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drethelin comments on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 - Less Wrong
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Certainly, the planning fallacy applies. And even if, for example, arbitrage worked the way it seems, and without the extra pitfalls that have been mentioned, there's a lot more to it than just swapping silver for gold and back. Harry's 11, he can't leave Hogwarts, his finances are tightly controlled by Dumbledore, 100,000 galleons = 1.7 million sickles ~= 17 tonnes of silver. Your dad doesn't just slip that into his back pocket. You're going to need help lifting it, security to guard it, vehicles to move it...
On the other hand, Harry has a lot of resources that haven't even been mentioned yet. There's a house in Godricks hollow for example, and the Granger's would probably be willing to contribute.
He hasn't even really made an accurate count of his vault. He described the stacks as a rough pyramid, but then estimates they're 20 wide and 60 tall - so in other words, each step of the pyramid is only three coins high. I made a small model out of poker chips, and it looks more like a flat than a stack. If it were a normal author, I'd figure the description was bad and the "estimate" was spot on, but EY is smart enough to realize that estimates aren't that accurate. Harry might have underestimated and already have 100,000. Of course, he might have over estimated instead.
Maybe he should learn a magical counting spell.
As far as transporting, Harry has a magical chest that contains entire rooms and can walk on its own. Dumbledore, Quirrel, or any bribeable adult wizard can teleport him to gringotts or to any muggle bank or jeweler he would like to go to, and there are definitely spells for swiftly transporting items across a room or whatever. I think by far a bigger problem would be getting any muggle bank to accept 17 tons of silver in a single transaction without any sort of possible background checks.
Luckily, there are magical methods. Confundus charm, say, or the Imperius curse. (Yes, that does have the downside of being unethical, so Harry probably would not do it.)