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: [![nonces histogram][8]][9]

Why are the hashes distributed this way, though?:

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

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][8]: 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: [![nonces histogram][9]][10]

Why are the hashes distributed this way, though?:

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

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

So, I plotted, with gnuplot, the nonce values vs. hashes for all the valid blocks in the blockchain, and I was very surprised to see that the nonce values that produce valid blocks are not uniformly distributed whatsoever:



They're heavily concentrated toward the max nonce value (0xffffffff).
^{(Also, in the last plot, you can really visualize the change in the difficulty and even see where the difficulty was decreased.)}

Isn't having such an uneven distribution of nonce values a big weakness in how Bitcoin does proof-of-work? Or does using extranonce even things out?

Doesn't this mean miners should concentrate only on large nonce values instead of wasting their time scanning the whole nonce space?

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: [![nonces histogram][8]][9]

Why are the hashes distributed this way, though?:

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

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

So, I plotted, with gnuplot, the nonce values vs. hashes for all the valid blocks in the blockchain, and I was very surprised to see that the nonce values that produce valid blocks are not uniformly distributed whatsoever:



They're heavily concentrated toward the max nonce value (0xffffffff).
^{(Also, in the last plot, you can really visualize the change in the difficulty and even see where the difficulty was decreased.)}

Isn't having such an uneven distribution of nonce values a big weakness in how Bitcoin does proof-of-work? Or does using extranonce even things out?

Doesn't this mean miners should concentrate only on large nonce values instead of wasting their time scanning the whole nonce space?

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

So, I plotted, with gnuplot, the nonce values vs. hashes for all the valid blocks in the blockchain, and I was very surprised to see that the nonce values that produce valid blocks are not uniformly distributed whatsoever:



They're heavily concentrated toward the max nonce value (0xffffffff).
^{(Also, in the last plot, you can really visualize the change in the difficulty and even see where the difficulty was decreased.)}

Isn't having such an uneven distribution of nonce values a big weakness in how Bitcoin does proof-of-work? Or does using extranonce even things out?

Doesn't this mean miners should concentrate only on large nonce values instead of wasting their time scanning the whole nonce space?