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**Non-Mafia Game Threads / Re: The Necro Wars**

« **on:**July 13, 2018, 09:34:14 pm »

Sometimes I feel like I'm the only one playingIs this post the current longest necro?

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Sometimes I feel like I'm the only one playingIs this post the current longest necro?

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My friends and I have been playing a fair bit of Splendor, and for the most part have settled upon a meta of play that is similar to the strategy Awaclus describes. Today we tried to answer the following question:

In a four-player game (so, 7 chips in each pile) with perfect luck for yourself and your opponent staying out of the way, what is the shortest possible game?

I found a little article with statistics on over 7000 games of splendor played online, and 3 games took 19 turns with none being shorter. However, it's not that hard to come up with a way that someone might get to 15 points faster than that with no opposition and perfect luck.

After a few hours of puzzling, the shortest game we could come up with was 15 turns to 15 points, which we managed to achieve in three essentially different ways. How many turns can you get to 15 points in? I think there is still a fair bit of unexplored space for solutions and possibly improvements and would be interested to see what the forum comes up with.

I'll add that we don't really have much idea how to show that a given solution is the best possible. We think we've pretty much proven that a game of splendor must take at least 11 turns, but that is almost surely not tight and it's unclear how to improve that bound with certainty.

In a four-player game (so, 7 chips in each pile) with perfect luck for yourself and your opponent staying out of the way, what is the shortest possible game?

I found a little article with statistics on over 7000 games of splendor played online, and 3 games took 19 turns with none being shorter. However, it's not that hard to come up with a way that someone might get to 15 points faster than that with no opposition and perfect luck.

After a few hours of puzzling, the shortest game we could come up with was 15 turns to 15 points, which we managed to achieve in three essentially different ways. How many turns can you get to 15 points in? I think there is still a fair bit of unexplored space for solutions and possibly improvements and would be interested to see what the forum comes up with.

I'll add that we don't really have much idea how to show that a given solution is the best possible. We think we've pretty much proven that a game of splendor must take at least 11 turns, but that is almost surely not tight and it's unclear how to improve that bound with certainty.

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The utility function I and my friends use for this and other multiplayer games is:

Let epsilon be a positive number that is way smaller than any conceivable positive probability of any particular event occurring in a game of dominion.

Winning is worth 1 point

2nd place is worth epsilon points

3rd place is worth epsilon squared points

The game ending one turn earlier is worth epsilon cubed points

Maximizing your expected points always leads to playing solely for the topmost uncertain outcome. This is equivalent to what most people are saying in this thread. Also, this makes it so that you play for a shorter game as soon as your placement is assured, no matter what it is. e.g., always taking the three-pile win if it's there.

Let epsilon be a positive number that is way smaller than any conceivable positive probability of any particular event occurring in a game of dominion.

Winning is worth 1 point

2nd place is worth epsilon points

3rd place is worth epsilon squared points

The game ending one turn earlier is worth epsilon cubed points

Maximizing your expected points always leads to playing solely for the topmost uncertain outcome. This is equivalent to what most people are saying in this thread. Also, this makes it so that you play for a shorter game as soon as your placement is assured, no matter what it is. e.g., always taking the three-pile win if it's there.

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this thread is far too active right now

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Oh wow things are changing fast now

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I know how run-time works in general, just not sure precisely what quantity *n* is referring to in this context. If it's the size of the list, I guess my question is exactly how the list is structured. Before I assumed that the list was infinite and it just started being periodic after some point and the period was around *n* or something. So now I don't have any real idea what a "linearly linked list" is. If it's like, each element points to its successor, or something, I'm not sure what stops you from just like going down the list until you get somewhere you've already been. If it's just a graph shaped like a P or something, then you're just looking for the vertex with degree three. I'm just trying to guess what this structure is at this point... I guess that's what I meant by "What information exactly are you given" - as in what's the data structure.

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I'm not sure I understand the question. What exactly is n supposed to be? What information exactly are you given and what does each query or whatever tell you?

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Yeah, there are lots of foolproof ways to set your starting deck up, especially because of donate. I didn't really feel the need to flesh that part of it out because that's not really the hard. I suppose the true statement of the final result here is:

For any ε > 0, there exists a positive constant integer c, such that for any positive integer n we can get (4 - ε) ↑↑ (n - c) points within n turns.

