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Author Topic: When to play Wishing Well  (Read 7047 times)

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GeoLib

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When to play Wishing Well
« on: May 28, 2014, 03:15:49 am »
+5

In his stream of a lesson to Jerni at 38:45 while playing a mass WW and Grand Market deck SCSN says that you should always play wishing well first because then if you wish wrong you can pick up the missed card with the GM. I had thought quite the opposite and was wondering the whole time why he kept playing WW instead of GM first. My thinking is that the more other draw cards you play first, the more information you have about the rest of your deck, and therefore the more accurate your wish. So say that you have a deck full of WW, silvers, and GM. Your hand has 1 GM and 1 WW. Which do you play first?

My thought is play GM first because then when you play WW you will have more information about your remaining deck composition. By this method you draw 1 from GM, 1 from WW, and 1*P(guess right) from WW. SCSN says to play WW first because then if you're wrong you can draw the remaining card with GM. By this method you draw 1 from WW, 1*P(guess right), and 1 from GM. So I don't see how playing WW first is the better move. As far as I can tell you are more likely to guess right and draw more cards by playing GM first.

So what are your thoughts on this? I'm especially interested to hear from SCSN, since he was the one who made the original claim with which I disagree. Am I missing something?
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Davio

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Re: When to play Wishing Well
« Reply #1 on: May 28, 2014, 03:30:08 am »
+3

Play WW last and improve your chances to guess right.

That's how I always do it. It's a bit silly to play WW's first and draw the misses with GM.
I mean, if you play WW, guess wrong, play GM, you draw the exact same cards as when you would have played GM first, then WW and guessed wrong. In both cases you just draw the top 2 cards of your deck.

You should use WW to maximize the chances of getting an extra card.
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GeoLib

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Re: When to play Wishing Well
« Reply #2 on: May 28, 2014, 03:32:20 am »
+1

Play WW last and improve your chances to guess right.

That's how I always do it. It's a bit silly to play WW's first and draw the misses with GM.
I mean, if you play WW, guess wrong, play GM, you draw the exact same cards as when you would have played GM first, then WW and guessed wrong. In both cases you just draw the top 2 cards of your deck.

You should use WW to maximize the chances of getting an extra card.

That is my thinking exactly, so I was wondering if I was missing something. I guess I'll just wait to see if SCSN chimes in.
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amalloy

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Re: When to play Wishing Well
« Reply #3 on: May 28, 2014, 04:07:37 am »
+4

In his stream of a lesson to Jerni at 38:45 while playing a mass WW and Grand Market deck SCSN says that you should always play wishing well first because then if you wish wrong you can pick up the missed card with the GM. I had thought quite the opposite and was wondering the whole time why he kept playing WW instead of GM first. My thinking is that the more other draw cards you play first, the more information you have about the rest of your deck, and therefore the more accurate your wish. So say that you have a deck full of WW, silvers, and GM. Your hand has 1 GM and 1 WW. Which do you play first?

My thought is play GM first because then when you play WW you will have more information about your remaining deck composition. By this method you draw 1 from GM, 1 from WW, and 1*P(guess right) from WW. SCSN says to play WW first because then if you're wrong you can draw the remaining card with GM. By this method you draw 1 from WW, 1*P(guess right), and 1 from GM. So I don't see how playing WW first is the better move. As far as I can tell you are more likely to guess right and draw more cards by playing GM first.

So what are your thoughts on this? I'm especially interested to hear from SCSN, since he was the one who made the original claim with which I disagree. Am I missing something?

It depends on what you need. Playing GM first maximizes the odds of a correct guess, and thus the number of cards you will draw on average. However, that's not always what you need: playing WW first allows you to "buy insurance", reducing your best case in exchange for improving the worst case.

Suppose you have remaining in your deck two Coppers, a Market, and a Province; in hand are a Market and a Wishing Well.

If you need to draw all three money cards to win the game, you play the Market first, then play Wishing Well, and wish for whatever money card you haven't yet drawn (succeeding if the Province is the bottom card of your deck, or if you drew the Market soon enough to draw all four cards). This is clearly superior to playing Wishing Well first, because you would have to guess among three cards instead of two.

