6

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I set out to test the claim: "**Every nonce has an equal chance of winning.**"

# Time Evolution

So, I plotted, with gnuplot, the nonce values vs. hashes for all the valid blocks in the blockchain:^{(Also, in the last plot, you can really visualize the change in the difficulty and even see where the difficulty was decreased.)}

# Histograms

It makes sense that the nonces found are skewed toward 0 because this is a selection effect: most everyone starts searching for nonces starting at 0, so the lower nonces are found first, even though there may be also higher nonces that could produce a winning block:

Why are the hashes distributed this way, though?:

2-D histogram of hashes and nonces (logarithmic color scale):

@Cryptognome Yes, silly me, I thought there were the same numbers of integers between equal intervals on a log graph…, viz., e.g.: log(100) - log(10) = log(1000) - log(100), but 100 - 10 < 1000 - 100. – Geremia – 2015-03-11T22:15:46.080

1Why is so much of this question struck out? If it's incorrect, just remove it. Striking it out makes it harder to read, and I can't even tell what the question is anymore. – Chris Hayes – 2015-03-12T01:37:03.467

I think the problem is that the initial question made no sense, as it was based on a false understanding of the presented graphs. However, as Chris already said: The question should either be edited to fit the answers it got, or deleted if it is not deemed useful. As it is I'd vote on "not useful". – Murch – 2015-03-12T11:45:53.453

Even if the graphs were correct, it wouldn't prove that nonces had an unequal chance of winning. If you look at the numbers on winning lottery tickets, 7 will be over-represented. But it's not because 7 comes up more as a winner, it's because people play 7 more. If, for example, many miners try nonces sequentially from zero and stop when they find a share, you'll see a lower incidence of higher nonces. – David Schwartz – 2015-03-13T06:01:03.820

@DavidSchwartz But these graphs are of winning nonces (nonces that produce a block), not all nonces tried. – Geremia – 2015-03-14T02:05:11.127

@Geremia Exactly. A chart of numbers on winning lottery tickets would show lots more 7's even though 7 is no more likely to win than any other number. – David Schwartz – 2015-03-14T19:38:36.067