←back to thread

The waiting time paradox: why is my bus always late? (2018)

(jakevdp.github.io)
219 points skadamat | 1 comments | 20 Aug 24 13:55 UTC | HN request time: 0s | source
Show context
xnorswap ◴[20 Aug 24 15:50 UTC] No.41301135[source]▶
My favourite corollary of this is that even if you win the lottery jackpot, then you win less than the average lottery winner.

Average Jackpot prize is JackpotPool/Average winners.

Average Jackpot prize given you win is JackpotPool/(1+Average winners).

The number of expected other winners on the date you win is the same as the average number of winners. Your winning ticket doesn't affect the average number of winners.

This is similar to the classroom paradox where there are more winners when the prize is poorly split, so the average observed jackpot prize is less than the average jackpot prize averaged over events.

replies(6): >>41301213 #>>41302432 #>>41302595 #>>41303568 #>>41304369 #>>41305006 #
pif ◴[20 Aug 24 15:58 UTC] No.41301213[source]▶
> The number of expected other winners on the date you win is the same as the average number of winners.

Sorry, but no! The total number of expected winners (including you) is the same as the average number of winners.

replies(3): >>41301245 #>>41301876 #>>41302414 #
1. mitthrowaway2 ◴[20 Aug 24 18:08 UTC] No.41302414[source]▶
You're both right! This is where the subjective Bayesian framework helps clarify things. The passive-voice term "expected winners" leaves ambiguous a key idea: Expected by whom?

The number of winners you expect depends on what information you have, namely, whether or not you know that you are holding a winning lottery ticket or not!