Werewolf Go Game 1

Leira · August 12, 2022, 4:02pm

Part 4: The Knave of Coins and The Hermit

Knave of coins Hermit

A feverish dream overcame one of the adventurers:

“Mine eye hath seen thine 2 520 fates.”
“Canst I prevail?”
“Nay”

Out of @richyfourtytwo , @Jon_Ko , @Gia and @NeilAgg , only one is on Team White. We know this for certain (as long as we assume the Strong Yebellz Hypothesis).

Here is the reason. There are two options:

Team White is settler-faction. In this case, the team would be @Vsotvep , @MystWalker , @Barbanaira , @yebellz and one more (other than Leira ).
Team White is rebel-faction. In this case, the team would be Vsotvep , MystWalker , Barbanaira and one more (other than Leira or yebellz ).

In other words, there are only 2 things left to disambiguate. Namely:

Question 1: Which one of those 4 is on Team White.

Question 2: Whether viscount Yebellz is on Team Black or Team White.

Once this composition is known, who is the amnesiac doesn’t matter anymore.

To disambiguate Question 1, the quickest way would be to split those four possibilities into 2 and 2. Then, with two possibilities left to disambiguate once more.

To disambiguate Question 2 is trickier. For as long as there is balance between Team Black and Team White, Yebellz can jump into one or the other at a moment’s notice, still maintaining plausibility for a win. If Yebellz favors one team over the other, it would be a risky wager: it would mean that he bets on that team without full information, and could very well end up losing by his own hand.

One option is for Yebellz to make a throw-in himself. But this isn’t ideal because he wastes a move. Another option is to make a throw-in into Yebellz’s group. Or something else.

I’ll explore this in detail in the next part.

For now, I will present 4 different perspectives, based on two assumptions:

Assumption 4: Vsotvep is a settler-believer. I call this the “Vsotvep Viewpoint Hypothesis” (VVH). I think Vsotvep’s earnestness deserves at least some consideration. He’s also made moves that, if he had True Sight, would seem strange.
For example, spending 4 moves just to capture one stone is inefficient, if not for the purpose of gathering information; that stone was dead. A better plan for a rebel Vsotvep might have been to extend and endure the fight. Revealing rebelliousness at that point might not have been a huge issue considering there is a large territorial gain that would give his team an edge.

Assumption 5: Leira is a settler-believer. I call this the “Leira Viewpoint Hypothesis” (LVH). Of course, I know this one to be true, but non rebels have no particular reason to believe it. I suppose I can put forward a few arguments.
First, I’ve always claimed uncertainty. Second, playing on C10 would have made no sense if I had True Sight, but it can be explained as a failed guess, or an information gathering move. Third, I complied with yebellz’s request, an objectively bad move if I had True Sight. Moreover, making two bad moves would be particularly taxing on a team that has fewer moves.

So, I will use Strict Board Logic, Strong Yebellz Hypothesis and Naive Richard Hypothsis in combination with assumptions 4 and 5.

Perspective 1: SBL + SYH + NRH (You don’t have an inclination towards believing Vsotvep or Leira).

Total Scenarios: 20 (click for details)

Player	settlers	rebels	spy	amnesiac
Leira (black)	65.00%	30.00%	0.00%	5.00%
Barbanaira (white)	35.00%	50.00%	0.00%	15.00%
Jon Ko (red)	50.00%	40.00%	0.00%	10.00%
NeilAgg (yellow)	50.00%	40.00%	0.00%	10.00%
Vsotvep (blue)	35.00%	50.00%	0.00%	15.00%
richyfortytwo (green)	80.00%	0.00%	0.00%	20.00%
Gia (pink)	50.00%	40.00%	0.00%	10.00%
MystWalker (teal)	35.00%	50.00%	0.00%	15.00%
yebellz (orange)	0.00%	0.00%	100.00%	0.00%

Perspective 2: SBL + SYH + NRH + VVH (You believe Vsotvep but not Leira)

Total Scenarios: 10 (click for details)

Player	settlers	rebels	spy	amnesiac
Leira (black)	30.00%	60.00%	0.00%	10.00%
Barbanaira (white)	70.00%	30.00%	0.00%	0.00%
Jon Ko (red)	30.00%	60.00%	0.00%	10.00%
NeilAgg (yellow)	30.00%	60.00%	0.00%	10.00%
Vsotvep (blue)	70.00%	0.00%	0.00%	30.00%
richyfortytwo (green)	70.00%	0.00%	0.00%	30.00%
Gia (pink)	30.00%	60.00%	0.00%	10.00%
MystWalker (teal)	70.00%	30.00%	0.00%	0.00%
yebellz (orange)	0.00%	0.00%	100.00%	0.00%

