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Author Topic: Strictly better than....  (Read 111039 times)

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Roadrunner7671

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Re: Strictly better than....
« Reply #350 on: December 01, 2015, 05:11:36 pm »
0

Worker's Village isn't strictly better than Village because it's cost is different.
So Upgrade and Remake might prefer a normal Village.
And Village can be better if it's the Bane.
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Jimmmmm

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Re: Strictly better than....
« Reply #351 on: December 01, 2015, 05:14:29 pm »
+2

I understand what strictly better means, and I understand what Plaza does.

Okay, consider a Village that also had the effect, "You may flip a coin. If you flip heads, +2 VP. If you flip tails, -1 VP (whatever that means)." Clearly it's usually better to flip the coin, but in doing so you risk repeatedly flipping tails. I don't think it's enough to say, "Well you could have just never flipped the coin." If optimal use of the card can have a negative effect (compared to the card we're comparing it to), I'd say it's not strictly better.

Except it is strictly better, because you could resolve to never use the coin flip effect except when it would 100% benefit you.  And yes, even with this randomness, I can design an edge case to make that happen:

- Two piles are empty and there's only one Ruins remaining.
- You are first player but 1VP behind.
- Your hand is all junk, you have $0.

Now you can safely use this ability for a chance at winning a game you are guaranteed to lose otherwise.  Strictly better.

But even accepting your argument, Plaza isn't like that.  There is no coin flip involved.

Plaza is technically strictly better than Village, but in practice it's possible to make all the right decisions and lose because you had a Plaza when you would have won with a Village.
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eHalcyon

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Re: Strictly better than....
« Reply #352 on: December 01, 2015, 05:44:14 pm »
0

Worker's Village isn't strictly better than Village because it's cost is different.
So Upgrade and Remake might prefer a normal Village.
And Village can be better if it's the Bane.

And that's why cost-caring cards are universal edge cases, which we've already discussed at length.

Not sure if anybody's brought up the Bane issue before.  That'll have to be another thing we add to the universal edge case list.

I understand what strictly better means, and I understand what Plaza does.

Okay, consider a Village that also had the effect, "You may flip a coin. If you flip heads, +2 VP. If you flip tails, -1 VP (whatever that means)." Clearly it's usually better to flip the coin, but in doing so you risk repeatedly flipping tails. I don't think it's enough to say, "Well you could have just never flipped the coin." If optimal use of the card can have a negative effect (compared to the card we're comparing it to), I'd say it's not strictly better.

Except it is strictly better, because you could resolve to never use the coin flip effect except when it would 100% benefit you.  And yes, even with this randomness, I can design an edge case to make that happen:

- Two piles are empty and there's only one Ruins remaining.
- You are first player but 1VP behind.
- Your hand is all junk, you have $0.

Now you can safely use this ability for a chance at winning a game you are guaranteed to lose otherwise.  Strictly better.

But even accepting your argument, Plaza isn't like that.  There is no coin flip involved.

Plaza is technically strictly better than Village, but in practice it's possible to make all the right decisions and lose because you had a Plaza when you would have won with a Village.

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.
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scott_pilgrim

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Re: Strictly better than....
« Reply #353 on: December 01, 2015, 06:04:45 pm »
+1

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.
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eHalcyon

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Re: Strictly better than....
« Reply #354 on: December 01, 2015, 06:09:20 pm »
0

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).
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scott_pilgrim

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Re: Strictly better than....
« Reply #355 on: December 01, 2015, 06:12:59 pm »
+1

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.
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eHalcyon

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Re: Strictly better than....
« Reply #356 on: December 01, 2015, 06:17:53 pm »
0

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.
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singletee

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Re: Strictly better than....
« Reply #357 on: December 01, 2015, 06:18:55 pm »
+2

Regret based on future events can't be taken into account when determining strict betterness. If you did, it would be a totally universal edge case and no card could be better than another unless "you win" were printed on the former or "you lose" on the latter.

wachsmuth

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Re: Strictly better than....
« Reply #358 on: December 01, 2015, 06:23:58 pm »
+4

Village is sometimes better than Worker's Village, because you could use the extra Buy to buy a Curse.
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scott_pilgrim

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Re: Strictly better than....
« Reply #359 on: December 01, 2015, 06:27:35 pm »
+2

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.