However, what if you only need two money cards? Then playing the Market first leaves you in danger: you might draw a Copper with your Market, then draw Province with Wishing Well, and be stuck on a 50/50 guess for the last card. Instead, play Wishing Well first.

  • If you draw the Market, then anything works: you are guaranteed the $2 you needed to draw, and you can choose to wish however you like.
  • If you draw Province, you should wish for Copper: either you are successful and get a Copper plus another guaranteed money-card draw from your Market; or you miss, but your Market draws the Market which is on top of your deck, and then you get another Copper.
  • If you draw a Copper, then wish for Province. If you hit it, your Market draws you another money card (and maybe two); if you miss, then your Market draws whatever money card was on top of your deck instead of Province.

Cases (2) and (3) above are conceptually the same, and don't really need to be argued separately, but are enumerated for completeness.

Edit: The same sort of argument can apply to a larger deck, eg if your "maximum" draw is overdrawing your deck, you can sacrifice some of the wasted extra draw in order to be more certain of drawing your entire deck.

Further Edit: So the rule of thumb I use is: if I need great draws, then I'll play the non-wishing cantrip first (here, GM), and then use the wishing card to pick up whatever it is I still need. If mediocre draws will suffice, and I want to ensure against really terrible draws, then I wish first, and aim for bad cards. If I successfully hit them, then I've avoided the bad turn I was going to have; if I miss, I get a decent turn anyway because I didn't have junk on top of my deck.

Maybe SCSN plays so well that mediocre draws will always suffice to win the game: that would explain why his rule of thumb is "WW first always"!
« Last Edit: May 28, 2014, 04:35:54 am by amalloy »
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SCSN

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Re: When to play Wishing Well
« Reply #4 on: May 28, 2014, 04:47:40 am »
+8

If all you cared about was maximizing your draw you obviously want to play your WWs as close to the bottom of your shuffle as possible, which would frequently entail playing other cantrips first. However, with only a single WW in hand and no other cantrips, the play with the highest expected positive change in your win % is very often wishing for a card other than the most likely one. Hence playing all your cantrips first forces you to make "suboptimal" guesses to avoid missing out on a key card, whereas saving a cantrip maximizes your draw conditional on minimizing the chance of missing said card.

To give a concrete example: assume there's one Goons left in your deck together with a ton of Coppers. Also assume that with just a single WW in hand, optimal play dictates wishing for Goons if you don't draw it. Then with both a WW and a single cantrip in hand, playing the cantrip first would force you to make a "suboptimal" (in the sense of not being most likely to succeed) WW guess, resulting most of the time in you drawing just 2 Coppers. If, on the other hand, you play WW first and now guess for Copper, you'll end up with 3 Coppers rather than 2 if the Goons isn't in the top 3 cards, without risking missing it because if it's revealed you can still draw it with your cantrip.

That said, I do think I misplayed it a bit in the video by mistakenly generalizing this concept to situations where you have multiple cantrips in hand. I should have played all but my last non-WW cantrip prior to the WWs to maximize correct guessing. Thanks for bringing this to my attention :)
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Re: When to play Wishing Well
« Reply #5 on: May 28, 2014, 05:03:36 am »
+5

This is the order you should play your cards:

1) cards that draw bad cards (such as Vagrant)
2) cards that draw random cards
3) cards that draw good cards (such as Sage)

The reason should be obvious: the random cards you draw are better if you have removed all of the bad cards from your deck, and worse if you have removed all of the good cards from your deck.

If you want to wish for a bad card, play WW first. If you want to wish for a good card, play WW last.
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Re: When to play Wishing Well
« Reply #6 on: May 28, 2014, 05:07:49 am »
+1

At least we can conclude that there's no one way to play it and there are several scenarios.

If you just want as many cards in hand as you can, you guess for the most likely card.
But as others pointed out, sometimes you don't want the most common card (most often Copper), but a specific card.

If you play WW first in that case, the hit % doesn't decrease that much, but your 'reward' for missing is knowledge about the next card. If it's a Gold for instance and you have $8 without drawing it with your last GM in hand, you can decide to leave it there and just buy a Province this turn instead of Province/Estate or Province/Silver...

My rule of thumb in the early game is to just increase my # of cards in hand and thus increase cycling by generally always guessing Copper (sometimes Estate), but I can see reasons to do it the other way around.