Perspective 3: SBL + SYH + NRH + LVH (You believe Leira but not Vsotvep)

Total Scenarios: 14 (click for details)

Player	settlers	rebels	spy	amnesiac
Leira (black)	92.86%	0.00%	0.00%	7.14%
Barbanaira (white)	7.14%	71.43%	0.00%	21.43%
Jon Ko (red)	64.29%	28.57%	0.00%	7.14%
NeilAgg (yellow)	64.29%	28.57%	0.00%	7.14%
Vsotvep (blue)	7.14%	71.43%	0.00%	21.43%
richyfortytwo (green)	92.86%	0.00%	0.00%	7.14%
Gia (pink)	64.29%	28.57%	0.00%	7.14%
MystWalker (teal)	7.14%	71.43%	0.00%	21.43%
yebellz (orange)	0.00%	0.00%	100.00%	0.00%

Perspective 4: SBL + SYH + NRH + VVH + LVH (You both Vsotvep and Leira)

Total Scenarios: 4 (click for details)

Player	settlers	rebels	spy	amnesiac
Leira (black)	75.00%	0.00%	0.00%	25.00%
Barbanaira (white)	25.00%	75.00%	0.00%	0.00%
Jon Ko (red)	50.00%	50.00%	0.00%	0.00%
NeilAgg (yellow)	50.00%	50.00%	0.00%	0.00%
Vsotvep (blue)	25.00%	0.00%	0.00%	75.00%
richyfortytwo (green)	100.00%	0.00%	0.00%	0.00%
Gia (pink)	50.00%	50.00%	0.00%	0.00%
MystWalker (teal)	25.00%	75.00%	0.00%	0.00%
yebellz (orange)	0.00%	0.00%	100.00%	0.00%

Part 5 (Epiloge): Judgement

Leira remembered his broken vows. There was a reason he chose to be a Hermit and not a Preacher. Despite its name, the Order does not impose silence on its acolytes. None of his peers cared if he actually spoke or not—except, possibly, Fray Xavier, who truly believes the hermit has never uttered a word in his life.

Still, Leira could not wait to go back to working in silence. He braced his holy book and continued.

So, this are my conclusions. I already presented the 4 scenarios that I deem most likely. But you need not believe them. We need to only focus on Questions 1 and 2.

Here is a quick path to disambiguate Question 1

Vsotvep throw-in at L10:

If captured, both Gia and Jon_Ko are on Team Black. Possible continuation with Gia J11, Leira K12.
If not captured, both richiefourtytwo and NeilAgg are on Team Back. Then Gia may proceed to attempt a capture at M11. There might be a quicker way, but I can’t think of any that does not unbalance the teams.

I believe if Team White refuses to make this throw-in now, or makes the condition that “only until we know if Gia is on Team Black”, they are just purposefully stalling more knowledge.

The main concern that I have is where should Jon_Ko and NeilAgg should play. Maybe both are on Team Black or maybe only one.

I’m thinking this is one possibility: Jon_Ko plays around F11, NeilAgg might play around J3. Yebellz can later keep the balance by playing around L6, we’ll see when we get there; we’d have more information by then.

As for Question 2

If Vsotvep gets captured, there’s a perfectly valid ponnuki to test Yebellz against. I think this is not ideal (because it wastes one confirmed settler move), but it is one way.

If Vsotvep is not captured, we’d know the following:

Team Black: Leira , NeilAgg , richiefourtytwo , +1
Team White: Vsotvep , MystWalker , Barbanaira , +1
yebellz team is unknown.

In this case, to keep the balance, two ponnukis can be created simultaneously, one by Team White and one by Team Black (given how the board is arranged, this takes only two turns each). yebellz can then choose where to throw-in.

I think the result of this would be a reasonably open and balanced board, but now, with knowledge of both teams.

But, of course I can’t force anyone.

So, you’ve asked for a plan, I’ve presented one. No plan is perfect, and this isn’t the exception, pretty sure it has many flaws. I think something like this should be revised after every move.