Right, I'm not claiming that you can't do that.  I'm agreeing with Jimm that you can improve your chances of winning in some particular situation by having Plaza rather than Village, but it's possible that in that same situation, you will lose because you had Plaza rather than Village, if you choose to maximize your chances of winning.

Another way of putting it is, you can choose to either play Plaza as if it is a Village, or play it as if your goal is to win the game of Dominion.  If you choose the former, then it is identical to Village.  If you choose the latter, then there can be cases where you would have won if you had had Village rather than Plaza.  That doesn't make Plaza "worse" than Village, and arguably it's still strictly better (depending on how "strictly better" is defined).  But you seem to be denying that this is possible, which I disagree with.
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eHalcyon

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Re: Strictly better than....
« Reply #360 on: December 01, 2015, 06:40:50 pm »
+2

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.

Right, I'm not claiming that you can't do that.  I'm agreeing with Jimm that you can improve your chances of winning in some particular situation by having Plaza rather than Village, but it's possible that in that same situation, you will lose because you had Plaza rather than Village, if you choose to maximize your chances of winning.

Another way of putting it is, you can choose to either play Plaza as if it is a Village, or play it as if your goal is to win the game of Dominion.  If you choose the former, then it is identical to Village.  If you choose the latter, then there can be cases where you would have won if you had had Village rather than Plaza.  That doesn't make Plaza "worse" than Village, and arguably it's still strictly better (depending on how "strictly better" is defined).  But you seem to be denying that this is possible, which I disagree with.

Again, if you accept this kind of argument, then no card could ever be strictly better than another by any reasonable definition.  Even an imaginary card that is identical to Village except it optionally grants you +1VP token on play could be worse, because it could give you a VP lead that leads you to take a risk that loses the game for you.

I acknowledge that you could play Plaza such that you would have lost whereas you would have won with Village, but I disagree that this is a way in that Plaza is worse and I disagree that this will happen when you make the right choice.  If you would have won with a regular Village, then you should have played your Plaza as a regular Village except when you are 100% sure that the discard won't come back to bite you later -- e.g. when you don't have any other action card to play after this -- which is still a strictly better effect than regular Village.  This is just a question of YMOSL now.  Don't blame the card for giving you a choice when this happens.  Blame your choice.
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Simon (DK)

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Re: Strictly better than....
« Reply #361 on: December 01, 2015, 06:42:16 pm »
0

How come cost is a universal edge case, but type isn't?
There's cards that share the same cost and cards that share types.
No 2 different costs can be strictly better than the other, but I'm pretty sure the same goes for types.

We don't say that about the cost itself.  "Universal edge case" was the term we ended up using for specific cards that can always be used to make one card better than another one which would otherwise be strictly superior.  For example, Possession is a universal edge case because I would want a weaker card in hand when you play Possession.  Likewise, the other universal edge cases also provide ways of making a card with a strictly inferior effect better to have in hand.

We name cost-caring cards like Forge, Remake, Upgrade as "universal" edge cases because they can make you prefer having (for example) Village over Mining Village.  Yes, there are cards that share the same cost, but no such pair of cards in Dominion will have one be strictly superior than the other.  That's also the reason why we are just discussing strictly superior effects rather than strictly superior cards.

By contrast, not counting type as a universal edge case doesn't invalidate every potential case of one card being strictly superior.  It's not universal.

I found this difficult to explain.  Does that make sense?

It makes perfect sense. Thanks :)
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Kirian

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Re: Strictly better than....
« Reply #362 on: December 01, 2015, 06:45:38 pm »
+2

You can name the Ace of Spades

Oh, that's why that is there?!?!  I never realized, haha.  I always thought it was just a for-funzies feature Goko/MF put in, like as a joke or something.  I guess it says "Name a card", not "Name a Dominion card", so technically you could say the Queen of hearts or something.  Or Hologram Raichu.

I like to name the Platinum Yendorian Express Card.

Nice reference.

I prefer to name the Race Card.
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Dingan

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Re: Strictly better than....
« Reply #363 on: December 01, 2015, 07:04:31 pm »
0

Strictly worse is strictly better when you're possessed.
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Simon (DK)

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Re: Strictly better than....
« Reply #364 on: December 01, 2015, 07:07:44 pm »
+2

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.

Right, I'm not claiming that you can't do that.  I'm agreeing with Jimm that you can improve your chances of winning in some particular situation by having Plaza rather than Village, but it's possible that in that same situation, you will lose because you had Plaza rather than Village, if you choose to maximize your chances of winning.

