It should be mentioned that when considering things like Cryonics in the Big World, you can't just treat all the other "you" instances as making independent decisions, they'll be thinking similarly enough to you that whatever conclusion you reach, this is what most "you" instances will end up doing. (unless you randomize, and assuming 'most' even means anything)

Seriously, I'd expect people to at least mention the superrational view when dealing with clones of themselves in decide-or-die coordination games.

Bester has only thought about it for a few seconds so there could be problems that would occur to someone who is knowledgeable about the wizarding economy if they thought about it for a bit.

Idea: Making the money back will be much more difficult than most people anticipate, including Harry.

Reason: Many wizards are highly motivated towards finance and would exhaust every opportunity to generate infinite gold. The rich wizards of the Wizengamot considered 100,000 galleons to be a lot of money.

First, imagine all the ways a wizard could make effectively infinite amounts of muggle money. Arbitrage. Use a time turner and win at the stock market. Use a time turner and win the super-lotto. Imperius (or love potion, false memory charm, groundhog day attack, etc) any billionaire and take part of their fortune. Mind trick some bankers with fake documents (as Dumbledore does in book 6). Go rob some banks with invisibility and teleportation (and/or a time turner). Use magic to secure a job with a 50 million dollar golden parachute with very generous terms. Make huge amounts of drug money as a courier via teleportation/portkey. Sell 5 galleon trinkets to muggle collectors for millions of dollars each. Etc., etc., etc..

Some of them are more risky, some of them are less risky, but I bet that any member of these forums could get at least $50 million in a week if we were wizards.

And yet, when they mention a price of 100,000 galleons people are shocked. The reaction does not look like it's 1/15th of a week's worth of effort he's got to worry about. Dumbledore views it as a major problem that Harry is 60,000 galleons in debt. We know from chapter 70 that it's a known thing that witches and wizards will trick a muggle with a love potion and rape them. Yet nobody thinks to slip Bill Gates a love potion, convince him to part with $2 billion, and blow Lucius out of the water with 100 million galleons. And these are among the most financially motivated people in all of wizardry, not the common population, who consider 2 million pounds as more than weekend spending money. I notice I am confused.

I'll brainstorm some possible explanations:

• Gringotts won't mint your gold for a nominal fee: Griphook could have been lying, mistaken, or omitted something. Maybe you bring in a ton of gold and they just laugh at it for not having a special magical signature. Unlikely but possible.

• Gold isn't available to purchase with muggle money: Wizards could own the gold exchanges and gold mines. They do nominal trading for electronics and jewelry, but the vast share of gold goes to the wizarding world. Possible, but it would drastically change the face of the real world (eg World Reserves would be a lie, and Ron Paul is a wizard).

• The Department of Magical Law Enforcement is way more effective than I imagine: They can find and intervene in not only all cases of magic misuse (eg imperius or bank robberies), but check other means like love potions. Seems unlikely, considering the current crime investigation and how the last war went. Result - Arbitrage and stock/lottery manipulation work.

• The wizarding world is full of complete inverse-omega class idiots: Always a good theory. But it doesn't sound right for the entirety of the wizarding world (including a ton of muggle-born) to act so completely stupid.

• The financial tycoons on Wizengamot actually do this: Maybe most of the Wizengamot fortunes exist due to questionable sources. That would explain the majority of evil people doing the voting. Still, that doesn't explain the reaction to the 100,000 galleons.

• The people who would do this are not on the Wizengamot: Maybe this does happen. Perhaps all the muggle-born realize how easy it is to live a life of luxury in the muggle world and do exactly that, and only venture into the magical world when the want to go shopping. They have the best conveniences of both worlds and none of the dangers of either. This... actually sounds kinda plausible. Plus, there isn't a great job market for muggle-born.

