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Author Topic: Cursed Bottle / Bottle Imp  (Read 9898 times)

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Commodore Chuckles

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Re: Cursed Bottle / Bottle Imp
« Reply #25 on: December 10, 2018, 10:29:25 pm »
0

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.

So you're saying there's only one Governor option that should always be picked? Which is it?
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #26 on: December 10, 2018, 10:59:50 pm »
+2

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.

So you're saying there's only one Governor option that should always be picked? Which is it?

No, that is not exactly what I am saying. I am saying that each time you play governor, there is only one Governor option that should be picked. It might not be the same every time. Assuming you could see your opponent's hand, it is not possible for both you and your opponent to want you to pick draw cards. Because the small amount of hidden information in dominion has a fairly large effect on what you should pick for governor, I have to hedge and assume you can see your opponent's hand. For bottle imp the effect of hidden information is much smaller.
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trivialknot

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Re: Cursed Bottle / Bottle Imp
« Reply #27 on: December 10, 2018, 11:12:21 pm »
+3

I agree with Heron, at least in 2P.  Paying more than $0 for Bottle Imp gives your opponent strictly more options than they would otherwise have.  You can always hope that by offering your opponent too many choices, they will end up choosing the wrong thing, but that's not a good strategy against a good opponent.

For an analogy, suppose there's an artifact that says, "At the beginning of each other player's turn, they may get +$1.  If they do, you draw a card."  In 2P, you don't want this artifact.  Even if it helps both players, a good opponent will only choose the +$1 when they believe it will help them more than you.

With 3 or more players it's different.  You could have two players "cooperate" against a third by swapping ownership of the Bottle Imp.
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Commodore Chuckles

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Re: Cursed Bottle / Bottle Imp
« Reply #28 on: December 10, 2018, 11:38:13 pm »
+2

Okay, I'm seeing the logic now. If you pay more than the minimum for the Bottle Imp, that means you're counting on them to take it away from you at some point, which means they shouldn't. Hmmmm... This clearly needs fixing if it's going to work at all.
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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #29 on: December 11, 2018, 09:17:05 pm »
0

I guess where I still see value in the card is that Dominion is not a perfect information game. Even if it's true that every decision can only increase the chances of winning for a single player; there are many times when it is not really possible to calculate which decision increases the chances for you. In that way, it's quite possible for both me and my opponent to want my opponent to take Bottle Imp from me. Throughout much of the middle of the game, it will not be clear whether it is better to have Bottle Imp or not. I may easily think that the best way to use Bottle Imp is to have it for a few turns and then lose it; while my opponent, having seen that I've taken it; may think that taking it away from me is still the better play.

In other words, it's not counting on your opponent to act irrationally. It's counting on them to simply have a different risk threshold than you do, or to have a different analysis than you do.
« Last Edit: December 11, 2018, 09:18:08 pm by GendoIkari »
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #30 on: December 12, 2018, 02:05:28 am »
0

I guess where I still see value in the card is that Dominion is not a perfect information game. Even if it's true that every decision can only increase the chances of winning for a single player; there are many times when it is not really possible to calculate which decision increases the chances for you. In that way, it's quite possible for both me and my opponent to want my opponent to take Bottle Imp from me. Throughout much of the middle of the game, it will not be clear whether it is better to have Bottle Imp or not. I may easily think that the best way to use Bottle Imp is to have it for a few turns and then lose it; while my opponent, having seen that I've taken it; may think that taking it away from me is still the better play.

In other words, it's not counting on your opponent to act irrationally. It's counting on them to simply have a different risk threshold than you do, or to have a different analysis than you do.

No matter what, you still would never want to pay more than the minimum amount for bottle imp.
Suppose that there are two gamestates of dominion which are almost identical. In state 1, you are deciding whether you want to do choice A, choice B, or choice C. You have no other choices. State 2 is exactly the same, except that for some reason you only have the options to do choice A and choice B.

Which state would you rather be in? Obviously it is state 1, since the options available to you are a superset to the options in state 2.

Now consider that you have just played cursed bottle. Your opponent currently has the bottle imp, and paid N for it. What options are available to you?
You could not take the bottle imp, or you could pay 1 to take the bottle imp, or you could pay 2, or ..., or you could pay N-1 to take the bottle imp.
If your opponent had instead paid N+1 for the bottle imp, you would have the exact same choices, plus the choice to pay N to take the bottle imp.
So, your options are a superset of the options from the original situation.
Therefore, you always prefer that your opponent pays N+1 for bottle imp rather than N.