Another way of putting it is, you can choose to either play Plaza as if it is a Village, or play it as if your goal is to win the game of Dominion.  If you choose the former, then it is identical to Village.  If you choose the latter, then there can be cases where you would have won if you had had Village rather than Plaza.  That doesn't make Plaza "worse" than Village, and arguably it's still strictly better (depending on how "strictly better" is defined).  But you seem to be denying that this is possible, which I disagree with.

Again, if you accept this kind of argument, then no card could ever be strictly better than another by any reasonable definition.  Even an imaginary card that is identical to Village except it optionally grants you +1VP token on play could be worse, because it could give you a VP lead that leads you to take a risk that loses the game for you.

I acknowledge that you could play Plaza such that you would have lost whereas you would have won with Village, but I disagree that this is a way in that Plaza is worse and I disagree that this will happen when you make the right choice.  If you would have won with a regular Village, then you should have played your Plaza as a regular Village except when you are 100% sure that the discard won't come back to bite you later -- e.g. when you don't have any other action card to play after this -- which is still a strictly better effect than regular Village.  This is just a question of YMOSL now.  Don't blame the card for giving you a choice when this happens.  Blame your choice.

Here's an example where the correct Plaza choice makes you loose the game:

You have 0$ to spend and have reduced costs by 6. If you gain the last Colony or the 3 last Duchies you win, otherwise you loose. After playing Plaza and drawing a card you have Horn of Plenty and Great Hall in your hand. In your deck you have a Horn of Plenty and 2 Poor Houses, but you don't know the order of them.

If you discard Horn of Plenty to the Plaza, there's 67 % chance that you'll draw a Poor House and win and 33 % chance you'll draw the Horn of Plenty and loose.

If you don't discard Horn of Plenty to the Plaza, there's 67 % chance that you'll draw a Poor House and loose and 33 % chance you'll draw the Horn of Plenty and win.

So to maximise your chance of winning, the correct choice is to discard your Horn of Plenty. But if the top card of your deck is Horn of Plenty, then you would have been better off with a Village, so you didn't have the choice.
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singletee

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Re: Strictly better than....
« Reply #365 on: December 01, 2015, 07:14:11 pm »
+1

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.

Right, I'm not claiming that you can't do that.  I'm agreeing with Jimm that you can improve your chances of winning in some particular situation by having Plaza rather than Village, but it's possible that in that same situation, you will lose because you had Plaza rather than Village, if you choose to maximize your chances of winning.

Another way of putting it is, you can choose to either play Plaza as if it is a Village, or play it as if your goal is to win the game of Dominion.  If you choose the former, then it is identical to Village.  If you choose the latter, then there can be cases where you would have won if you had had Village rather than Plaza.  That doesn't make Plaza "worse" than Village, and arguably it's still strictly better (depending on how "strictly better" is defined).  But you seem to be denying that this is possible, which I disagree with.

Again, if you accept this kind of argument, then no card could ever be strictly better than another by any reasonable definition.  Even an imaginary card that is identical to Village except it optionally grants you +1VP token on play could be worse, because it could give you a VP lead that leads you to take a risk that loses the game for you.

I acknowledge that you could play Plaza such that you would have lost whereas you would have won with Village, but I disagree that this is a way in that Plaza is worse and I disagree that this will happen when you make the right choice.  If you would have won with a regular Village, then you should have played your Plaza as a regular Village except when you are 100% sure that the discard won't come back to bite you later -- e.g. when you don't have any other action card to play after this -- which is still a strictly better effect than regular Village.  This is just a question of YMOSL now.  Don't blame the card for giving you a choice when this happens.  Blame your choice.

Here's an example where the correct Plaza choice makes you loose the game:

You have 0$ to spend and have reduced costs by 6. If you gain the last Colony or the 3 last Duchies you win, otherwise you loose. After playing Plaza and drawing a card you have Horn of Plenty and Great Hall in your hand. In your deck you have a Horn of Plenty and 2 Poor Houses, but you don't know the order of them.

If you discard Horn of Plenty to the Plaza, there's 67 % chance that you'll draw a Poor House and win and 33 % chance you'll draw the Horn of Plenty and loose.

If you don't discard Horn of Plenty to the Plaza, there's 67 % chance that you'll draw a Poor House and loose and 33 % chance you'll draw the Horn of Plenty and win.

So to maximise your chance of winning, the correct choice is to discard your Horn of Plenty. But if the top card of your deck is Horn of Plenty, then you would have been better off with a Village, so you didn't have the choice.

