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Author Topic: Cursed Bottle / Bottle Imp  (Read 9897 times)

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Commodore Chuckles

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Cursed Bottle / Bottle Imp
« on: December 09, 2018, 12:58:57 pm »
+3



Wacky idea, inspired by Robert Louis Stevenson's short story The Bottle Imp https://en.wikipedia.org/wiki/The_Bottle_Imp. In the story, the Bottle Imp grants wishes, but if you still have it when you die, you go to hell. You can sell it, but only for less money than you bought it with. This leads to the following paradox: No sane person would buy it for 1 cent, because they'd be unable to sell it (In the story you can't "buy" it for free; here you can get it for $0 but then you're stuck with it). But then no sane person would buy it for 2 cents, because they'd be unable to find a buyer. And so on. But at the same time, buying it for, say, $100 seems perfectly sensible.

So, is this even a remotely good idea? Is the Imp good enough that the first person to get a Bottle will often just pay $0 and keep the Imp?
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Fly-Eagles-Fly

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Re: Cursed Bottle / Bottle Imp
« Reply #1 on: December 09, 2018, 01:10:20 pm »
0

Definitely interesting, I really like that Bottle Imp does exactly what Wish does, but it's really hard to tell if it would actually work.
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ClouduHieh

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Re: Cursed Bottle / Bottle imp
« Reply #2 on: December 09, 2018, 02:19:57 pm »
0

Also I feel like since it’s a cursed bottle, that when you buy it you should gain a curse too. Or cursed bottle should be a treasure/curse. Then it would be more themed. And I certainly would still buy at least 1 regardless.

And that would cap people from emptying the cursed bottle supply bottle. And then artifact wouldn’t get passed around every other turn. You would get to use for a couple of turns, before someone took it away from ya. And ouch whoever ends up getting it last. But is still like it. It might be worth a gamble. Sorta like my angry bees (state). Except not as painful.

But still an awesome card.
« Last Edit: December 09, 2018, 02:24:46 pm by ClouduHieh »
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #3 on: December 09, 2018, 03:42:26 pm »
0

I don't really see many situations where you would pay more than 0 for this. Either it's good to have so why would I want to pay more for it / let my opponent take it or it's bad so why would I take it at all.
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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #4 on: December 09, 2018, 05:22:54 pm »
0

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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #5 on: December 09, 2018, 05:26:20 pm »
0

I don't really see many situations where you would pay more than 0 for this. Either it's good to have so why would I want to pay more for it / let my opponent take it or it's bad so why would I take it at all.

Because it's better to have it for a while and then lose it than it is to have it forever.
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faust

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Re: Cursed Bottle / Bottle Imp
« Reply #6 on: December 10, 2018, 12:57:04 am »
+1

The problem is that there will be boards where Bottle Imp is strong enough that you want to have it for the whole game. If you're building for a megaturn, then you don't mind the -13 VP all that much. And if you have such games, then the player who gets to play Cursed Bottle first just wins. In that sense this is a worse Magic Lamp, which is thematic, but from a gameplay perspective not advisable.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #7 on: December 10, 2018, 02:41:53 am »
+2

I don't really see many situations where you would pay more than 0 for this. Either it's good to have so why would I want to pay more for it / let my opponent take it or it's bad so why would I take it at all.

Because it's better to have it for a while and then lose it than it is to have it forever.

I don't really see it. When would it be good to buy bottle imp for 1? Either my opponent will take it from me very soon because bottle imp is good, and I will never get it back, or I should never have bought bottle imp at all.

In other words, if it is good for my opponent to take bottle imp for 0, why wasn't it good for me?
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #8 on: December 10, 2018, 05:42:31 am »
0

I don't really see many situations where you would pay more than 0 for this. Either it's good to have so why would I want to pay more for it / let my opponent take it or it's bad so why would I take it at all.

Because it's better to have it for a while and then lose it than it is to have it forever.

I don't really see it. When would it be good to buy bottle imp for 1? Either my opponent will take it from me very soon because bottle imp is good, and I will never get it back, or I should never have bought bottle imp at all.

In other words, if it is good for my opponent to take bottle imp for 0, why wasn't it good for me?
GendoIkari made a pointed which is generally correct whereas you assumed somehow willy-nilly that 1 is the only potentially optimal deviation from your suggested dominant strategy of always paying 0. This is probably only the case in non-mirrors; with opponents also going for Cursed Bottle it is easy to imagine situations in which prices around 3-6 will get paid for Bottle Imp.
In general the strength of Bottle Imp depends on how early you get it and its weakness is dependent on whether there are alternative sources of VPs and, as already discussed, how many opponents went for Cursed Bottle. If nobody goes for it your suggested dominant strategy of paying $0 is obviously braindead.

I totally agree with faust that one has to watch out for this not being broken because it might be too often the optimal strategy to pay $0 and deal with the negative VPs. But your claim that 0 is always optimal seems highly dubious without any playtesting experience to back it up.