Conversely, you should always pay N for bottle imp rather than N+1; i.e. you should always pay the minimum amount.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #31 on: December 12, 2018, 02:19:22 am »
0

you should always pay the minimum amount.
Perhaps this is indeed the dominant strategy. I seriously doubt it given that you don't consider the trade-offs of the card at all but whatever, perhaps it is.

Via paying more you might give your opponents a noose to hang themselves in. It is like trap moves in chess, they are never the best moves on a hypertheoretical level but I am not God playing against God, I am a flawed human playing against other flawed humans and in real games, depending on my opponent, playing for trap moves could actually lead to a higher win percentage than playing the theoretically best move.
If you think e.g. that the best play for you would be to use of Bottle Imp is for just a few turns (because then the marginal benefit of extra cards diminshes while the -13VPs loom larger) and if you think at the same time that your opponent thinks otherwise (you can perhaps tell from his play,  he might have no other gainers) you can try to exploit that.

So this is not even necessarily a trap move but just the natural reaction to observing your opponent.

You argument basically boils down to the claim that giving your opponent fewer options is good. Well, no. We can take chess again and pick a not-so-bad player, the current World champion. He actually often does play theoretically inferior moves and tries to create problems for the opponent, mostly in endgame positions. If the other guy has little time on the clock giving him a simple choice is a worse course than giving him a complicated choice, even if the latter is slightly inferior on hypertheoretical level.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #32 on: December 12, 2018, 02:43:20 am »
+1

Ok, to anyone who believes paying minimum amount is not optimal, I offer a challenge:

Assume that $1 is the minimum amount you can pay for bottle imp.
Construct ANY scenario where your opponent has bottle imp, you have played cursed bottle, and would be happier if your opponent had paid $1 for bottle imp than if they had paid >$1.

Hard mode: Same as the above, but you are playing open-hand dominion, where you can always see your opponent's hand.

I believe normal mode to already be very difficult and to have no solutions which are not extreme edge cases. Prove me wrong.

Actually, I believe both modes to be impossible without assuming that you are a bad player
« Last Edit: December 12, 2018, 03:06:25 am by heron »
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #33 on: December 12, 2018, 06:05:46 am »
+1

Ok, to anyone who believes paying minimum amount is not optimal, I offer a challenge:

Assume that $1 is the minimum amount you can pay for bottle imp.
Construct ANY scenario where your opponent has bottle imp, you have played cursed bottle, and would be happier if your opponent had paid $1 for bottle imp than if they had paid >$1.

Hard mode: Same as the above, but you are playing open-hand dominion, where you can always see your opponent's hand.

I believe normal mode to already be very difficult and to have no solutions which are not extreme edge cases. Prove me wrong.

Actually, I believe both modes to be impossible without assuming that you are a bad player
That's super easy. If I misevaluated the strength of Bottle Imp, not having the option to get it is actually good. Not at the very moment I have to make the choice, then I am pissed. But if I win the game due to this lack of an option I see that it was in hindsight good.

It is like playing with people who have never played with Thief or Pirate Ship. Suppose you play a variant in which they get the option to use Pirate Ship and Thief as two extra, private piles. Of course they are happy, more choice is never a bad thing according to you, right? But because they are unfamiliar with the cards they overvalue Treasure-trashing and lose the game.

Now I guess you would label them bad players but they aren't, they are just unfamiliar with a particular category of cards.
Bottle Imp is also a new card and like with all new cards even good players will frequently misevaluate their strength until they have enough experience.
I totally agree with you that if the game consists of good players who have played often enough (and given how complex it is and how harsh the -13VPs are, 2 or 3 games will definitely not suffice!) with Bottle Imp and rarely misevaluate it, paying more than the minimum amount is probably wrong.
But if you are unsure about it and would like it most to only get a few plays out of Bottle Imp and then hope to get rid of it, creating the option for your opponent to make you achieve that very goal isn't bad play but good play. Other factors like psychology and his deck state also influence this decision. If he is in dire need of gaining and if you can "read" (we are human beings and prone to biases, I know e.g. whose players in my gaming group are village piel drivers and this knowledge informs my play) him and know that he will go for Bottle Imp, paying $1 or $2 extra for Bottle Imp could be a smart gamble.

