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[flies]

If you have a 4/3 opening (not 3/4), then on your first turn, buy Doctor and overpay 1.  The overpay effect will reveal a copper (60%) or an estate (40%), trashing either of which is generally desirable.  The second turn will most likely be C/C/C/E/E, and Doctor is guaranteed to appear in either the second (1 in 6) or third turn (5 in 6) or rarely both.  While this substantially reduces the expected cash value of the third turn as compared with a Silver/Silver opening, it affords very rapid trashing.  In addition, this opening usually provides $3 on turns 2 and 3 which, if used to buy silver, will substantially increase your average buying power thereafter.

I just added the above note to the wiki article on Doctor http://wiki.dominionstrategy.com/index.php/Doctor#Strategy_Article

[flies]

the probabilities are screwing with me a bit.  No matter what you trashed, the second hand will be 4 cards + one card from the first turn: 4 coppers, one estate, and the doctor.  So the chance of the doctor on turn two is 1/6 (17%).  If the doctor does not appear in the second turn, then it certainly will appear in the third, but if it does appear in the second turn then it could also appear in the third assuming you play it and succeed in trashing something.  So shouldn't the probability of the doctor appearning in turn 3 be higher than 5/6?  My head brokeded.

[SirPeebles]

I don't feel qualified to comment on your analysis, but it would probably be best to wait for a bit of feedback before adding this to the wiki.  Or maybe not?

[flies]

well, if someone wants to take it down, that's ok, i guess.  I'm being bold in adding it as per wikipedia guidelines (http://en.wikipedia.org/wiki/Wikipedia:Be_bold).  Some of the probabilities might be a bit off, but the general idea is certainly sound.

[ftl]

Seems reasonable, I think it's fine to add to the wiki. 

[meandering mercury]

At the beginning of turn 2, you have a 1 in 6 chance of drawing Doctor.

If you don't draw Doctor (5 in 6), you'll get it in turn 3; your draw deck is only 5 cards anyway.

If you do draw Doctor on turn 2, then you play it. Say you trash one card and you buy a Silver. Your draw deck is now 4 cards. On turn 3, you draw one card from (shuffled) discard, 1 or 6 which is Doctor (note that you have total 10 cards; each time you delete a card with Doctor, you've replaced it with something else). Hence, you had a 1 in 6 chance of drawing Doctor on turn 2; then a 1/6 * 1/6 chance of drawing it on turn 3. The probability is 1/36 + 5/6 = 86%, not 83%.

However, the exact probability is not really something you can calculate because it depends on player decisions -- which card you choose to name, which card you choose to buy, etc. If you draw Doctor on turn 2, your draw deck is CCCEE, and you have a legitimate choice between naming C and E (E is probably better, but in some cases C may be better). Instead of buying Silver, you might certainly buy a card like Wishing Well or Village, etc, which would serve as a cantrip.

[Warfreak2]

I think 1/6 and 5/6 are clearly the appropriate probabilities, just the events should be worded "you first draw Doctor on T2" and "you first draw Doctor on T3". Yes, you can draw Doctor on T3 after playing it on T2, but we are usually more interested in how early we can start using a card.

Turning over a Copper on my $4 Doctor, after my opponent turned over an Estate, is one of those annoying moments.

[flies]

At the beginning of turn 2, you have a 1 in 6 chance of drawing Doctor.

If you don't draw Doctor (5 in 6), you'll get it in turn 3; your draw deck is only 5 cards anyway.

If you do draw Doctor on turn 2, then you play it. Say you trash one card and you buy a Silver. Your draw deck is now 4 cards. On turn 3, you draw one card from (shuffled) discard, 1 or 6 which is Doctor (note that you have total 10 cards; each time you delete a card with Doctor, you've replaced it with something else). Hence, you had a 1 in 6 chance of drawing Doctor on turn 2; then a 1/6 * 1/6 chance of drawing it on turn 3. The probability is 1/36 + 5/6 = 86%, not 83%.

However, the exact probability is not really something you can calculate because it depends on player decisions -- which card you choose to name, which card you choose to buy, etc. If you draw Doctor on turn 2, your draw deck is CCCEE, and you have a legitimate choice between naming C and E (E is probably better, but in some cases C may be better). Instead of buying Silver, you might certainly buy a card like Wishing Well or Village, etc, which would serve as a cantrip.

This is right on.  (I wanted T2 probability to add with T3 probability to make one, but they're not mutually exclusive.  brain fixed.)