I like the card(s) a lot. Even though I don't know the short story it sounds incredibly thematic and the inverse auction seems pretty interesting. Not that it is strictly necessary as players would do something like this automatically but instead of the "amount of Coins last paid for it" I would try a wording with tokens that remain on Bottle Imp in order to track the previous price.
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Jimmmmm

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Re: Cursed Bottle / Bottle Imp
« Reply #9 on: December 10, 2018, 05:44:58 am »
0

I think heron is right - giving your opponent a choice is strictly worse than not giving them that choice.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #10 on: December 10, 2018, 11:27:42 am »
0

I think heron is right - giving your opponent a choice is strictly worse than not giving them that choice.
In non-mirrors, choosing -13VPs is strictly worse than choosing 0VPs.

If the card is simple you can analyse theoretically and come up with a clear result without having ever played with the card. This is not one of those simples cases though. The best strategy depends on VP sources, the moment when you gain Cursed Bottle and when you play it, the number of opponents, whether and if how many of your opponents have Cursed Bottles, how long the game will still take which determines the relative worth of an auto-Wish each turn and numerous other factors.

So authoritative, general, black-and-white statements about these cards are impossible without having actually played with them in at least 5-10 games.
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Chappy7

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Re: Cursed Bottle / Bottle Imp
« Reply #11 on: December 10, 2018, 03:53:13 pm »
+1

With the wording as it is, can you actually pay $0? It says to pay any amount of $.  Is 0 an amount of $?
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faust

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Re: Cursed Bottle / Bottle Imp
« Reply #12 on: December 10, 2018, 04:14:37 pm »
+1

With the wording as it is, can you actually pay $0? It says to pay any amount of $.  Is 0 an amount of $?
Going by the ruling on Stonemason overpay, I would assume not.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #13 on: December 10, 2018, 05:49:46 pm »
+2

I think you guys are mostly missing my point.

Suppose my opponent has bottle imp, and I have the opportunity to take it. Doing so will affect my win probability by delta. If delta is positive, then I will happily take the bottle imp. My opponent will say, "Darn! I should have paid the minimum amount for bottle imp to prevent this from happening!".

Suppose delta is negative. Then I will not take the bottle imp. My opponent will say, "Hm. I guess it didn't matter how much I paid for bottle imp."

Since there is some tiny amount of hidden information in dominion, it is possible for two optimal opposing players to disagree on the sign of delta, but that seems exceedingly rare. The true win probability is zero-sum.
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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #14 on: December 10, 2018, 06:03:05 pm »
0

I think you guys are mostly missing my point.

Suppose my opponent has bottle imp, and I have the opportunity to take it. Doing so will affect my win probability by delta. If delta is positive, then I will happily take the bottle imp. My opponent will say, "Darn! I should have paid the minimum amount for bottle imp to prevent this from happening!".

Suppose delta is negative. Then I will not take the bottle imp. My opponent will say, "Hm. I guess it didn't matter how much I paid for bottle imp."

Since there is some tiny amount of hidden information in dominion, it is possible for two optimal opposing players to disagree on the sign of delta, but that seems exceedingly rare. The true win probability is zero-sum.

This is why the original Bottle Imp story is a paradox. You can show through induction that it is never good to take it (or in the Dominion case, that if it is good to take it, it's best to take it for . And yet at the same time, taking it for can seem perfectly reasonable.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #15 on: December 10, 2018, 06:35:31 pm »
0

I think you guys are mostly missing my point.

Suppose my opponent has bottle imp, and I have the opportunity to take it. Doing so will affect my win probability by delta. If delta is positive, then I will happily take the bottle imp. My opponent will say, "Darn! I should have paid the minimum amount for bottle imp to prevent this from happening!".

Suppose delta is negative. Then I will not take the bottle imp. My opponent will say, "Hm. I guess it didn't matter how much I paid for bottle imp."

Since there is some tiny amount of hidden information in dominion, it is possible for two optimal opposing players to disagree on the sign of delta, but that seems exceedingly rare. The true win probability is zero-sum.

This is why the original Bottle Imp story is a paradox. You can show through induction that it is never good to take it (or in the Dominion case, that if it is good to take it, it's best to take it for . And yet at the same time, taking it for can seem perfectly reasonable.

The paradox is based on humans behaving irrationally. If humans behaved rationally, then there is no paradox. It is just obviously correct to never take the bottle in the story. I expect good dominion players to also behave rationally if they are trying to win the game.
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Limetime

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Re: Cursed Bottle / Bottle Imp
« Reply #16 on: December 10, 2018, 06:54:00 pm »
+1

It works better if you change less to more.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #17 on: December 10, 2018, 07:00:30 pm »
0

The paradox is based on humans behaving irrationally. If humans behaved rationally, then there is no paradox. It is just obviously correct to never take the bottle in the story. I expect good dominion players to also behave rationally if they are trying to win the game.
You ignore time and player interaction:
Paying a lot for Bottle Imp can prevent the opponent from going for Cursed Bottle at all respectively make it temporarily unable (depending on how good his economy is) for him to get Bottle Imp while you could later pay for it again, but then e.g. $0.