In trying to decide what to do first, I think information is key. Cards that reveal the top card and sometimes draw it, like Vagrant and Herald, may give you crucial information on what to do next.

Also, mind your shuffles! A lot of times I just choose not to play a draw-and-reveal card, because I've just one card remaining in my draw pile and a lot of my good cards are already in play.
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amalloy

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Re: When to play Wishing Well
« Reply #7 on: May 28, 2014, 05:42:51 am »
+1

This is the order you should play your cards:

1) cards that draw bad cards (such as Vagrant)
2) cards that draw random cards
3) cards that draw good cards (such as Sage)

The reason should be obvious: the random cards you draw are better if you have removed all of the bad cards from your deck, and worse if you have removed all of the good cards from your deck.

If you want to wish for a bad card, play WW first. If you want to wish for a good card, play WW last.

I mean, your reason may be obvious, but it's not correct in general. For example, if the only good cards left in my deck are two Mountebanks, then I'd rather play my Golem before I happen to draw them with a Scheme; otherwise my Golem draw nothing at all!
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amalloy

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Re: When to play Wishing Well
« Reply #8 on: May 28, 2014, 05:50:03 am »
0

To give a concrete example: assume there's one Goons left in your deck together with a ton of Coppers. Also assume that with just a single WW in hand, optimal play dictates wishing for Goons if you don't draw it. Then with both a WW and a single cantrip in hand, playing the cantrip first would force you to make a "suboptimal" (in the sense of not being most likely to succeed) WW guess, resulting most of the time in you drawing just 2 Coppers. If, on the other hand, you play WW first and now guess for Copper, you'll end up with 3 Coppers rather than 2 if the Goons isn't in the top 3 cards, without risking missing it because if it's revealed you can still draw it with your cantrip.

I'd like to borrow your example deck to reinforce that it depends.

In this scenario, if your top priority is to get Goons in hand this turn, and having as many Coppers as possible is a secondary priority, then it is (as you say) correct to play WW first and wish for Copper. This succeeds if Goons is any one of the top three cards in your deck; playing the other cantrip first finds the Goons just as often, but doesn't draw you an extra Copper nearly as often.

But say your top priority is to draw $4; that is, you need your Goons and two Coppers as well, to hit some key price point, and having Goons but only $3 will be little consolation. In that case, playing WW first is wasteful: if you wish for Copper and reveal Goons, you've consigned yourself to drawing just $3 when $4 was possible. Instead, you play GM first, and then WW: by this time, either you've drawn the Goons and can safely wish for Copper, or you haven't and must hope a Goons is coming up. This gets you $4 anytime it is possible to do so.
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Awaclus

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Re: When to play Wishing Well
« Reply #9 on: May 28, 2014, 06:48:04 am »
0

This is the order you should play your cards:

1) cards that draw bad cards (such as Vagrant)
2) cards that draw random cards
3) cards that draw good cards (such as Sage)

The reason should be obvious: the random cards you draw are better if you have removed all of the bad cards from your deck, and worse if you have removed all of the good cards from your deck.

If you want to wish for a bad card, play WW first. If you want to wish for a good card, play WW last.

I mean, your reason may be obvious, but it's not correct in general. For example, if the only good cards left in my deck are two Mountebanks, then I'd rather play my Golem before I happen to draw them with a Scheme; otherwise my Golem draw nothing at all!
That's an edge case, though. Most cards don't give you +actions per card they manage to draw.
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Re: When to play Wishing Well
« Reply #10 on: May 28, 2014, 07:34:37 am »
+7

Although in theory "it depends" is the correct answer, in practice I almost always play my wishing wells next-to-last.
Only when I know exactly why I should play it last I make an exception.

It's very common to want card A but have a lot more of card B in your deck.

I tried to explain this more then a year ago (can't find the thread) but failed as most people continued to disagree with me. Apparently SCSN wasn't one of them.
That, or we're both wrong :)
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Re: When to play Wishing Well
« Reply #11 on: May 28, 2014, 07:51:09 am »
0

So then the real question is: how often do you run into an exception where you're not naming the most common card?

