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[gman314]

At least when you open with it. In fact, sometimes as an opener it's better than some other power $2s.

I was looking at councilroom's openings list and noticed that Pearl Diver/Trading Post was quite high up. I thought "Well, that's probably just because Trading Post is a good opener." But then the weird thing is that PD/TP is better than TP/-. Pearl Diver is better than nothing.

So, I looked at the list of Pearl Diver openings and then for its top five partners (Trading Post, Mountebank, Witch, Upgrade and Vault) and saw that in all those cases, Pearl Diver was at least slightly better than nothing. But what was really surprising was when PD beat some power $2s. For instance, Mountebank/PD is better than Mountebank/Lighthouse.

So, is Pearl Diver actually a decent opener, or is this just because of the curiosities of statistics?

[Tables]

For instance, Mountebank/PD is better than Mountebank/Lighthouse.

Well, yeah, if you're opening Mountebank when there's Lighthouse on the board, of course it's going to do less well than when it isn't (not saying it's bad, still probably good, but man, Lighthouse is going to tame Mountebank somewhat at least).

Otherwise... Pearl Diver being better than nothing is hardly surprising. In many decks (generally, ones without terminal draw) it can't hurt you and will occasionally do something very nice, like saving a key card from missing the reshuffle, so it's not surprising it's better than opening without it.

[DG]

But what was really surprising was when PD beat some power $2s. For instance, Mountebank/PD is better than Mountebank/Lighthouse.

Mountebank/lighthouse is always played in a kingdom where there is a good defense to mountebanks.

Trading posts perform best with good drawing and the pearl diver can add quality of drawing alongside cards that add quantity of drawing. You also get some extra options such as either not playing the pearl diver or trashing the pearl diver with the trading post, depending upon the hand and draw deck.

[popsofctown]

Witch would be the most surprising of those.  But it really makes sense, it slightly decreases the odds your Witch misses the reshuffle so that's going to outweigh drawing it dead.

But yeah, it is better than nothing..

[serakfalcon]

But what was really surprising was when PD beat some power $2s. For instance, Mountebank/PD is better than Mountebank/Lighthouse.

The problem is the statistics aren't corrected for all the cards in the set, so Mountebank/PD is going to come up a lot of times when there is no defense to mountebank, but with mountebank/lighthouse, there's always a defense to mountebank. It really says more about mountebank than it does PD

[popsofctown]

I don't know if you were trying to say this or not, but your post made me realize that the presence of pearl diver leaves an 8/9's of normal chance that some reaction is available to answer Mountebank.    Or that there are powerful 3-4 dollar cards in general that can answer the opening.

[heatthespurs]

But what was really surprising was when PD beat some power $2s. For instance, Mountebank/PD is better than Mountebank/Lighthouse.

The problem is the statistics aren't corrected for all the cards in the set, so Mountebank/PD is going to come up a lot of times when there is no defense to mountebank, but with mountebank/lighthouse, there's always a defense to mountebank. It really says more about mountebank than it does PD

This is where statistics could be misleading at times...

So what it actually shows is Mountebank/PD > Young Mountebank/Lighthouse... which make senses

[achmed_sender]

PD is also great with power 5s when you're able to grab them from bottom of the pile. Otherwise, the cards would have missed the reshuffle.

[SirPeebles]

A problem with Witch/- is that you're left with 11 cards, so Witch's draw causes it to miss the reshuffle if played turn 4.  An astute Witch/PD player who draws PD with no Witch on T3 will choose not to play the PD.

[DG]

An astute Witch/PD player who draws PD with no Witch on T3 will choose not to play the PD.

Are you sure on that? There's a 1/7 chance of drawing the witch for turn 3. You also remove the 2/7 chance of the witch missing that shuffle anyway. Also a turn 4 shuffle forced by playing the witch will leave a draw deck of 5-6 cards, not such a problem. A witch played on turn 4 can also put a curse into an opponent's discard before their reshuffle.

[Watno]

Not to forget playing Pearl Diver gives you an extra card you might buy something better with.

[Morgrim7]

Not to forget playing Pearl Diver gives you an extra card you might buy something better with.

But if you didn't buy the Pearl Diver, the card you drew would have been in your hand anyway.

[SirPeebles]

An astute Witch/PD player who draws PD with no Witch on T3 will choose not to play the PD.

Are you sure on that? There's a 1/7 chance of drawing the witch for turn 3. You also remove the 2/7 chance of the witch missing that shuffle anyway. Also a turn 4 shuffle forced by playing the witch will leave a draw deck of 5-6 cards, not such a problem. A witch played on turn 4 can also put a curse into an opponent's discard before their reshuffle.

It does not remove the 2/7 chance of missing a reshuffle, but rather increases the chance to 6/7, which was the main point I was trying to make.  Sure there are a few benefits of playing the PD, like giving a chance at drawing that extra Copper into T3 for a better purchase, which situationally could be crucial.  But mostly you're gambling on whether the top card is Witch.  If it is, you draw it now.  Otherwise you guarantee the Witch misses the reshuffle.  I'm not sure I understand your point of the draw deck size for the reshuffle.  If you play Witch triggering a shuffle you'll have Witch in play and six cards in hand, with the remainder in your draw deck.  So whether the shuffle happens T4 or T5 the draw deck is the same size, except for the potential T4 purchase, but then the T4 purchase is probably a decently nice card.  Your point of getting a Curse into your opponents deck before his or her shuffle is a good one though, (P2 has extra incentive to play Witch T3, while P1 has extra incentive to play Witch before T5).