For me, to agree to a plan I put forward 4 conditions:

It must not burden one team more than the other. Each team makes sacrifices, each team wastes roughly the same amount of moves.
It must have escape hatches: If you turn out to be on the unexpected team, you must still stand a chance. If someone bails, there should be counterplay.
It should be as quick as possible. Not waiting for yose. Not creating a closed board.
It should keep balance among most, if not all, hypothetical distributions of colors (which are only 8 at this point, down from 126).

If, on the other hand, there is no proposal for something mutually beneficial, we might as well escalate right now into full-on battle. I don’t know my teammates, but I trust that our faction will show superior strength and resilience. I can live with the uncertainty. Can you?

yebellz · August 12, 2022, 5:03pm

Well, thank you for the entertaining stylization. However, I think that the gist to slow Team White, which is naturally motivated by your membership on Team Black.

I think that it still remains vital that @Gia tries to capture @Leira. Any deviation from that seems to be stalling the revelation of information.

Another possibility for Team White is attempt collaborative captures of other players. They are three and can quickly surround and test capture another play to check them.

Luckily, @Leira and @Vsotvep are known to be on opposing teams, so I know I don’t have to do much work to refute point-by-point. I’ll leave it to @Vsotvep to say much more.

However, I worry that we might be monopolizing the conversation too much. I think it is vital to hear more from @Jon_Ko and @NeilAgg.

NeilAgg · August 12, 2022, 5:08pm

I have read the book published by @Leira and I am not sure I have gained any more knowledge about the world than before it.

I do agree with one conclusion:
It is better to find out more information about allegiances sooner than later. I support any mode of play which leads to that.

yebellz · August 12, 2022, 5:09pm

@NeilAgg, are you willing to throw in at L10?

Vsotvep · August 12, 2022, 5:11pm

Still too busy to respond properly, but at least free enough to make one remark:

I agree with most of what the Hermit computes, although I don’t share the same outlook on the validity of the hypotheses implied by the narrative. But, if indeed we are both settler-believers, that is pretty much a given. However, I look through the eyes of the Hermit being a rebel-believer, which makes things different.

First, I agree that Question 1 and 2 are indeed the only things that matter at the moment (hence also assume yebellz is the spy):

Out of Gia , Jon_Ko , richyfourtytwo and NeilAgg , only one can be on team White, and the other three are necessarily on team Black.
Yebellz is either on team Black or team White.

I also believe that the plan offered is good for the purpose of finding the alignment of the players, but not necessarily good for the settlers.

I fear for a worst-case scenario:

I do not get captured by L10, Gia (the amnesiac) does not capture M11 and yebellz turns out to be on team White (by either destroying a settler eye, or by the settler team passing a move, but I see no better way to discover which team yebellz is on either).

With the suggested moves of F11 and J3, in this scenario, rebels Jon Ko and NeilAgg manage to place two strategical throw-ins that work perfectly together with the stone at tengen. The settlers have no way of knowing who is who until yebellz has been tested, which is presumably at the soonest at the end of next round, during which more damage can be done.

Edited to add: Well, this scenario cannot happen, but something similar can be the actual situation.

Leira · August 12, 2022, 5:18pm

Ok, fair. Can you suggest something else for Jon_Ko and NeilAgg? I mean, I truly struggle, to be honest. Should they play small, should they make a preemptive ponnuki?

I suggested J3 because if Yebellz is team White, I’d reckon the stone is dead. Whereas if Yebellz is on team Black, the stone would be an extension. But I’m not married to those placements. There can be better ones.

Edit:

I don’t think a throw-in by NeilAgg is a fast way to gather information. Both outcomes do not balance. If we are lucky, it gets captured and we learn a ton. If not, we learn very little.

NeilAgg · August 12, 2022, 5:21pm

Yes

yebellz · August 12, 2022, 5:24pm

Oh, are you assuming that @NeilAgg is Team Black? Interesting…

Leira · August 12, 2022, 5:25pm

Not really. If NeilAgg is on team White, and you are also on Team white, you basically control the whole west and south. I think that’s big enough to warrant that move.

Vsotvep · August 12, 2022, 5:35pm

For me personally, it’s most likely that both are on the opposite team, so I’d suggest they play something useless.

I don’t reckon throw-ins are necessarily dead, because we’re dealing with double and potentially triple moves.