Let's say you have 2 Coppers, 1 Estate left in your deck after you draw with WW, and already have $8 with 1 buy.

a) You could wish for a Copper (67%) and have $9 and draw 1 Copper, 1 Estate and 3 fresh cards if you're right.
33% of the time you'll draw 2 Coppers, 1 Estate and 2 fresh cards.

b) You could wish for an Estate (33%) and have $8 and draw 2 Coppers and 3 fresh cards next turn.
67% of the time you'll draw 2 Coppers, 1 Estate and 2 fresh cards.

I honestly don't know which is better in these kinds of situations: The increased cycling chance with 1 dead card, or less cycling with 1 less dead card.
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Re: When to play Wishing Well
« Reply #12 on: May 28, 2014, 08:42:13 am »
0

By playing wishing wells early and wishing for the worst cards you are eliminating the union of two events - bad cards at the top of the deck and wrong wishes. This can be important when that's the only situation that will prevent you drawing the whole deck.
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Re: When to play Wishing Well
« Reply #13 on: May 28, 2014, 10:38:12 am »
+2

Although in theory "it depends" is the correct answer, in practice I almost always play my wishing wells next-to-last.
Only when I know exactly why I should play it last I make an exception.

It's very common to want card A but have a lot more of card B in your deck.

I tried to explain this more then a year ago (can't find the thread) but failed as most people continued to disagree with me. Apparently SCSN wasn't one of them.
That, or we're both wrong :)
I remember that post. I think what I took away from it is that playing the WWs second to last is preferrable when you're hoping to draw a specific card like Bridge or Goons in a deck full of other stuff like Copper. If instead you just want to maximize draw, then you'd play the WWs last.
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LastFootnote

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Re: When to play Wishing Well
« Reply #14 on: May 28, 2014, 10:38:31 am »
+1

If all you cared about was maximizing your draw you obviously want to play your WWs as close to the bottom of your shuffle as possible, which would frequently entail playing other cantrips first. However, with only a single WW in hand and no other cantrips, the play with the highest expected positive change in your win % is very often wishing for a card other than the most likely one. Hence playing all your cantrips first forces you to make "suboptimal" guesses to avoid missing out on a key card, whereas saving a cantrip maximizes your draw conditional on minimizing the chance of missing said card.

To give a concrete example: assume there's one Goons left in your deck together with a ton of Coppers. Also assume that with just a single WW in hand, optimal play dictates wishing for Goons if you don't draw it. Then with both a WW and a single cantrip in hand, playing the cantrip first would force you to make a "suboptimal" (in the sense of not being most likely to succeed) WW guess, resulting most of the time in you drawing just 2 Coppers. If, on the other hand, you play WW first and now guess for Copper, you'll end up with 3 Coppers rather than 2 if the Goons isn't in the top 3 cards, without risking missing it because if it's revealed you can still draw it with your cantrip.

Your example is an interesting one, and I admit that it would not have occurred to me to play the Wishing Well first for this reason. In this very specific situation, you are correct that playing it first will help maximize the number of Coppers you draw without sacrificing any chance of drawing Goons. Thanks for the lesson! But your example doesn't come close to proving—or even showing—that playing Wishing Wells first is better in general.

The fallacy is that, in your example, all the non-Goons cards are Coppers. This gives you the luxury of effectively wishing for "non-Goons". In most real situations, this is a luxury you won't have. Let's say instead that your remaining deck has a single Goons along with some mix of Coppers, Estates, and Silvers. Your hand includes a Wishing Well and a Great Hall. You want to maximize your chance of drawing Goons and, secondarily, draw as many cards as possible (or drawing another, secondarily important card, or whatever). In this case, you probably want to name Goons whether you play Wishing Well first or second. In a random, unknown deck, the Goons is as likely to be your 2nd card as your 3rd card. You've got the same chance to get your Goons either way.

The advantage to playing your other cantrips first is that you have more information with which to make your wish. And I'm not just talking about information about what's left in your deck and what you're therefore most likely to draw. I mean information about what card you most want to draw. Let's say I have a Great Hall and a Wishing Well and one Action left. Say I play my Wishing Well first and draw a Silver. Maybe I'd wish for Copper because it's most likely to succeed. It's a Margrave. I play Great Hall and draw the Margrave. Play the Margrave, draw 3 dead Action cards. If I play my Great Hall first, I draw the Margrave with Wishing Well. Now I know that a Village would drastically improve my turn and I can wish for that.
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SCSN

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Re: When to play Wishing Well
« Reply #15 on: May 28, 2014, 12:06:39 pm »
+1

My example is generic because, in the absence of cards like Cartographer or Apothecary, Wishing Well presupposes a fairly uniform deck with high densities of only a few cards that thus make good wishes.

