In what way is the Elder Wand more powerful than a regular wand?

Question

The Elder Wand is more powerful than a regular wand, as we see Harry use it to repair his seemingly irreparable wand.

We have also seen that every time the wand had been used in front of the readers in a duel, the wand didn't lose (Dumbledore vs Voldemort in the Ministry for Magic, Harry vs Voldemort at Hogwarts). Draco disarming Dumbledore doesn't count, as Dumbledore didn't defend himself.

In what way is the Elder Wand more powerful? Does it just amplify the strength of normal magic for a normal wizard (Harry using a plain Reparo spell to mend his wand)? Does it always succeed in everything its owner wants it to do (winning every battle, for example)? Does it grant new magic that a wizard wouldn't be able to do with a normal wand? All of the above? None of the above? Some of the above?

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An example question the answer here should also be able to answer: can an underage wizard in training easily create a corporeal Patronus using the Elder Wand?

Answer 1

The Elder Wand’s power is from it learning from many masters.

Dumbledore says the main reason the Elder Wand has become so powerful is because it’s spent centuries accumulating power and experience from many masters.

“Believers in the Elder Wand, however, hold that because of the way in which it has always passed allegiance between owners — the next master overcoming the first, usually by killing him — the Elder Wand has never been destroyed or buried, but has survived to accumulate wisdom, strength, and power far beyond the ordinary.”
_{^{- The Tales of Beedle the Bard}}

Wands absorb experience from their owners, so a wand that’s passed through the hands of many powerful wizards over the centuries would have absorbed quite a lot of experience.

“As can be seen, Godelot considers his wand to be a helpmeet, almost an instructor. Those who are knowledgeable about wandlore²⁶ will agree that wands do indeed absorb the expertise of those who use them, though this is an unpredictable and imperfect business; one must consider all kinds of additional factors, such as the relationship between the wand and the user, to understand how well it is likely to perform with any particular individual. Nevertheless, a hypothetical wand that had passed through the hands of many Dark wizards would be likely to have, at the very least, a marked affinity for the most dangerous kinds of magic.”

Most wizards prefer a new wand that would shape to their style of magic than a secondhand one, and wands are usually left with their owners after the owner’s death, so most wands remain with one owner and don’t get passed on through centuries like the Elder Wand.

“Most witches and wizards prefer a wand that has “chosen” them to any kind of secondhand wand, precisely because the latter is likely to have learned habits from its previous owner that might not be compatible with the new user’s style of magic. The general practice of burying (or burning) the wand with its owner, once he or she has died, also tends to prevent any individual wand learning from too many masters.”

Though the Elder Wand may or may not have been somewhat more powerful than other wands at the point of its creation, likely the main reason it’s so powerful is because it’s absorbed experience from very many powerful wizards for centuries of use.

Spells cast with the Elder Wand are more effective than normal.

The Elder Wand seems to make spells cast with it more effective. When Harry’s wand breaks, Hermione tries and fails to fix it so that it’s useable again by using Reparo.

“R – Reparo.’

The dangling half of the wand resealed itself. Harry held it up.

‘Lumos!’

The wand sparked feebly, then went out.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)}}

Harry asks Ollivander, a skilled and knowledgeable wandmaker, to fix his wand, and Ollivander tells him he doesn’t know of any possible way to fix a wand as damaged as his was.

“Ollivander held out a trembling hand and Harry placed the two barely connected halves into his palm. ‘Holly and phoenix feather,’ said Ollivander in a tremulous voice. ‘Eleven inches. Nice and supple.’

‘Yes,’ said Harry. ‘Can you –?’

‘No,’ whispered Ollivander. ‘I am sorry, very sorry, but a wand that has suffered this degree of damage cannot be repaired by any means that I know of.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 24 (The Wandmaker)}}

Despite that same spell not working when Hermione (who is equally skilled as Harry) tried it, Harry is able to fix his broken wand by casting Reparo on it with the Elder Wand.

“He laid the broken wand upon the Headmaster’s desk, touched it with the very tip of the Elder Wand and said, ‘Reparo.’

As his wand resealed, red sparks flew out of its end. Harry knew that he had succeeded.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 36 (The Flaw in the Plan)}}

The exact same spell that failed to fix his wand before succeeded when cast with the Elder Wand.

