You could run vanitygen to guess the private key to any Bitcoin address. It might take a few billion years.

Time to find a billion computers to run it on

It could also take just one day if you are lucky. It impossible to predict, just like the future of bitcoin.

Equivalent of a bitcoin lottery?

If you want to play the Bitcoin lottery, it's a far better idea to focus your computing power on solo mining. You have far more chance guessing a 25 bitcoin block than getting a valid private key.

No. If you delete the wallet, the contained Bitcoins make poof.

You basically delete the private key and won't be able to sign a transaction with it ever.

It's like what happens when your wallet gets burned in a fire. That cash is gone forever.

Actually the Bureau of Engraving and Printing will replace damaged or destroyed US currency if they can determine to their satisfaction how much has been destroyed. They replace over $30 million of currency yearly. The most common causes of mutilation are are fire, water, chemicals, explosives; animal, insect or rodent damage; and petrification or deterioration by burying.

See http://moneyfactory.gov/uscurrency/damagedcurrency.html There's also an article with some interesting stories: http://usatoday30.usatoday.com/news/nation/2001/06/2001-06-0...

[I'm not intending this as an argument about Bitcoin, but as something people might find interesting.]

Read a story, man's dog ate several hundred dollars, man fished remains out of dog poop, US government printed man new hundred dollar bills.

Damaged US Currency can be replaced ONLY if: (1) 51% or more of the bill is recovered (in some form) (2) the serial number of the bill can be identified

(Or at least that's what I was told during a tour of a US Mint several years ago.) Money burned up in a fire is not replaceable.

Except it can be reprinted. The cash is gone, but the total money supply is not irreversibly reduced.

Correct. Except most of us don't keep all our money in our wallet or under our mattress. We keep it in a bank. Which is insured by the federal government. Bitcoin is akin to keeping all your money in a big bag in a single location if you don't back it your digital wallet offsite.

That is the local effect, which is the same for cash vs bitcoin and different for deposit vs bitcoin (though of course there is nothing preventing bitcoin-denominated deposits). The global effect for bitcoin is more like nuking a bit of gold - you have reduced the total supply permanently - whereas for cash we can just print more.

Hmm, so that means that someone who solved the crypto problem (say, NSA) could simply take over [presumably] abandoned wallets, which would be nearly undetectable compared to other uses of such attacks, but could still have a huge impact on Bitcoin ecosystem simply due to the large mass of such wallets.

Correct.

And this is one of many reasons why it will become increasingly important to beef up the security and robustness of the Bitcoin network and ecosystem. It has some of the same failure modes as traditional bank/government-backed currency. But it also has a set of a different kind of failure modes that should also be minimized or mitigated.

Not without knowing the private key for the bitcoin address in question.

No way if you lost your wallet.dat