I find it hard to find a better position as well. Perhaps they can play at A1 and B2, creating another eye that I could throw-in for similar information as me playing at L10.

I’m not sure if NeilAgg should play at L10, since the team of none of the three players involved is known. It would be a wasted move for a player that is (for me) most likely to be on a team opposite to mine, though.

I should say that the scenario above that I sketched contains a contradiction, since Gia and Jon Ko can’t be both rebels if I survive L10… I’m truly too tired to come up with good counters at this moment.

I’ll leave it to yebellz to carefully consider which moves Jon Ko, NeilAgg and I should play. Leira’s plan is hard to bring down, and doesn’t seem to contain inconsistencies, but I fear for subtle manipulation. Also, we’re literally on opposite teams, so I have to object.

Leira · August 12, 2022, 5:37pm

Ok ok, I have a proposal. They both pass

The balance right now is very delicate. Then you make the throw-in. Does that suit you?

Edit: Sorry, I do see a problem. If Jon_Ko is rebel and NeilAgg is not, then the astrologer might ignore the passing

Vsotvep · August 12, 2022, 5:43pm

Hm, I’m not entirely sure either…

Another bad scenario (arguably even worse than my flawed “worst-case”) is that I get captured, which makes Gia’s capture of your stone unnecessary (less wasted moves for team Black), and yebellz gets captured as well, meaning three passes for the settlers (one due to your suggestion of passing, one by my throw-in, one by yebellz’ throw-in) and it saves two wasted moves for the rebels, while keeping more eyespace in the top right.

I find it all really tricky…

Vsotvep · August 12, 2022, 5:47pm

I’m sorry, but I really have to sleep now.

yebellz · August 12, 2022, 5:47pm

We can gain information from this throw-in.

If @NeilAgg is captured

Then we know that Pink and Red are on the same team, and Yellow is on the other. It is impossible to believe that Pink and Red are on Team White, if you believe that I am the true Spy, since putting Pink and Red on Team White would create a team of five without me. Thus, Pink and Red must be on Team Black and Yellow must be on Team White.

If @NeilAgg is not captured

Then Yellow must be on the same team as at least one of Red or Pink. Those two cannot both be on Team White (as it would create a 5-player team contradicting the belief that I am the Spy), and thus Yellow must be on Team Black.

Thus, I think that @NeilAgg throw-in at L10 will confirm whether Yellow is either on Team Black or Team White, depending on whether or not they are captured.

Leira · August 12, 2022, 5:51pm

Leira made a gesture to someone outside the hut.

Soon, Fray Xavier came with a set of blankets and offered the merchant some accomodation

Fray Xavier: I apologize, My Lord. We don’t have any beds, but I assure you the hay at the granary is very comfortable. Father Leira doesn’t speak, but I’m certain he bids you a good night’s sleep.

yebellz · August 12, 2022, 5:51pm

Passing does not help. It slows down the revelation of information.

Better that they remove a liberty, create an atari, or even put their own stone in peril to set up a later capture test.

Leira · August 12, 2022, 5:53pm

This is actually… True. Yeah, you’re right. Nevermind, I do not oppose this move anymore. I was sloppy once more.

Vsotvep · August 12, 2022, 5:53pm

Ah, yes, I see now…

The merchant mumbled some embarrassed words about failing to make simple epistemic deductions as he closed his eyes and fell asleep.

Leira · August 12, 2022, 5:58pm

Uhmmm, let me think a bit more. If NeilAgg is not captured, we do know that they’d be on Team Black. We would not know any other member though.

So, let me back track my steps. This is still unbalanced in terms of information gathering. But, to be exact, let me use the Oracle once more, be right back.

Leira · August 12, 2022, 6:07pm

Yeah, no, I checked.

Only assuming you’re the spy, there are 32 different scenarios. Of those 32, 8 are compatible with the capture, and 24 are not. So, there’s a 25% chance of capture. A capture would be lucky and fruitful but not a likely outcome.

Here’s what’s missing:

A capture would reveal the full composition of both Teams except for yebellz. That is because NeilAgg would be on team White, whereas Jon_Ko, Gia, and richiefourtytwo would be on Team Black.

A non capture would reveal only one member of Team Black, the other 3 still uncertain.

So no, sorry to go back on what I said (twice), but I remain convinced that Vsotvep’s throw-in is better.

Edit: It would have been great, though, if true .