Spire negotiation game is more subtle than you think...

[michmarc]

I was tweaking my spire solver to fix a minor bug and came across an unexpected result. It turns out that the optimal way to play the spire depends on exactly how much you value the goods being used (relative to the other goods asked for).

As a simple example, you're playing a round with 4 different goods to choose from. You guess AABCD as your original guess and get back the answer CCSSS (first two correct and the last three 'someone else'). Great -- you are guaranteed success as the only two possibilities are AACDB and AADBC. Now what?

We assume that the value of the goods to you is A<=B<=C<=D. And let's put a comparative value on the goods.

Let me describe three strategies:
1) Guess AACDB. If that's wrong, then guess AADBC.
2) Guess AAAAB. If B was right, guess AACDB; otherwise guess AADBC.
3) Guess AAABB. If the first B was right, guess AADBC; otherwise guess AACDB.

If all goods cost the same (10, 10, 10, 10): Strategy 1 costs either 30 or 60 for an average cost of 45. Strategy 2 costs 50 or 60 for an average cost of 55. Strategy 3 always costs 50. #1 is best.

If you think A is much cheaper than B, (10, 30, 30, 30): Strategy 1 costs 90 or 180 for an average cost of 135. Strategy 2 costs 50 for the first guess and either 60 or 90 for the second guess for a total average of 125. Strategy 3 costs 70 for the first guess and 60 for the second for a total cost of 130. #2 is best.

If you think B is cheap enough relative to A but expensive enough relative to C and D (10, 15, 30, 30): Strategy 1 costs 75 or 150 for an average cost of 112.5. Strategy 2 costs 35 for the first guess and either 60 or 75 for the second for an average cost of 102.5. Strategy 3 costs 40 for the first guess and 60 for the second for a total cost of 100. #3 is best.

Deep.

This also directly affects whether or not you should give up halfway through and start over or press on hoping to get lucky.

 

[DeletedUser22644]

But more often than not in my experience you are better off going in the 4 goods model ABCDA, since the Program is more linear than random. Many time a simple L to R pattern not withstanding the cost makes for a better outcome.

ABCDA - BCDAB - CDABC with the expected changes for Cleared spots and Not needed items but in most cases even when the outcome for pass 1 and 2 is always someone else I have found that the 3rd pass clears all quite a few times. Hence the Linear progression.

I do not see how going by value makes any sense in pass 1 and more likely will complicate the concept.

Al

 

[Deleted User - 3932582]

I was tweaking my spire solver to fix a minor bug and came across an unexpected result. It turns out that the optimal way to play the spire depends on exactly how much you value the goods being used (relative to the other goods asked for).

Not sure why this is an unexpected result A trivial example to prove that would be like this: you only have one ghost and 2 goods available left (A and B), with no other information. So it's a 50/50 proposition - but it is only true if you value A and B the same. If you have a preference for one vs another, then you should pick the one that is cheaper to you.

The value also usually looks quite a bit simpler in the end game. You'd normally have goods you care about (e.g. orcs, maybe seeds, maybe coins) vs the ones that have basically zero value (pretty much everything else). Depends on if you cater L3 and/or tournaments.

I do not see how going by value makes any sense in pass 1 and more likely will complicate the concept.

Value would determine which goods you will put up multiples of.

 

[DeletedUser22644]

@MinMax Gamer, in pass one where you know nothing, the value should be in the example given of 4 choices of trying to eliminate or condense the options and responses. I agree if the choices were fully random then yes the lowest value makes sense.

Note what each player sets as a low value can very quite a bit depending on stage of the game.

However, since the true random nature is not present and the patterns are in a linear progression then you are better using the order of chests and ignoring the value.

Now that is how I see it and if wrong please correct me

 

[Deleted User - 3932582]

However, since the true random nature is not present and the patterns are in a linear progression

Hm, and how did you determine that?

 

[DeletedUser22644]

Observation of the diplomacy option bottom to top of the spire over multiple accounts. It is clear that when you used the left to right order and shift as needed for cleared ghosts and to avoid duplications/repeats you can see that the left to right pattern hold true way more often than not and that the programmers did not fully include a random generator in the placement of the chests.

 

[Chriger]

Observation of the diplomacy option bottom to top of the spire over multiple accounts. It is clear that when you used the left to right order and shift as needed for cleared ghosts and to avoid duplications/repeats you can see that the left to right pattern hold true way more often than not and that the programmers did not fully include a random generator in the placement of the chests.

Hmm, multiple spire accounts over multiple weeks is likely not enough data points, even if you were recording and analyzing the data.

If you haven't done that, it's just an observation, and likely not accounting for how powerful something like confirmation bias can be.

 

[DeletedUser22644]

Not trying to Prove my point I clearly stated it was my observation, but I stand by the observations I made.

Do you have an alternate opinion or just playing devils advocate?

 

[Deborah M]

Not trying to Prove my point I clearly stated it was my observation, but I stand by the observations I made.

Do you have an alternate opinion or just playing devils advocate?

I do the same thing. Not because I necessarily expect the results to be any better than some other strategies, just because I am not a fan of the Spire so I don't want to overthink it. If I really don't want to use my inventory I can battle to the top. Alas, I dislike battling even more than I dislike having to overthink negotiating.

 

[ajqtrz]

My strategy, and I "convince" all, is to do the ABCD (A or E) the first round. The goal is to find which of the (up to 5) are "not needed." If there are less than 6 the first round does the trick. Second round goal is to reduce the choices to 2 "wrong person" if possible, since that means you just reverse the two and you are done. To do this I stagger the round and put, from left to right, each still valid good on the still unconvinced opponents from left to right again. This, almost all the time (but not quite) gets me to 2 or 3 left. If two usually I can figure out by looking at the two unconvinced left and finding which of them has already received an offer of one of the goods left. If I find one of the two that way, the other is almost always the remaining. By careful thought I get this one about 90% of the time. If there are three it's about the same but the percentage drops to about 70% of the time. Overall I spend about 200 diamonds to complete the tower and get about 200 diamonds back with my fs participation level and the ocassional chest reward.

Finally, when I'm faced with 3 or more choices left after the 2nd round, if I can't eliminate more than one or two through logic, (which I almost always can), I look to two things. First, how many times has the resource been accepted? If it's 2 then it's less likely a 3rd opponent will want it so I choose something else. AND if all the choices have been evenly chosen by the opponents and I'm left with two options I choose the one on the left as it's both cheaper and, in my observation, more likely to be the one desired.

Like I said, I at least break even on the diamonds and get the fun and profit of everything else, including the 3 magic residences, 2 magic workshops, 3 genies, and a whole lot of instants besides.

 

[Deleted User - 3932582]

If it's 2 then it's less likely a 3 opponent will want it

Why do you think so?

 

[ajqtrz]

Why do you think so?

Mostly experience -- which just means intuition -- the process by which experience skips the rational, concrete, counting and calculating and goes to a more direct (and less reliable but over time close to as accurate) sense of the matter.

AJ