The Elder Wand is absolutely not unbeatable in a duel, however.

Though it is a powerful wand, the Elder Wand clearly isn’t unbeatable as its owners have been beaten several times throughout history, as Dumbledore points out.

“What must strike any intelligent witch or wizard on studying the so-called history of the Elder Wand is that every man who claims to have owned it²⁸ has insisted that it is “unbeatable,” when the known facts of its passage through many owners’ hands demonstrate that has it not only been beaten hundreds of times, but that it also attracts trouble as Grumble the Grubby Goat attracted flies.”
_{^{- The Tales of Beedle the Bard}}

In addition to Dumbledore’s defeat of Grindelwald, there’s at least one other known case of a wizard beating the owner of the Elder Wand in a duel - Loxias, who beat Barnabas Deverill.

“All that is certain is that a wand called the “Eldrun²⁷ Wand” by its owner, Barnabas Deverill, appeared in the early eighteenth century, and that Deverill used it to carve himself out a reputation as a fearsome warlock, until his reign of terror was ended by the equally notorious Loxias, who took the wand, rechristened it the “Deathstick,” and used it to lay waste to anyone who displeased him.”
_{^{- The Tales of Beedle the Bard}}

Though the Elder Wand is powerful, being unbeatable in a duel is not one of its powers.

Answer 2

To start with, the wand is of excellent quality:

Virtually every detail of the Elder Wand hints at something unique or exceptional by a wandmaker’s standards.

Elder wood is not a favoured material in wand-making. However, it is still included in Garrick Ollivander’s notes:

Only a highly unusual person will find their perfect match in elder, and on the rare occasion when such a pairing occurs, I take it as certain that the witch or wizard in question is marked out for a special destiny.
Wand Woods: Writing by J.K. Rowling

Stranger still, the Elder Wand’s core substance is Thestral hair. There are no Ollivander notes to go by – it wasn’t a material he chose to work with – but we do know that Thestrals have a strong connection with death, plus the magical properties of invisibility, flight and an uncanny ability to find their destination. How this affects the wand is uncertain, but it does hint towards some seriously powerful magic.
_{Pottermore: Everything we know about the Elder Wand}

Its main strength likely is that wands grow with experience, and the Elder wand has been passed down from one powerful wizard to another who is powerful enough to defeat them (or brutal enough to murder them in their sleep):

Unlike the Resurrection Stone and Invisibility Cloak, which were handed down through the Gaunt and Potter family lines respectively, the Elder Wand was repeatedly seized by power-hungry wizards. In the words of Xenophilius Lovegood: ‘The bloody trail of the Elder Wand is splattered across the pages of wizarding history.’

[...]

As Dumbledore stated in Tales of Beedle the Bard, ‘Those who are knowledgeable about wandlore will agree that wands do indeed absorb the expertise of those who use them.’ With the volume of dark deeds attributed to the Elder Wand, that is a terrifying thought.
_ibid

Answer 3

I would add that in Deathly Hallows, Ollivander notes that “the best results, however, must always come where there is the strongest affinity between wizard and wand,” adding that they share “an initial attraction, and then a mutual quest for experience — the wand learning from the wizard; the wizard from the wand.”

That the Elder Wand had such a lengthy list of masters certainly helps explain why it was so powerful generally. But I think there are a few more clues as to why it performed certain acts of otherwise-unknown magic.

For instance, I believe it learned love in the service of Albus Dumbledore, who mastered it not for personal gain, but as an act of service to others. I think this helps explain why Harry’s “expelliarmus” worked the way it did — forcing Voldemort’s curse back onto himself. Certainly, Harry had mastered the wand — but this was somewhat indirect, as he disarmed its previous master but not the wand itself.

As for the “reparo” spell that finally worked, perhaps that was an instance of the wizard (Harry) learning from the (Elder) wand that repair — in other words, healing — may be seen by some (like Hermione and Ollivander) as impossible, but is certainly not out of reach, even after a painful history.

Answer 4

Theoretically, the Elder Wand cannot fail to win you a duel, but Dumbledore beat Grindelwald so either Dumbledore found a way to beat Grindelwald without literally dueling him (like what happened to the third brother) or the Elder Wand isn’t quite what it’s promised.