If your deck contains cards as varied as Estate, Copper, Silver, Great Hall, Village and Margrave, the addition of Wishing Well is both awful and totally unnecessary (you have Margrave for draw, after all), so your example shouldn't really come up much in practice if you're building your decks correctly. It's a bit like saying that Herald and Scrying Pool are bad cards because of all the Silvers and Golds they'd be running into. You design your deck around these cards, you don't just randomly have them in your average deck.

Yes, sometimes you get a WW or two early on and they become useless later, but, as should be clear from the context, my instructions apply to the decks where WW functions as a pseudo-lab, not where it has become a lottery ticket, in which case you might as well just aim for the jackpot.
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Re: When to play Wishing Well
« Reply #16 on: May 28, 2014, 12:23:51 pm »
+2

My example is generic because, in the absence of cards like Cartographer or Apothecary, Wishing Well presupposes a fairly uniform deck with high densities of only a few cards that thus make good wishes.

If your deck contains cards as varied as Estate, Copper, Silver, Great Hall, Village and Margrave, the addition of Wishing Well is both awful and totally unnecessary (you have Margrave for draw, after all), so your example shouldn't really come up much in practice if you're building your decks correctly. It's a bit like saying that Herald and Scrying Pool are bad cards because of all the Silvers and Golds they'd be running into. You design your deck around these cards, you don't just randomly have them in your average deck.

Yes, sometimes you get a WW or two early on and they become useless later, but, as should be clear from the context, my instructions apply to the decks where WW functions as a pseudo-lab, not where it has become a lottery ticket, in which case you might as well just aim for the jackpot.

Maybe your definition of "early on" differs from mine, but I am much more likely to buy Wishing Wells in the mid-game as deck lubricant when I have an extra buy and $3 to spend and nothing better to buy. Early on I'd prefer something that actually helps my economy, even if it's Silver. Are you honestly telling me that you'd rather buy Silver or nothing in the mid-game rather than a Wishing Well? That doesn't jive with what I know of you. So saying that you'd never buy Wishing Well if you weren't basing a strategy around it is nonsense.

Even in a fairly uniform deck, the operative word is "fairly". The example you gave supposes a deck that only has two kinds of cards remaining, which is quite rare. If nothing else, you'll often have Provinces at some point. As long as your deck has more than two kinds of cards, playing your Wishing Well first and naming a junk card starts to become worse. You may name the wrong junk card and in doing so not get to draw the power card you otherwise would have.
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Re: When to play Wishing Well
« Reply #17 on: May 28, 2014, 01:00:25 pm »
+1

Wishing Well, like Shanty Town, often is a great open due to its high chance of being a Lab early on (100% even, if you draw it on T4). I'm rarely getting it in the mid-game unless I'm constructing my deck around it or there are conditions that make it better than just a lottery ticket.

Quote
Even in a fairly uniform deck, the operative word is "fairly". The example you gave supposes a deck that only has two kinds of cards remaining, which is quite rare. If nothing else, you'll often have Provinces at some point. As long as your deck has more than two kinds of cards, playing your Wishing Well first and naming a junk card starts to become worse. You may name the wrong junk card and in doing so not get to draw the power card you otherwise would have.

This doesn't matter. As long as you have some sort of uniformity you almost always want to play the Wishing Well first and name the most likely card. The card doesn't have to be junk. In the video I was always naming Wishing Well whenever that was the most likely card. If there are multiple cards close in terms of being the most likely, what you name next will often change with what you draw.
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GeoLib

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Re: When to play Wishing Well
« Reply #18 on: May 28, 2014, 02:43:44 pm »
0

If all you cared about was maximizing your draw you obviously want to play your WWs as close to the bottom of your shuffle as possible, which would frequently entail playing other cantrips first. However, with only a single WW in hand and no other cantrips, the play with the highest expected positive change in your win % is very often wishing for a card other than the most likely one. Hence playing all your cantrips first forces you to make "suboptimal" guesses to avoid missing out on a key card, whereas saving a cantrip maximizes your draw conditional on minimizing the chance of missing said card.