So yeah, it looks like this entire argument boils down to differences of perspective: theoretical or pragmatic. As God isn't in my playing group I have little interest in hypertheoretical arguments that assume perfect play.

Do you play chess or are you married? These are the most obvious examples that illustrate why lack of options isn't automatically bad. While a chess engine only cares about finding the best move according to its evaluation function a real human player sometimes plays a slightly inferior move that creates options for his opponent to go wrong or a very inferior move that creates the option for this opponent to go very wrong aka a trap. So even a deterministic game like chess features risk management.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #34 on: December 12, 2018, 01:04:50 pm »
0

By your own admission, you did not answer my challenge:
"Not at the very moment I have to make the choice, then I am pissed."

Your chess analogy is irrelevant. I make no claims about number of options available. Only about when the options available in one state are a superset of the options available in another state.

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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #35 on: December 12, 2018, 01:31:57 pm »
+1

It seems like the same logic can be used to say that in any game with an auction mechanic, the mechanic doesn't work because the optimal thing is simply for the first player who bids to bid the exact correct amount that the thing is actually worth. If both players know exactly that paying $51 for the up-for-bid power plant reduces your chances of winning, while paying $50 for it increases your chances of winning, then the right move is simply to immediately bid $50. Bidding any less than that allows your opponent the chance to be the one to bid $50 himself.

Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.

Except, these mechanics DO work, because of 3 main factors:

1) Neither player knows exactly the correct amount. While there is some statistical calculation possible to determine the exact dollar amount where your chances go from increasing to decreasing if you win the auction, neither player is capable of actually making that calculation.

2) There is a risk/reward prospect at play. Purchasing the plant for more money may be riskier; but each player may have a different threshold for how much risk they are willing to take.

3) Humans are not robots; there is psychology at play here. The idea that you may want to bid a little bit higher, in hopes that your opponent bids even higher, just to cost him more money, comes into play. The slowly increasing cost of the power plant makes it harder to judge the exact point where it is way too expensive. Bidding on a plant is also egging your opponent on to bid higher.

All 3 of these reasons should apply just as well to Bottle Imp.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #36 on: December 12, 2018, 01:49:56 pm »
+1

By your own admission, you did not answer my challenge:
"Not at the very moment I have to make the choice, then I am pissed."
You seemingly missed the part where I pointed out that at the end of the game, retroactively, in hindsight, you might realize that this lack of an option was good you as it prevented you from making a mistake.

You are totally right that from a game theoretical perspective more options are usually (the obvious exception are prisoner dilemmas and other cooperation issues) good. But if you lack perfect knowledge less options can be useful. Which is why seatbealts are mandatory and we take try to take away the option from running over the street without looking left and right via teaching our children to do so. I even sometimes reduce my options of eating crisps via not buying them as lacking the option to eat more crap than I already do is beneficial for me.

Your chess analogy is irrelevant. I make no claims about number of options available. Only about when the options available in one state are a superset of the options available in another state.
Sure, some stupid mathematical sophistry (dude, any sane person would interpret what you wrote in your challenge as: "one extra option") is more important while talking about Dominion than insights from another game.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #37 on: December 12, 2018, 01:56:00 pm »
+1

Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.
Great post. I'd like to add that it also depends on the precise rules of the auction and on how granular the currency is. If we stick with your Power Grid example, what also comes into play is that the worth of a power planet is not equal for all players. Well, that's also so in the real world, here the marginal benefit of getting an asset also differs among people which is why it would be stupid to immediately bid your willing to pay. That Picasso might be worth 5 for you but if everybody else is unwilling to pay more than 1 a starting bid of 5 would unnecesarily cost you 4.
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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #38 on: December 12, 2018, 02:09:56 pm »
+1

Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.
Great post. I'd like to add that it also depends on the precise rules of the auction and on how granular the currency is. If we stick with your Power Grid example, what also comes into play is that the worth of a power planet is not equal for all players. Well, that's also so in the real world, here the marginal benefit of getting an asset also differs among people which is why it would be stupid to immediately bid your willing to pay. That Picasso might be worth 5 for you but if everybody else is unwilling to pay more than 1 a starting bid of 5 would unnecesarily cost you 4.

