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[ehunt]

I see a lot of folks asking if they should wish for what's on top of their deck, or what they really want in their hand. Of course the answer is that it depends, but here's one concise thing you can say that's true at any point in the game.

You should wish for the card that maximizes (probability that you will draw the card) * (benefit of drawing the card).


Examples:
early game - you know your deck has three estates and a copper. What do you wish for? You have a 75% chance of improving your next hand by ridding it of an estate, and a 25% chance of a money. If that copper is the key to the game (e.g. it's your only chance to get your first witch before reshuffling and your opponent has a witch already), you will take it. If not (e.g. it's the difference between a silver and a caravan) you should wish for an estate.

turn three - after playing WW, you have five copper in hand; your deck contains 2 coppers, 3 estates, and a silver. What do you wish for? Well, if you were going to buy a 5 like minion or witch anyway, you may as well wish for an estate. If all the 5s are terrible, you wish for a copper -you're throwing away a 50% chance of "scouting yourself" for a 33% chance of a gold, which is reasonable. It's very rare that you'd wish for the silver here - you'd need a powerful seven on the board and also a five that you'd always prefer over gold.

Late game - you're playing a vault deck. If you drew your wishing well with a gold or a silver and a bunch of junk, you should wish for your vault even if the probability is very low, because it's a certain province if you're right. On the other hand, if you draw your wishing well with pure junk, you  DON'T want to wish for a vault - wish for the most probable junk, to increase the chances of vault/gold collision.

[WrathOfGlod]

One important rule for wishing is that in the most common case where you have a key card you are searching for you should only wish for it with the last draw.
Example: Let us suppose you have village-wwX2 in hand and are searching for your torturer, you should play the village first and then use the first ww for copper and only the second one for the torturer.
The reason is that if the torturer is within the range of cards that the earlier draws will pick up you will get it anyway so there is no use wishing for it.
The second implication is that wishing well should be played after all other cantrips

[DG]

There are actually a lot of different wishing well strategies. Such as :

- You've got 8 coins to spend with no +buys. You might as well wish for an estate or province with a chance of improving the next draw since you can't improve the current draw.
- You've got a good drawing deck that can still fail with worst draws. You can wish for terminal cards that might prevent your deck drawing through, assuming that if another drawing card is on your deck then it will continue your drawing later in the turn anyway.
- Deck testing. If you've got a lookout or native village in hand you can play the wishing well and wish for your best card. You'll either take the best card into hand or leave an average/poor card on top of your deck, allowing you to play the lookout safely.
- Putting so many wishing wells into your deck that you can wish for wishing wells.
- Wishing for cards that are not even in your deck, just so that you can keep a precise number of cards in your draw deck.

[Markov Chain]

I see a lot of folks asking if they should wish for what's on top of their deck, or what they really want in their hand. Of course the answer is that it depends, but here's one concise thing you can say that's true at any point in the game.

You should wish for the card that maximizes (probability that you will draw the card) * (benefit of drawing the card).

Even that isn't right, because you will draw the card anyway; the question is usually whether you draw it this turn or next (or sometimes, whether it misses the shuffle).  Thus, unless a card is particularly high or low in value this turn, you should wish for the card most likely to fulfill the wish.

For example, suppose you have 4 coppers and 4 silvers left (and other cards).  If you wish for a copper and one of those cards is on top, you have a 1/2 chance of getting a copper and otherwise start next turn with a silver; if you wish for a silver, you have a 1/2 chance of getting a silver and otherwise start next turn with a copper.  So, is the difference between copper and silver greater with your known hand this turn or with a random hand next turn?  If you have $4, it could go either way depending on how valuable the $5 cards are versus gold.

Reshuffles are an important issue.  If you have two cards left, one a copper and one a silver, you should wish for the silver if it makes any difference at all in what you can do this turn.  The reason is that you are about to reshuffle, and if your wish isn't granted, the remaining card will miss the reshuffle and will only be played once next time through your deck.

And there are times that you should wish for something less likely to come up because the benefits are so great.  If you have a Tournament, you may wish for a province, or vice versa.  If you have $6, you may well wish for a silver rather than a copper even if you have much more copper, because a copper won't help you and a silver will give you a province.  If you have $8 already, you may wish for an estate or province, so that you improve your deck if the wish is granted.  If you have two terminals, you may wish for a village.

[ehunt]

All these examples are consistent with the rule (which just says you should maximize expected benefit =probability*benefit; benefit here doesn't mean benefit to the current hand). In the copper/silver case, if I wasn't going to use the extra money, then robbing my next hand would hurt me and I would subtract that from the benefit factor before computing. Same with reshuffling. In the tournament case, the benefit of drawing that province is huge, which overwhelms the probability factor (but I can see cases where I wouldn't wish for a province, e.g., if there's seventy cards left in my deck, only 1 of them is a province, and a copper would give me 8 money).

I see a lot of folks asking if they should wish for what's on top of their deck, or what they really want in their hand. Of course the answer is that it depends, but here's one concise thing you can say that's true at any point in the game.

You should wish for the card that maximizes (probability that you will draw the card) * (benefit of drawing the card).

Even that isn't right, because you will draw the card anyway; the question is usually whether you draw it this turn or next (or sometimes, whether it misses the shuffle).  Thus, unless a card is particularly high or low in value this turn, you should wish for the card most likely to fulfill the wish.

For example, suppose you have 4 coppers and 4 silvers left (and other cards).  If you wish for a copper and one of those cards is on top, you have a 1/2 chance of getting a copper and otherwise start next turn with a silver; if you wish for a silver, you have a 1/2 chance of getting a silver and otherwise start next turn with a copper.  So, is the difference between copper and silver greater with your known hand this turn or with a random hand next turn?  If you have $4, it could go either way depending on how valuable the $5 cards are versus gold.

Reshuffles are an important issue.  If you have two cards left, one a copper and one a silver, you should wish for the silver if it makes any difference at all in what you can do this turn.  The reason is that you are about to reshuffle, and if your wish isn't granted, the remaining card will miss the reshuffle and will only be played once next time through your deck.

And there are times that you should wish for something less likely to come up because the benefits are so great.  If you have a Tournament, you may wish for a province, or vice versa.  If you have $6, you may well wish for a silver rather than a copper even if you have much more copper, because a copper won't help you and a silver will give you a province.  If you have $8 already, you may wish for an estate or province, so that you improve your deck if the wish is granted.  If you have two terminals, you may wish for a village.