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Comment by ikken | Hacker News Reader

This reminds me the bet in the bitcoin community [1]. If on average bitcoin blocks are produced every 10 minutes, and you learn that 5 minutes ago someone found a block, what is the average time you will wait for the next block? It turns out it's 10 minutes, not 5 minutes as you would intuitively think. (it's a memoryless process, so average expected time till block is always the same - 10 minutes - no matter how many blocks were recently found).

In other words, when you're waiting for bitcoin transaction to be confirmed and go to check how long ago the most recent block was produced, in order to estimate how soon the next one will come - you're doing it wrong. Even if previous block was found 9 minutes ago, you're average waiting time for the next block is still 10 minutes.

[1]. https://www.reddit.com/r/btc/comments/7rs8ko/dr_craig_s_wrig...

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And a related counterintuitive fact (again, assuming 10 minutes):

1. If you pick a block randomly (uniformly), its average length is 10 minutes.

2. If you pick a point t0 in time randomly (uniformly), the average length of the block you're in is 20 mins (and the average length from t0 to next block is 10 mins, and the average length from previous block to t0 is also 10 mins (and, needless to say, 10+10=20...)).

Here's an even simpler example: a flip of a fair coin.

Suppose this is your first flip, one would intuitively think that there is 50% chance of H and 50% T.

Suppose you flipped once and got H. For your second flip, one might intuitively think that since the number of times getting H over the long run is 50% of the total flips, and we already have a flip of H, to "balance it out" the next flip should have a smaller probability of getting H. Instead that is wrong. The next flip still has 50% chance of H.

Suppose further that one has performed N flips, all of them H. One might even think that because of the way the geometric distribution works, it is very unlikely for the next flip to be H again. Instead that is wrong. The next flip still has 50% chance of H.

This is actually wrong. The average expected time till next block is almost never 10 minutes because hashpower goes on and offline all the time. It gets adjusted every 2016 blocks based on historical block timing so that if no changes occur then future blocks would be 10 minutes on average - but changes always happen so this is never accurate. As such, you do learn something by looking at prior block times.

What you say is not a rebuttal of the parent comment. Parent explicitly said that average block times are 10mins in the assumption. The most recent block time doesn't change that.

Parent is talking about bitcoin, where that is false. If they are assuming the average, then they're assuming something false.

the important thing is that it doesn't matter what the parent assumed.

whether the actual time is 10 minutes or 100 years, knowing that somebody else solved one recently doesn't speed up your time to find one

Of course it doesn't speed up your own time, since you have perfect information about your own hashpower. But it does tell you information about the total hashpower that's online, statistically.

I'll give an extreme example to make this clearer. Suppose 10X hashpower just came online an hour ago. It's quite likely that ~60 blocks have been found in the last hour, assuming the difficulty adjustment hasn't happened since. Seeing this, one could deduce that hashpower went up by ~10 and that the expected time till next block is roughly 1 minute instead of 10.

Now, in most cases hashpower doesn't change that drastically but it remains true that recent block times give you more than 0 information about hashpower and therefore about the expectation for future block times.

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