If you only look at "worth" as "how good is it for me to have", then yes. But really, you getting it is also your opponent not getting it. From that perspective, it should be worth exactly the same to both players. As in, even if it would be a horrible plant for me to have personally, it could be so good for my opponent to have that it's still better for me to have it over all.
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Screwyioux

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Re: Cursed Bottle / Bottle Imp
« Reply #39 on: December 12, 2018, 02:11:00 pm »
+1

Having read the story, I appreciate how faithful this is to it.

Balance-wise, it's super powerful the way it's worded now and you'll usually just want to pay $0 so you can keep the Imp forever.

Suggestions would be:

1. Just have the Imp gain Wishes instead of acting like a Princed Wish. It's weaker that way but still plenty powerful.
2. There needs to be SOME means of counterplay-- either that there's always a way to steal the Imp, or that the person with it has a harsher punishment for keeping it, one that will scale with whatever board the Imp might show up on.
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heron

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Re: Cursed Bottle / Bottle Imp
« Reply #40 on: December 12, 2018, 02:13:43 pm »
0

It seems like the same logic can be used to say that in any game with an auction mechanic, the mechanic doesn't work because the optimal thing is simply for the first player who bids to bid the exact correct amount that the thing is actually worth. If both players know exactly that paying $51 for the up-for-bid power plant reduces your chances of winning, while paying $50 for it increases your chances of winning, then the right move is simply to immediately bid $50. Bidding any less than that allows your opponent the chance to be the one to bid $50 himself.

Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.

Except, these mechanics DO work, because of 3 main factors:

1) Neither player knows exactly the correct amount. While there is some statistical calculation possible to determine the exact dollar amount where your chances go from increasing to decreasing if you win the auction, neither player is capable of actually making that calculation.

2) There is a risk/reward prospect at play. Purchasing the plant for more money may be riskier; but each player may have a different threshold for how much risk they are willing to take.

3) Humans are not robots; there is psychology at play here. The idea that you may want to bid a little bit higher, in hopes that your opponent bids even higher, just to cost him more money, comes into play. The slowly increasing cost of the power plant makes it harder to judge the exact point where it is way too expensive. Bidding on a plant is also egging your opponent on to bid higher.

All 3 of these reasons should apply just as well to Bottle Imp.

Thanks for bringing up an actually reasonable argument.
Here are some reasons I disagree (first overall, and then corresponding to each of your three points). It basically boils down to, for bottle imp the bidding goes the wrong way (the less you pay, the bigger your reward).

In auction games, I believe that bidding tends to go around in a circle increasing. Maybe player A can bid 5, then player B bids 7, then player C bids 8, then player A goes again and bids 9. Why didn't player A bid 9 to begin with? The answer is that the gamestate has changed. Since their first bid, player A has learned what the other two players think they should bid, and has updated their bid accordingly.

On the other hand, if for some reason player A already knew that for all players it was good to purchase the auction prize for 9 or less and bad to purchase it for 10 or more, then yes player A should immediately bid 9. Cursed bottle does not have this circular bidding mechanic (although even if it did, you would always want to fold or bid min amount).


1. In the case of cursed bottle, the correct amount is either the minimum amount or not to take cursed bottle. So in fact it is very possible to compute the exact amount.
2. This does not come into play with cursed bottle. Paying more for the bottle imp is both a higher cost and a lower reward. On the other hand, if you had to pay more than the previous time, it could work very nicely.
3. Again, this doesn't apply to cursed bottle because of how you have to underbid. Like, am I going to buy bottle imp for 6 hoping that my opponent will spend 5 on it? That's nonsense; they are losing less than me, and regardless they can still just buy it for min amount.
You could also do something silly like pay a lot for bottle imp on a board where it is bad to have (if such a board even exists!), hoping that your opponent will take it away from you. This is kind of nonsense also, clearly ignoring psychology this is just worse than not getting bottle imp, and if you allow psychology your opponent should be suspicious the moment you pay more than min amount.







Holunder:
I think that you are trolling, sorry if you aren't, I won't respond to you anymore.




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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #41 on: December 12, 2018, 02:23:27 pm »
0

Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.
Great post. I'd like to add that it also depends on the precise rules of the auction and on how granular the currency is. If we stick with your Power Grid example, what also comes into play is that the worth of a power planet is not equal for all players. Well, that's also so in the real world, here the marginal benefit of getting an asset also differs among people which is why it would be stupid to immediately bid your willing to pay. That Picasso might be worth 5 for you but if everybody else is unwilling to pay more than 1 a starting bid of 5 would unnecesarily cost you 4.