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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #18 on: December 10, 2018, 07:17:37 pm »
0

The paradox is based on humans behaving irrationally. If humans behaved rationally, then there is no paradox. It is just obviously correct to never take the bottle in the story. I expect good dominion players to also behave rationally if they are trying to win the game.
You ignore time and player interaction:
Paying a lot for Bottle Imp can prevent the opponent from going for Cursed Bottle at all respectively make it temporarily unable (depending on how good his economy is) for him to get Bottle Imp while you could later pay for it again, but then e.g. $0.

No... paying a lot for Bottle Imp makes it easier, not harder for the opponent to get the imp.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #19 on: December 10, 2018, 07:38:23 pm »
0

My mistake. The general point still stands though, you ignore time and the very real possibility of high initial prices for Bottle Imp because nobody wants to end up with those -13VPs. The strength of Bottle Imp changes over time, from being very valuable early in the game towards being progressively worse and then sharply becoming a very bad card at the end of the game. This means that strength evaluation changes over the course of the game and thus will its ownership.

You are simply wrong about this being good/bad in a particular Kingdom. It is like pretending that Hireling is always good/bad in Kingdom ABC while ignoring time, while ignoring that it is much stronger early on.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #20 on: December 10, 2018, 07:59:08 pm »
0

My mistake. The general point still stands though, you ignore time and the very real possibility of high initial prices for Bottle Imp because nobody wants to end up with those -13VPs. The strength of Bottle Imp changes over time, from being very valuable early in the game towards being progressively worse and then sharply becoming a very bad card at the end of the game. This means that strength evaluation changes over the course of the game and thus will its ownership.

You are simply wrong about this being good/bad in a particular Kingdom. It is like pretending that Hireling is always good/bad in Kingdom ABC while ignoring time, while ignoring that it is much stronger early on.

Note that my hypothetical scenario where one player has the option to take the bottle imp is true at any point in time.

It is true that in many games I would like to have the bottle imp at the beginning in order to build, and then I would probably like to get rid of it towards the end of the game. The point that many people seem to be ignoring is that if it is good for me to have my opponent take the bottle imp away from me, then it is bad for my opponent to take it away.

Or like Jimmmmmmm said, giving your opponent a choice is always worse than not giving them a choice.
If my opponent can choose to take the imp away for $1, $2, or $3, or not take the imp, that is better for them than being able to take the imp away for either $1 or $2 (or not taking it), which is better than only being able to take the imp away for $1 (or not), which is better for them than not being able to take the imp.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #21 on: December 10, 2018, 08:29:00 pm »
0

Or like Jimmmmmmm said, giving your opponent a choice is always worse than not giving them a choice.
If my opponent can choose to take the imp away for $1, $2, or $3, or not take the imp, that is better for them than being able to take the imp away for either $1 or $2 (or not taking it), which is better than only being able to take the imp away for $1 (or not), which is better for them than not being able to take the imp.
You ignore the -13VPs as well as the fact that paying $0 destroys not just options for your opponent but also for you.

If you pay $2 you always have the option of getting rid of Bottle Imp. Your opponent might not have Cursed Bottle or his evaluation of the strength of Bottle Imp might change because the game is nearing the end.

Dominion is not a static game, evaluations of card strength change all the time. You cannot simply ignore such dynamic aspects.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #22 on: December 10, 2018, 09:06:58 pm »
0

"If you pay $2 you always have the option of getting rid of Bottle Imp."

No.... you cannot get rid of bottle imp unless your opponent takes it from you.
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Commodore Chuckles

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Re: Cursed Bottle / Bottle Imp
« Reply #23 on: December 10, 2018, 09:19:24 pm »
0

It works better if you change less to more.

I had thought of that, yes. We already have an upward auction in the form of Mountain Pass, though, so I posted this version because I was wondering if it could work (and because it matches the story better this way).

The point that many people seem to be ignoring is that if it is good for me to have my opponent take the bottle imp away from me, then it is bad for my opponent to take it away.

It's not necessarily that simple. Consider Governor: It's usually better for you if your opponent chooses +3 cards instead of Gold, because +1 card for you is usually better than a Silver. Does this mean your opponent should always choose Gold over +3 cards? No, because the +3 cards usually helps them more as well. It's the same with Bottle Imp: taking it away from you can be good for you and them at the same time.
« Last Edit: December 10, 2018, 09:25:03 pm by Commodore Chuckles »
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #24 on: December 10, 2018, 09:31:09 pm »
+1

The point that many people seem to be ignoring is that if it is good for me to have my opponent take the bottle imp away from me, then it is bad for my opponent to take it away.

It's not necessarily that simple. Consider Governor: It's usually better for you if your opponent chooses +3 cards instead of Gold, because +1 card for you is usually better than a Silver. Does this mean your opponent should always choose Gold over +3 cards? No, because the +3 cards usually helps them more as well. It's the same with Bottle Imp: taking it away from you can be good for you and them at the same time.

This is flawed reasoning. Only one player can win, every decision decreases one player's win% and increases the others. In this sense no decision can help both players.
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