Gambler’s FallacyMost blocks take nowhere near 10 minutes to arrive; the average of the exponential distribution is almost meaningless to everyday-life usage questions of “how long will this take?”, and the exponential distribution generally defies human intuition.
I still like my rendition, even though D_W established that "technically" my framing is not accurate. I still like it.. because it is fun.. tick tock next block.
It is classic
Gambler’s Fallacy.No, I am not trying to be persnickety. The Bitcoinland urban legend of “blocks take about 10 minutes” is Gambler’s Fallacy: A practical expectation that you are “due” for a win based on a statistical average.
Don’t forget that Bitcoin’s mining algorithm
is a giant lottery—and that on the flipside, many Provably Fair crypto-casinos use SHA2 to roll virtual dice. Waving hands over some important technical differences, it is useful to keep that in mind.
In practice, although they are discrete and not continuous processes, games of chance that pick winners based on a uniform distribution can be usefully modelled as Poisson processes. Wins accordingly have a statistically “expected” arrival time based on the average of an exponential distribution—just like Bitcoin’s 10-minute
target for blocktimes, a targeted average calculated over numerous blocks.
By this model, the “fastest” quartile of wins feels
so lucky that it gets gamblers excited—just like how 25% of Bitcoin blocks arrive within 173 seconds. The
median is much faster than the
average, which means that fully half of all games
feel luckier than they really are. Tell me, how many times have you exclaimed, “Wow, I am so lucky—the confirmation of my tx was much faster than I expected!”?
The “slowest” quartile of wins then drains the gamblers’ funds as they keep playing, believing themselves “due” for a win. Those are the blocks that seem to take forever, as you are awaiting confirmation. That long tail is
long, indeed!
The exponential distribution plays games with your head. It defies and exploits human intuitions in almost every possible way. It is a dice site’s best friend.
Maybe some stats textbooks say the same thing. Maybe not. I figured this out myself, many moons ago.
* death_wish loves the exponential distribution.