If you only look at "worth" as "how good is it for me to have", then yes. But really, you getting it is also your opponent not getting it. From that perspective, it should be worth exactly the same to both players. As in, even if it would be a horrible plant for me to have personally, it could be so good for my opponent to have that it's still better for me to have it over all.
True that, I totally forgot anti-kingmaking in Power Grid, that you sometimes gotta pay more than you wanted to stop somebody from ending the game.
Also, while talking about this game, while it is not related to Bottle Imp as there is no auction involved, the resource market works like real markets, i.e. you got sunspot equilibiria, expectations unrelated to fundamentals driving prices and so on. If players think that other player think about them that they think that uranium will be in high demand, these very players will buy a lot of uranium. No irrationality involved, just believes and expectations driving the system.
Which brings us back to Bottle Imp: your expectations about how other players behave will influence the amount you pay for it.
« Last Edit: December 12, 2018, 02:43:52 pm by Holunder9 »
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #42 on: December 12, 2018, 02:53:09 pm »
0

On the other hand, if for some reason player A already knew that for all players it was good to purchase the auction prize for 9 or less and bad to purchase it for 10 or more, then yes player A should immediately bid 9.
You assume again perfect rationality and perfect information. Human beings are not perfect so player A could gamble, bid 9 and hope that everybody else undervalues the asset.
It also depends on how granular the currency is. If you could e.g. bid 9,01 there is little cost in not gambling and not immediately bidding 9.


Quote
1. In the case of cursed bottle, the correct amount is either the minimum amount or not to take cursed bottle. So in fact it is very possible to compute the exact amount.
I wanna see these computations. Seriously, I know nothing about solving stochastic games and your knowledge about it could probably help a lot in creating decent Dominion bots.
I hope that the irony comes through. No human being calculates the optimum amount for Mountain pass or Bottle Imp while playing the game, not even experts in stochastic game theory. We use heuristics, rules of thumb.


Quote
2. This does not come into play with cursed bottle. Paying more for the bottle imp is both a higher cost and a lower reward. On the other hand, if you had to pay more than the previous time, it could work very nicely.
Huh? Bottle Imp doesn't have two upsides, it has an upside and a downside. If another player takes Bottle Imp away at a moment which is good for you because the costs of -13VPs outweighs the benefit of auto-Wishes each turn you are happy that he does it.
And, this is crucial, the other player might not behave irrationally at all! His deck could differ a lot from yours so for him the benefits of auto-Wishes outweigh the -13VPs.


3. Again, this doesn't apply to cursed bottle because of how you have to underbid. Like, am I going to buy bottle imp for 6 hoping that my opponent will spend 5 on it? That's nonsense; they are losing less than me, and regardless they can still just buy it for min amount.
Ccreating an option for you to get rid of -13VPs is always good. Creating an option for you to get rid of auto-Wish is always bad. You ignore this basic trade-off of the card the entire time.
In a situation in which you have played Cursed Bottle, have 6 Coins and want to buy an Ironmonger (because that is the b best card right now) you have 2 Coins left. There isn't any difference cost-wise between paying 0, 1 or 2 for Bottle Imp so your choice depends on how direly you want to hang onto it and how much you value the option that somebody might snatch it away from you. The best option is Kingdom-, time-, deck- and player-dependent.

Quote
Holunder:
I think that you are trolling, sorry if you aren't, I won't respond to you anymore.
You do implicitly assume stuff which is not always automatically the case in a real game of Dominion: that decks are symmetric, that the evaluation of the strength of a card is equal among players and constant over time, that nobody makes mistakes and so on. I might disagree too harshly with these assumptions but I have no interest in trolling you; this is about the game, not the players.
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Commodore Chuckles

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Re: Cursed Bottle / Bottle Imp
« Reply #43 on: December 12, 2018, 07:02:41 pm »
+2

I've come to agree with the people who say the $0 option is a problem. It's true that there can be some mind games involved in raising your bid, but that's not what I had in mind when I made the card in the first place. Regardless, I appreciate the interesting discussion it generated.

I tried to replicate the mechanics from the story as close as possible, but the fundamental problem is that Dominion is a zero-sum game and the Bottle Imp in the story isn't. When you sell it in the story, you don't care what the buyer is going to do with it, you just want to get rid of it. In Dominion, you do care what the other guy will do with it.

