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

(jakevdp.github.io)
219 points skadamat | 2 comments | 20 Aug 24 13:55 UTC | HN request time: 0s | source
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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.

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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.

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xnorswap ◴[20 Aug 24 16:02 UTC] No.41301245[source]▶
No, it's 1+average number of winners.

If the odds of winning are 1 in 14 million, and 28 million tickets are sold, then you expect there to be 2 winners.

If look at your ticket and see you've won the lottery, then the odds of winners are still 1 in 14 million, and out of the 27,999,999 other tickets sold, you expect 2 other winners, and now expect 3 winners total, given you have won.

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1. melenaboija ◴[20 Aug 24 17:00 UTC] No.41301753[source]▶
You are making an assumption you did not explain before and makes it confusing, you don’t know the number of winning tickets or the number of winning tickets affects the prize quantity, and not all lotteries work like that.
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2. xnorswap ◴[20 Aug 24 18:46 UTC] No.41302765[source]▶
I'm essentially assuming the UK lottery (from 96-200x) rules, where players:

Pick 6 numbers from 49, so odds are independent, and roughly 1 in 14m.

The prize jackpot is determined from a set percentage from the ticket sales, and is shared between jackpot winners.

How much the jackpot prize is therefore determined by total sales and how many winners there are.

I'm also assuming your individual ticket contribution doesn't materially affect either the prize pool or the number of people playing. For a large N, small p, this holds true.