@Peter R " I still find it weird how that average is exactly twice the interblock average (if you average enough trials)."

Yeah, that is interesting. It must be a property of processes where the events are randomly distributed and independent from each other.

One can imagine other distributions where this is not the case, for example if you had 100 minute window with 9 blocks found in the first minute, and one block found in the 99th minute. In that case, for a random point in time, your "expected" time between blocks would be something close to 99 minutes.

Or if blocks come every 10 min like clockwork, then the expected time between blocks would be 10 minutes.

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@Norway, I think the expected waiting time would be something longer than 5 minutes.

If the buses show up exactly every ten minutes according to a schedule, then your expected waiting time will be 5 minutes.

But, if there is some randomness, then sometimes the buses will be close together, and sometimes they will be far apart. If you just show up at a random time, it will be more likely that you are in one of the longer gaps between buses. And in these longer gaps, your waiting time will likely be longer, which will outweigh the times you happen to just miss one bus, but catch one that is close behind it.

In an extreme case, imagine the buses travel in clumps of two. So every 20 minutes, two buses go by very close to each other. You can see that in this case, you can expect to wait 10 minutes on average.