To give a concrete example: assume there's one Goons left in your deck together with a ton of Coppers. Also assume that with just a single WW in hand, optimal play dictates wishing for Goons if you don't draw it. Then with both a WW and a single cantrip in hand, playing the cantrip first would force you to make a "suboptimal" (in the sense of not being most likely to succeed) WW guess, resulting most of the time in you drawing just 2 Coppers. If, on the other hand, you play WW first and now guess for Copper, you'll end up with 3 Coppers rather than 2 if the Goons isn't in the top 3 cards, without risking missing it because if it's revealed you can still draw it with your cantrip.

That said, I do think I misplayed it a bit in the video by mistakenly generalizing this concept to situations where you have multiple cantrips in hand. I should have played all but my last non-WW cantrip prior to the WWs to maximize correct guessing. Thanks for bringing this to my attention :)

Ah. This makes a lot of sense and was not clear to me in the video. Thank you for improving the way that I think about wishing well! I think it does not necessarily generalize to a situation where you have more deck diversity, as LF points out, though I agree that WW is just way less relevant in that case.


Even in a fairly uniform deck, the operative word is "fairly". The example you gave supposes a deck that only has two kinds of cards remaining, which is quite rare. If nothing else, you'll often have Provinces at some point. As long as your deck has more than two kinds of cards, playing your Wishing Well first and naming a junk card starts to become worse. You may name the wrong junk card and in doing so not get to draw the power card you otherwise would have.

Notably, the deck that he was playing when he made this comment had only WW, Silver, and GM.
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Re: When to play Wishing Well
« Reply #19 on: May 28, 2014, 03:06:40 pm »
+1

Another reason to play Wishing Well late is that it is much easier to choose what to wish later on. Suppose you're aiming for a Province, and your deck has Copper as the most common money card, but also Gold. If you're playing the WW early on, you'll probably wish for Copper because it is most common. If it is your last card however, you can decide based on the amount of money you have before you wish: If you have $7, you wish for Copper; if you have $5 or $6, you wish for Gold. If you already have $8 or more, you can wish for land (or Copper) to improve your next draw.
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theblankman

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Re: When to play Wishing Well
« Reply #20 on: May 28, 2014, 03:33:43 pm »
0

Notably, the deck that he was playing when he made this comment had only WW, Silver, and GM.
Trashed the trasher to opponent's Bishop?  Or Governor and got one of the mentioned cards back?  I can't think of many ways to have that deck without at least one leftover trasher/TfB in there... but I could easily see WW, Silver, GM and one Chapel.
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pacovf

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Re: When to play Wishing Well
« Reply #21 on: May 28, 2014, 03:37:06 pm »
0

Notably, the deck that he was playing when he made this comment had only WW, Silver, and GM.
Trashed the trasher to opponent's Bishop?  Or Governor and got one of the mentioned cards back?  I can't think of many ways to have that deck without at least one leftover trasher/TfB in there... but I could easily see WW, Silver, GM and one Chapel.

Also, island.
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Re: When to play Wishing Well
« Reply #22 on: May 28, 2014, 03:44:04 pm »
+2

Notably, the deck that he was playing when he made this comment had only WW, Silver, and GM.
Trashed the trasher to opponent's Bishop?  Or Governor and got one of the mentioned cards back?  I can't think of many ways to have that deck without at least one leftover trasher/TfB in there... but I could easily see WW, Silver, GM and one Chapel.

Also, island.
Right. WW, Silver, GM, one Chapel and Island.
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Re: When to play Wishing Well
« Reply #23 on: May 28, 2014, 03:49:11 pm »
+2

Notably, the deck that he was playing when he made this comment had only WW, Silver, and GM.
Trashed the trasher to opponent's Bishop?  Or Governor and got one of the mentioned cards back?  I can't think of many ways to have that deck without at least one leftover trasher/TfB in there... but I could easily see WW, Silver, GM and one Chapel.

Ok. I lied. There was also a trading post.
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