Right, but the question being asked is "Which card would I rather have in hand right now?", not "Which card would I like to have had given what happened afterwards?".

Simon (DK)

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Re: Strictly better than....
« Reply #366 on: December 01, 2015, 07:27:03 pm »
0

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.

Right, I'm not claiming that you can't do that.  I'm agreeing with Jimm that you can improve your chances of winning in some particular situation by having Plaza rather than Village, but it's possible that in that same situation, you will lose because you had Plaza rather than Village, if you choose to maximize your chances of winning.

Another way of putting it is, you can choose to either play Plaza as if it is a Village, or play it as if your goal is to win the game of Dominion.  If you choose the former, then it is identical to Village.  If you choose the latter, then there can be cases where you would have won if you had had Village rather than Plaza.  That doesn't make Plaza "worse" than Village, and arguably it's still strictly better (depending on how "strictly better" is defined).  But you seem to be denying that this is possible, which I disagree with.

Again, if you accept this kind of argument, then no card could ever be strictly better than another by any reasonable definition.  Even an imaginary card that is identical to Village except it optionally grants you +1VP token on play could be worse, because it could give you a VP lead that leads you to take a risk that loses the game for you.

I acknowledge that you could play Plaza such that you would have lost whereas you would have won with Village, but I disagree that this is a way in that Plaza is worse and I disagree that this will happen when you make the right choice.  If you would have won with a regular Village, then you should have played your Plaza as a regular Village except when you are 100% sure that the discard won't come back to bite you later -- e.g. when you don't have any other action card to play after this -- which is still a strictly better effect than regular Village.  This is just a question of YMOSL now.  Don't blame the card for giving you a choice when this happens.  Blame your choice.

Here's an example where the correct Plaza choice makes you loose the game:

You have 0$ to spend and have reduced costs by 6. If you gain the last Colony or the 3 last Duchies you win, otherwise you loose. After playing Plaza and drawing a card you have Horn of Plenty and Great Hall in your hand. In your deck you have a Horn of Plenty and 2 Poor Houses, but you don't know the order of them.

If you discard Horn of Plenty to the Plaza, there's 67 % chance that you'll draw a Poor House and win and 33 % chance you'll draw the Horn of Plenty and loose.

If you don't discard Horn of Plenty to the Plaza, there's 67 % chance that you'll draw a Poor House and loose and 33 % chance you'll draw the Horn of Plenty and win.

So to maximise your chance of winning, the correct choice is to discard your Horn of Plenty. But if the top card of your deck is Horn of Plenty, then you would have been better off with a Village, so you didn't have the choice.

Right, but the question being asked is "Which card would I rather have in hand right now?", not "Which card would I like to have had given what happened afterwards?".

I'm not saying that Plaza isn't strictly better than Village.
And after reading it again I realize what eHalcyon was saying with his last post and agree with it.

I just simply saw a sub-puzzle that I thought was fun finding an answer to :)
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Jimmmmm

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Re: Strictly better than....
« Reply #367 on: December 01, 2015, 07:30:37 pm »
0

Worker's Village isn't strictly better than Village because it's cost is different.
So Upgrade and Remake might prefer a normal Village.
And Village can be better if it's the Bane.

And that's why cost-caring cards are universal edge cases, which we've already discussed at length.

Not sure if anybody's brought up the Bane issue before.  That'll have to be another thing we add to the universal edge case list.

I understand what strictly better means, and I understand what Plaza does.

Okay, consider a Village that also had the effect, "You may flip a coin. If you flip heads, +2 VP. If you flip tails, -1 VP (whatever that means)." Clearly it's usually better to flip the coin, but in doing so you risk repeatedly flipping tails. I don't think it's enough to say, "Well you could have just never flipped the coin." If optimal use of the card can have a negative effect (compared to the card we're comparing it to), I'd say it's not strictly better.

Except it is strictly better, because you could resolve to never use the coin flip effect except when it would 100% benefit you.  And yes, even with this randomness, I can design an edge case to make that happen:

- Two piles are empty and there's only one Ruins remaining.
- You are first player but 1VP behind.
- Your hand is all junk, you have $0.

Now you can safely use this ability for a chance at winning a game you are guaranteed to lose otherwise.  Strictly better.

But even accepting your argument, Plaza isn't like that.  There is no coin flip involved.