Something doesn't add up. The Wizengamot is full of bright, ambitious people, most of whom have dedicated their lives to finance (makes 4 unlikely). If they're arguing over lucrative ink importation rights it means they've already figured out arbitrage. They wouldn't worry about importing ink, if they weren't leveraging different prices between the market where they're purchasing ink and the market where they're selling ink. Something as simple as triangle arbitrage should be figured out immediately. If wizards already discovered arbitrage, but they don't try and arbitrage in the muggle markets directly, it would be evidence that 1 or 2 is in play. 3 and 5 are already unlikely, so I guess 1&2 or 6 make sense.

I'd be interested to see if Harry actually manages to make infinite money, and if so what it means about the world.

Arbitrage trick is overengineering. Just trade on forex and use time turner to go back and choose the deal.

With 40 000 galleons even going back a few minutes could suffice.

I'm pretty sure the solution is as follows (I've already posted it in TV tropes forum). I'm ROT13, if anyone still wants to figure it out: Yhpvhf Znysbl pynvzrq gb unir orra haqre Vzcrevhf ol Ibyqrzbeg. Ibyqrzbeg jnf qrsrngrq ol Uneel Cbggre. Sebz Serq & Trbetr'f cenax jr xabj gung xvyyvat gur jvmneq gung unf lbh haqre gur Vzcrevhf phefr perngrf n qrog. Erfhyg: Yhpvhf Znysbl naq rirel bgure Qrngu rngre pynvzvat gb unir orra vzcrevbfrq ner abj haqre yvsr qrog gb Uneel Cbggre. Ur pna fgneg erqrrzvat.

That's just the usual limit on information not traveling more than six wall-clock hours back in time, total. It doesn't say or imply that you can't loop yourself more than six times within a small stretch of wall-time.

any more than that and information is traveling more than 6 hours back. (at least from the perspectives of the earliest and latest self-clone)

I believe the only restriction is on not traveling back more than six hours by wall-clock time. It's never stated that you can't travel back into the same hour more than six time using more than one Time-Turner.

I'm still completely confused: what happened with the rock?

This comment gave me the obvious-in-retrospect idea of cloning things with a Time-Turner. Consider:

• You can make up to six copies of yourself, plus all the items you can carry in magical pouches, which will coexist for slightly less than an hour. Or fewer copies that will coexist for longer.
• If you have n Time-Turners, you can end up with 6n copies of yourself + items.
• We have seen that a single Time-Turner can take along an Animagus in a pouch. I speculate that many Animagi (perhaps in separate pouches) can be taken. You can thus use a single Time Turner to duplicate people besides the one actually using it. It's even possible that non-Animagi can be duplicated, if there's some suitable charm for temporarily turning people into animals, maybe.
• You could probably also duplicate Fawkes.
• If Dumbledore ever really goes to fight a serious battle, he'll go as an army of multiple-of-six Dumbledores. Some of them will magically disappear every hour until only one remains, but imagine the firepower!
• Why did Voldemort ever need the Death Eaters? He should have just stolen a few Time-Turners from the ministry. No-one could have resisted an attack by an army of Voldemort clones, super-coordinated by virtue of half the clones remembering being the other half a few hours ago.
• How are new Time-Turners made? Assuming it's not a lost art, and can be done in under 5 hours, then someone could start cloning himself, make new Turners while back in time, use those to keep cloning himself, and eventually reach literally unlimited populations of himself inside the same time period of a few hours. Those populations could then cooperate on some... trickier problems.

This is all starting to remind me of the Seventh Voyage of Ijon Tichy... It looks like I'll have to draw diagrams.

Can someone teach me how?

I just needed an example using definite numbers(so you can judge retrospectively), and not a sequence that millions of people would pick like 1,2,3,4,5,6. For sake of argument, assume I found them on the back of a fortune cookie. Or better yet, just stick a WLOG at the front of my sentence.

And I agree, buying lottery tickets implies a bad way to make decisions, even if you wind up winning. I'm hardly trying to shill for Powerball here. Just saying winning the lottery is always a good thing, even if playing it isn't.