! It’s quite fun to read out this problem, so don’t scroll down to the discussion below until you want to see the analysis that gives it away.

See this post for my detailed analysis.

@shinuito

I guess I’m not sure in what situations you’d offer a draw instead of going to scoring.

In my earlier abstract example involving Alice, Bob, and Charlie, I was envisioning something like this:

Editable board

Where the players are:
Alice
Bob
Charlie

If they all pass and go to scoring, then they might count Charlie’s stones as dead and the rest of the stones as alive. This would give Bob the win.

Alice would want to claim that Bob’s stones in the bottom right are dead, but needs the cooperation of Charlie to accomplish that.

Thus, Charlie could choose to help Alice win instead of Bob, and maybe he would wish to do that in order to spite Bob. Alternative, he might wish to simply let Bob win in order to spite Alice.

However, given his position as the kingmaker, he could instead try to persuade both Alice and Bob to vote for the three-way draw, by threatening to punish whoever does not comply. If Alice and Bob are very risk averse, they may just readily comply with accepting a three-way draw.

However, yet again, maybe Alice and Bob really hate the idea of Charlie weaseling their way into a draw in this way, denying either of them from getting win, so maybe they might both refuse to accept a draw, and simply tell Charlie to pick a winner at random. This could make sense, if both Alice and Bob would rather prefer a 50% win, 50% loss lottery to a 100% three-way draw outcome.

[Aumpa]

Saying that best rational play in chess results in a draw is the best conjecture, just as I’m suggesting for 5-player-9x9-Diplo-Go. Chess hasn’t been solved as a draw even by the best AI. And while 5p99DG is certainly complicated, I think rational play to force a draw is well within player capacity already, unlike chess. This is because of the flexibility of directing an attack towards any other player on any turn.

I think the Alice, Bob, and Charlie scenario is unlikely to arise out of 5p99DG. Alice and Bob would have effectively had to beat three other players, eliminating two, for a chance at getting that position.

Certainly, by complications of diplomacy and irrational play (e.g., a player not caring if they lose, in other words not even really playing) it’s possible for one to win, or a have a 2, 3, or 4-way draw after some have been eliminated. I’ve always asserted since the beginning that it’s drawish with rational play. I should add that that level of rational play is within player capacity.