Plaza is technically strictly better than Village, but in practice it's possible to make all the right decisions and lose because you had a Plaza when you would have won with a Village.

Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

The randomness comes from not knowing what you'll draw.

Say you play a Plaza, and have only one Treasure in your hand, a Copper. You also have, say, a Ruined Library. The rest of your deck is almost all junk, so you know that if you keep the Copper in hand, there's only a very small chance that you'll draw your Stables and then with that draw enough to buy the last Province and win the game. Due to durations, you know you'll have $7 next turn, and you also know your opponent's deck well enough to know there's only a very small chance they'll be able to buy a Province on their next turn. So the right decision is to discard the Copper, getting you to $8 next turn, buy a Duchy and give up a very small chance of winning this turn for a very high chance of winning next turn.

And of course, by some miracle you would have drawn your Stables and then enough to buy a Province and your opponent got an unlikely Province hand, leaving you wishing your Plaza was a plain old Village instead.
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eHalcyon

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Re: Strictly better than....
« Reply #368 on: December 01, 2015, 07:53:29 pm »
0

The randomness comes from not knowing what you'll draw.

Say you play a Plaza, and have only one Treasure in your hand, a Copper. You also have, say, a Ruined Library. The rest of your deck is almost all junk, so you know that if you keep the Copper in hand, there's only a very small chance that you'll draw your Stables and then with that draw enough to buy the last Province and win the game. Due to durations, you know you'll have $7 next turn, and you also know your opponent's deck well enough to know there's only a very small chance they'll be able to buy a Province on their next turn. So the right decision is to discard the Copper, getting you to $8 next turn, buy a Duchy and give up a very small chance of winning this turn for a very high chance of winning next turn.

And of course, by some miracle you would have drawn your Stables and then enough to buy a Province and your opponent got an unlikely Province hand, leaving you wishing your Plaza was a plain old Village instead.

Right, but the question being asked is "Which card would I rather have in hand right now?", not "Which card would I like to have had given what happened afterwards?".

You should be wishing that you had made a different choice, not that you weren't given a choice to begin with.
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Jimmmmm

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Re: Strictly better than....
« Reply #369 on: December 01, 2015, 07:58:24 pm »
+2

The randomness comes from not knowing what you'll draw.

Say you play a Plaza, and have only one Treasure in your hand, a Copper. You also have, say, a Ruined Library. The rest of your deck is almost all junk, so you know that if you keep the Copper in hand, there's only a very small chance that you'll draw your Stables and then with that draw enough to buy the last Province and win the game. Due to durations, you know you'll have $7 next turn, and you also know your opponent's deck well enough to know there's only a very small chance they'll be able to buy a Province on their next turn. So the right decision is to discard the Copper, getting you to $8 next turn, buy a Duchy and give up a very small chance of winning this turn for a very high chance of winning next turn.

And of course, by some miracle you would have drawn your Stables and then enough to buy a Province and your opponent got an unlikely Province hand, leaving you wishing your Plaza was a plain old Village instead.

Right, but the question being asked is "Which card would I rather have in hand right now?", not "Which card would I like to have had given what happened afterwards?".

You should be wishing that you had made a different choice, not that you weren't given a choice to begin with.

I'm not wishing anything. I'm just saying with correct use of Plaza in that situation you lose, whereas with Village you win. Sometimes it's bad to be given a choice.
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markusin

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Re: Strictly better than....
« Reply #370 on: December 01, 2015, 09:19:03 pm »
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Well it's a good thing that strictness is very much a technical thing to discuss.

But I disagree.  If you would have won with a village, then clearly you did not make the right decision somewhere along the line.  Plaza doesn't have any sort of randomness attached to it that would lead you to make the right decision and come out for the worse.

You don't know the order of the cards in your deck; that could possibly lead you to prefer to not have discarded a treasure, even though probabilistically it would have been the right play.  For example, you choose to discard a Copper because you have 100 cards in your deck and only one of them is a Spice Merchant.  You then play a draw card and pick up the Spice Merchant, and now you regret having discarded the Copper.

If this is a big enough problem that you would lose the game, then discarding is the wrong choice.  Instead, you can just always choose not to discard unless you are certain that Spice Merchant will not be drawn (usually because it's already in your discard).

I can make the probability of drawing Spice Merchant arbitrarily small by making my deck as large as I want.  At some point, the expected payoff will have to be so small that taking the coin token is better on average.

And yet you can still follow that rule to only use the discard when you are entirely 100% certain.