[jomini]

Pearl diver vs nothing is pretty easy to explain. You have an ~3.8% chance of rescuing your power five from the bottom of the deck (5/12 for Pdiver being in T3 and 1/11 for the five to be bottom decked as we will always play Pdiver and not care if it misses the shuffle). Without draw, Pdiver effectively a zero space card so you still only have a base 1/11 chance of missing the 5 on the first shuffle (this is the same benefit of 5/nothing). That 1/11 chance of your 5 being bottom decked represents the single biggest draw luck that can nerf a power 5 opening, when you bottom deck a Mountebank you have effectively opened 0/0/5 and gotten lucky on the 5. I could be wrong, but when I think missing the power 5 in the reshuffle is the biggest reason why dominant openings lose.

The other big thing is that Pdiver openings tell you about the other 2's. Think about the power 2's. Most of them actually hurt power 5 openings - Lighthouse makes it easy to block devastating power 5 attacks. Chapel heavily mitigates not just the cursing attacks, but can also stop up the discard attacks if there are also cards like Watchtower, Library, Menage, etc. out. Squire can allow you to quickly slingshot up to a power 5 attack (mitigating the advantage of opening 5/2) and make trashing attacks like the Knights risky. Even Moat can reduce the power of attacks (e.g. Council room/Ghost ship is nowhere near as good with Moat in the kingdom) a good bit. Chapel/Mountebank is stronger than Pdiver/Mntbnk, but opening Mntbnk is much stronger when trashing isn't in the kingdom.

 
Buying Pdiver for 2 signals that there wasn't a better 2 out and the lack of such power 2's often means the Mountebank or whatever is that much stronger. Even outside of the 2's, Pdiver takes up a kingdom slot and signals that there are lower odds of some other strategy being dominant. Witch/nothing is still quite strong, but Pdiver/Witch signals that you have lower odds of having Masquerade, Ambassador, or some other hard counter in the kingdom.

And of course there are all the other ways Pdiver can actually be directly beneficial, people who open something like Margrave/Pdiver are much more likely to have any of the following out than Margrave/nothing:
1. Using it to activate cards like Conspirator, Horn of plenty, or Peddler.
2. Using it to help diversophiles like Menage or Harvest.
3. Using it with Tr/Kc/Prssn/Golem to gain action balance.
4. Using it with an action-only Tfb like Graverobber or Prssn.
5. Using it go gain top deck knowledge (e.g. Native Village) or when you have top deck knowledge (e.g. Apothecary).

Pdiver is normally easily better than nothing with a power 5 - it has a non-negligible chance of saving a missed shuffle and it has enough possible uses that the winning rate may more reflect boards where Pdiver is additionally useful rather than just being cantrip.

[Watno]

An astute Witch/PD player who draws PD with no Witch on T3 will choose not to play the PD.

Are you sure on that? There's a 1/7 chance of drawing the witch for turn 3. You also remove the 2/7 chance of the witch missing that shuffle anyway. Also a turn 4 shuffle forced by playing the witch will leave a draw deck of 5-6 cards, not such a problem. A witch played on turn 4 can also put a curse into an opponent's discard before their reshuffle.

It does not remove the 2/7 chance of missing a reshuffle, but rather increases the chance to 6/7, which was the main point I was trying to make.  Sure there are a few benefits of playing the PD, like giving a chance at drawing that extra Copper into T3 for a better purchase, which situationally could be crucial.  But mostly you're gambling on whether the top card is Witch.  If it is, you draw it now.  Otherwise you guarantee the Witch misses the reshuffle.  I'm not sure I understand your point of the draw deck size for the reshuffle.  If you play Witch triggering a shuffle you'll have Witch in play and six cards in hand, with the remainder in your draw deck.  So whether the shuffle happens T4 or T5 the draw deck is the same size, except for the potential T4 purchase, but then the T4 purchase is probably a decently nice card.  Your point of getting a Curse into your opponents deck before his or her shuffle is a good one though, (P2 has extra incentive to play Witch T3, while P1 has extra incentive to play Witch before T5).

There are 7 cards remaining in your deck, so 7 possible positions for witch.
If the witch is the top card, it wont miss the reshuffle anyway.
If it's the bottom or second to bottom card, playing PD allows you to play it T4, while otherwise you wouldn't have. This then causes you to shuffle when playing Witch mid turn. This causes Witch to miss the reshuffle, but so do the other 4 cards in your hand as well as the first card you draw with witch. So you have 6 cards missing the reshuffle, which means that you only have 7 cards in the draw pile the witch missed. If you don't play PD, and Witch is in the bottom 2 cards, 1 other card misses the reshuffle allowing with it, making you have to go through an 11 card deck before you get your Witch again.

So in 2/7 situations playing PD makes Witch miss a "small reshuffle" instead of a "big reshuffle", in 4/7 situations it makes witch miss a "small reshuffle" instead of no reshuffle at all.
And then there's the advantage of an extra card T3 if you play PD, which could mean a better buy or a curse in your opponent's deck before he reshuffles.

Though the decision ultimately depends on the value of the rest of your T3 hand and player order, this is more in favor of not playing PD than i expected.

[popsofctown]

A problem with Witch/- is that you're left with 11 cards, so Witch's draw causes it to miss the reshuffle if played turn 4.  An astute Witch/PD player who draws PD with no Witch on T3 will choose not to play the PD.

The statistics favoring Pearl Diver probably arise from the less astute among us dead drawing the pearl diver and profitting.