Again it doesn't make much sense to use big-O notation when the rate of growth is hyper-exponential like this. Really the answer is "we can pretty much make our score grow at the same general rate as 4 ↑↑ n does".

For any ε > 0, there exists a positive constant integer c, such that for any positive integer n we can get (4 - ε) ↑↑ (n - c) points within n turns.

Again it doesn't make much sense to use big-O notation when the rate of growth is hyper-exponential like this. Really the answer is "we can pretty much make our score grow at the same general rate as 4 ↑↑ n does".

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It's okay, the necro game thread prompted me several times back in the day...I would have taken it tonight too :/ I blame the necro game thread for prompting you

That is what did it!

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I would have taken it tonight too :/ I blame the necro game thread for prompting you

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Postdarn I was hoping you wouldn't bother

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MuhahahahahahaOh no I accidentally moved away to college

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If this doesn't start soon I should probably out too :/I have to /out

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What were the other four?

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If this doesn't start soon I should probably out too :/

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This is what I meant. I read somewhere that it'd been proven, though I have no idea how. Seems plausible though!Not strictly speaking "almost all," though, because there are infinite real numbers which are not normal.I'm assuming that liopoil meant almost all with respect to Lebesgue measure.

Which, I imagine that's true, though I don't know for sure.

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Yeah, but like, how stupid would it be if pi weren't normal? Almost all real numbers are normal.

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I played this a little while ago and it was pretty cool, and obviously makes a good point. I did have one issue with it though...

The game only considers a small finite set of strategies, from which the best performing strategy against the others over time was the "cheat only after you're pretty sure that you're opponent is a cheater" strategy. The game makes it seem like that strategy is some sort of "long term equilibrium". And I'm sure that in the real world where we play similar games, it may be. But for this specific game, it isn't actually. The rules of the game state:

(this later became any variable number of rounds, but for now we'll assume that the game lasts at most 7 rounds).

Then if a game gets to a 7th round, you know that it's the last round. So if I take the copycat strategy and modify it to "copy what your opponent did in the previous round, unless this is the 7th round, in which case, cheat no matter what", then I will beat the copycat strategy in the long run. Similar for all of the modified strategies that sometimes cooperate. And then we can go further: once all of the strategies cheat in the 7th round, it becomes pointless to cooperate in the 6th round... and so on.

So I think that the game needs to be modified further to truly get the desired outcome. Maybe something like: "after each round, roll a 6-sided die, and if it's not a 6, play again".

The game only considers a small finite set of strategies, from which the best performing strategy against the others over time was the "cheat only after you're pretty sure that you're opponent is a cheater" strategy. The game makes it seem like that strategy is some sort of "long term equilibrium". And I'm sure that in the real world where we play similar games, it may be. But for this specific game, it isn't actually. The rules of the game state:

Quote

you'll play anywhere between 3 to 7 rounds. (You won't know in advance when the last round is)

(this later became any variable number of rounds, but for now we'll assume that the game lasts at most 7 rounds).

Then if a game gets to a 7th round, you know that it's the last round. So if I take the copycat strategy and modify it to "copy what your opponent did in the previous round, unless this is the 7th round, in which case, cheat no matter what", then I will beat the copycat strategy in the long run. Similar for all of the modified strategies that sometimes cooperate. And then we can go further: once all of the strategies cheat in the 7th round, it becomes pointless to cooperate in the 6th round... and so on.

So I think that the game needs to be modified further to truly get the desired outcome. Maybe something like: "after each round, roll a 6-sided die, and if it's not a 6, play again".

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I think town has a lot to gain by sending messages to each other, so I'm not sure that would be worth it. Scum could win without communicating with each other

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They didn't need to lynch me, they could have lynched any townie and guaranteed the winidea: one of the town PRs (monkey?) gains a tiebreaker ability

like "each night u can target someone who will be lynched at eod the next day in the event of a tie" and else scum just wins it

Ya. Making Kubo lynchproof would be one idea. Part of the setup is coming to a 3v3, and making the coin flip one way or another.

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It would be nice if you could at least reveal what the win conditions are and how many people have each win condition... too many games have gone wrong for me because of uncertainty about that

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OK, good game! Anyone want to post the mafia QT?