With that in mind, I've made an alternate version that's less faithful but is simpler and I think it plays better. Only Cursed Bottle is changed:



Now it's impossible to lock everyone else out. In the beginning of the game it will bounce back and forth every turn, but then as things wind down the players will have to decide if they want to be stuck with it in the end.
« Last Edit: December 12, 2018, 07:03:42 pm by Commodore Chuckles »
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Jimmmmm

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Re: Cursed Bottle / Bottle Imp
« Reply #44 on: December 12, 2018, 08:52:14 pm »
0


I think this is much more interesting.



What about an Event which says something like:
"Take the Bottle Imp. If you do, gain a card cheaper than any other card gained from Cursed Bottle this game."

Obviously the Event would have to be cheap and the penalty would have to be a lot smaller (and the Imp not provide a bonus).
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Shvegait

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Re: Cursed Bottle / Bottle Imp
« Reply #45 on: December 12, 2018, 10:33:34 pm »
+1

What if instead of Cursed Bottle you made an Event: "Buy the Bottle Imp"

Cost $0

If there are any coin tokens on this, you may pay $1 for each coin token on this to take the Bottle Imp. If you do, remove a coin token from this.

Setup: Put X coin tokens on this. (Maybe 8, 9, 10? It's probably significant in 2 player whether this amount is odd or even.)


Then you still get the decreasing cost thing as the game goes on, but you take away the player's ability to send the cost to the minimum.
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GendoIkari

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Re: Cursed Bottle / Bottle Imp
« Reply #46 on: December 13, 2018, 03:59:06 pm »
+1

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

So some discussion about first edition Scheme vs second edition Scheme in the rules thread has made me realize that this isn't always correct!

If one choice is strictly worse than another choice, then giving your opponent a choice is actually strictly better than forcing the better choice on your opponent!

As a stupid basic example, a card that says "Each opponent chooses one: +1, or +2" is strictly better than a card that says "Each opponent gets +2". (Pretty sure having an extra VP token is about the only resource left that it can't be bad to have).

Yes, every rational opponent will always choose the +2 option. But by giving them options, you give them the possibility of making a mistake and choosing +1.

The silliness goes away somewhat when it's not always so obvious which choice is strictly better; such that your opponent actually may be likely to make the wrong choice.
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faust

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Re: Cursed Bottle / Bottle Imp
« Reply #47 on: December 14, 2018, 01:02:09 am »
+1

The silliness goes away somewhat when it's not always so obvious which choice is strictly better; such that your opponent actually may be likely to make the wrong choice.
But this only works if you think you have a significantly better understanding of what the best choice is, i.e. if you assume that your opponent is a worse player than you.
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Holunder9

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Re: Cursed Bottle / Bottle Imp
« Reply #48 on: December 14, 2018, 03:18:54 am »
0

The silliness goes away somewhat when it's not always so obvious which choice is strictly better; such that your opponent actually may be likely to make the wrong choice.
But this only works if you think you have a significantly better understanding of what the best choice is, i.e. if you assume that your opponent is a worse player than you.
No. GendoIkari specifically pointed out that the choice is meant to be complicated and murky, when even the best players in the world could mess up. Also, as the card offers the choices and not the player, how well player A understands it has nothing to do with how likely player B is to make a mistake.

When you are close to time control in chess and the opponent has little time on their clock (they get extra time after the time control), making a move that gives him more options is often better than one that gives him fewer options, even if the former is slightly inferior to the latter. This has nothing to do with player strength, playing like this is smart even if you are the the less skilled player or even if you don't understand the current position particularly well. Give them enough rope and they'll hang themselves.

You could argue that due to the time constraints, at the very moment of choice the player who got served more options is currently the worse player, not due his skills but due to the bad time situation.
But, to get back to Bottle Imp, this is pretty much the very situation we all are in when we play with a fairly unusual new card, we are then all (situationally) bad players.


Maths has been mentioned a few times in this thread and I think a lot of people come towards this either from plain intuition (intuitively more options imply freedom and are perceived as good although being in a huge mall with a huge selection of products can also make you feel the other way around) or from something like optimization where a larger option space is better than a smaller one.
But we talk about games, not decisions made by individuals in a void, so you gotta take strategtic interaction into account. And if you come towards this from game theory you are not surprised about more options being potentially bad.
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