4 ms·

> If a node can present a lottery ticket of rarity one-in-a-million, the network can conclude the node did about a million lottery tickets’ worth of work, on av

by vages 5y ago

> If a node can present a lottery ticket of rarity one-in-a-million, the network can conclude the node did about a million lottery tickets’ worth of work, on average. This is not true. You will have scratched far fewer tickets on average than one million. If you have one million tickets, one of them guaranteed to be a winner, you will on average scratch exactly half of them (500 000) before finding the winning ticket. If you have an infinite supply of tickets, each with a 0.000,001 chance of winning, the number becomes higher, but the number of tickets scratched on average is still lower than one million. Finding an error regarding something I know makes me skeptical about the rest of the article.

rich_sasha 5y ago
If there’s a million tickets and you know one of them is a winner, then yes. If you have an effectively infinite stream of tickets and each have a 1 in X probability of winning, you will indeed go through X on average.
- denton-scratch 5y ago
  Yeah, I think that's right. The hypothesis was that on average, one in a million cards is a hit. That implies that if you scratch a million cards, you have a 50:50 chance of a hit. That the author got this basic thing wrong doesn't inspire much confidence in the rest of his reasoning.
  - rich_sasha 5y ago
    Well, I guess in real life blockchains it’s like the latter case. You have a block and look for a nonce. There is an effectively infinite stream of nonces (“lottery tickets”). You have no guarantee that even one works, other than statistical hope. So then if probability of a match is 1 in X, you expect to have to do X attempts. I have other issues with the article but this bit seems ok.
    - denton-scratch 5y ago
      /me not a statistician! I'm not clear how "expected no. of attempts for X" is related to the probability of X. And I seem to be struggling to recall what little I used to know about probability. I'd welcome a (link to a) clear unpacking of this scenario. I'm feeling rather stupid, as if I've had a stroke and lost a mental faculty. It seems to be a straightforward and obvious scenario, but I've lost confidence in my reasoning about it.

by vages 5y ago

rich_sasha 5y ago

If there’s a million tickets and you know one of them is a winner, then yes. If you have an effectively infinite stream of tickets and each have a 1 in X probability of winning, you will indeed go through X on average.

denton-scratch 5y ago
Yeah, I think that's right. The hypothesis was that on average, one in a million cards is a hit. That implies that if you scratch a million cards, you have a 50:50 chance of a hit. That the author got this basic thing wrong doesn't inspire much confidence in the rest of his reasoning.
- rich_sasha 5y ago
  Well, I guess in real life blockchains it’s like the latter case. You have a block and look for a nonce. There is an effectively infinite stream of nonces (“lottery tickets”). You have no guarantee that even one works, other than statistical hope. So then if probability of a match is 1 in X, you expect to have to do X attempts. I have other issues with the article but this bit seems ok.
  - denton-scratch 5y ago
    /me not a statistician! I'm not clear how "expected no. of attempts for X" is related to the probability of X. And I seem to be struggling to recall what little I used to know about probability. I'd welcome a (link to a) clear unpacking of this scenario. I'm feeling rather stupid, as if I've had a stroke and lost a mental faculty. It seems to be a straightforward and obvious scenario, but I've lost confidence in my reasoning about it.