Right, I'm not claiming that you can't do that.  I'm agreeing with Jimm that you can improve your chances of winning in some particular situation by having Plaza rather than Village, but it's possible that in that same situation, you will lose because you had Plaza rather than Village, if you choose to maximize your chances of winning.

Another way of putting it is, you can choose to either play Plaza as if it is a Village, or play it as if your goal is to win the game of Dominion.  If you choose the former, then it is identical to Village.  If you choose the latter, then there can be cases where you would have won if you had had Village rather than Plaza.  That doesn't make Plaza "worse" than Village, and arguably it's still strictly better (depending on how "strictly better" is defined).  But you seem to be denying that this is possible, which I disagree with.

Again, if you accept this kind of argument, then no card could ever be strictly better than another by any reasonable definition.  Even an imaginary card that is identical to Village except it optionally grants you +1VP token on play could be worse, because it could give you a VP lead that leads you to take a risk that loses the game for you.

Exactly. If you consider how a card affects our decision making when determining what is strictly better, than even a "strictly better" Monument that gives 2VP instead on 1VP per play would not be strictly better because it can cause your opponent to fall further behind and take the risk of breaking PPR when he or she wouldn't have if you had played "original" monument, in a situation where your opponent breaking PPR costs you the game.

I would have to say worsened decision making would need to be a universal edge case. I mean, what about a village that optionally lets you see your opponent's hand, and doing so causes you make a different play than you normally would have and which nets a worse result?
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managore

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Re: Strictly better than....
« Reply #371 on: December 01, 2015, 11:07:45 pm »
0

Strictly worse is strictly better when you're possessed.

You really have to ignore Possession (and Masq and card cost and the-card-is-worse-because-it-might-make-you-make-a-bad-decision) or you end up with precisely zero cards being strictly better than any other card.
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Roadrunner7671

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Re: Strictly better than....
« Reply #372 on: December 01, 2015, 11:10:11 pm »
0

Strictly worse is strictly better when you're possessed.

You really have to ignore Possession (and Masq and card cost and the-card-is-worse-because-it-might-make-you-make-a-bad-decision) or you end up with precisely zero cards being strictly better than any other card.
So, in conclusion, there is no card that is universally better than any other card.

I'n glad it took us 15 pages to reach this development
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markusin

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Re: Strictly better than....
« Reply #373 on: December 01, 2015, 11:33:16 pm »
+1

Strictly worse is strictly better when you're possessed.

You really have to ignore Possession (and Masq and card cost and the-card-is-worse-because-it-might-make-you-make-a-bad-decision) or you end up with precisely zero cards being strictly better than any other card.
So, in conclusion, there is no card that is universally better than any other card.

I'n glad it took us 15 pages to reach this development

15 pages backed by a long history of obsessing over edge cases.

There's an edge case for pretty much everything now it seems. It used to be the case that there was no real edge case for playing Adventurer before Poor House when revealing both to Golem, but Storyteller changed that.

IMB4 there's actually 8 pages.
« Last Edit: December 01, 2015, 11:35:44 pm by markusin »
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scott_pilgrim

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Re: Strictly better than....
« Reply #374 on: December 01, 2015, 11:51:25 pm »
+3

I feel like everything I said is being strawmanned.  I never said (or even implied, I think) that Plaza is not strictly better than Village, or that you should ever buy Village over Plaza when universal edge cases are not considered.  I said exactly what I said, that there are cases in which you would have been better off with Village than Plaza, given that you play optimally with both.  Of course it is a universal edge case, I can construct a similar case in which Village is better than Worker's Village.

You should be wishing that you had made a different choice, not that you weren't given a choice to begin with.

There's no such thing as "wishing" in Dominion (unless you're playing Wishing Well).  I won't be wishing I made a different choice.  I'll be wishing the more likely thing happened, the one that I was playing too.  I didn't make the wrong choice.  The cards came up in the wrong order.

If I bet you $1,000 that you will not get a 6 when you roll a standard fair die, and you do get a 6, I won't regret making the bet, because I know I did the right thing.  I'll be disappointed that it didn't work out, but if you offered to let me do it again, I totally would, because it's always going to be the right thing to do (unless I decide that losing $1,000 is 5 times worse for me than how good gaining $1,000 would be).  If the ends justify the means, as you seem to be arguing, then there's no practical use of the term "optimal play", because the optimal play is (usually) only determinable in retrospect.
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