What is the average number of chests that generate per mineshaft?

Exactly what is said on the tin. I couldn't find sufficient information on the official wiki to determine this statistic.

Solution 1:

About 5 ½

With a bit of command help, I was able to explore a variety of randomly generated Mineshafts and instantly get the total number of chest Minecarts, by detecting them as entities (minecraft:chest_minecart). After visiting a few tens of Mineshafts (>40), I was able to extrapolate some average stats per Mineshaft, including spawner rates:

• 5½ chest Minecarts (for comparison - about 1.5 gold apples per complex)
• a median of 5 chests, with ~80% of the Mineshafts having 3-9 chests
• about 3 spawners

A not-so-accurate graph of the probability to find the given count of chests:

The blue line represents the actual statistics, the yellow one the ideal probability values. Since the total number of mineshafts is 44 (low for accurate stats, but good for rough calculations), the chance to find, let's say, exactly 5 chests is (~7/44) * 100 ≈ 15%

You can also find no minecarts at all - the chances for this are quite high (just under one from ten). Finding over 12 is rare. In practice, one will locate averagely around 4-5 chests, with some remaining unlooted.