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Comment by paxys | Hacker News Reader

Maybe, but even then I doubt the scheme was well thought out. He had 100,000 bills but the total number of serial numbers is many magnitudes greater than that. The chance that he'd actually have a hit was close to zero. And that is assuming the contest was legitimate in the first place.

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Seems like the classic form of this contest would be for the radio DJ to pull a bill out of his wallet and read that serial number over the air...

Haha this is what I was thinking. Did anyone ever actually win this prize?

IIRC serial numbers aren't unique. Even if the DJ was doing that, there would still be a chance. (albeit extremely small)

> A unique combination of eleven numbers and letters appears twice on the front of the note. Each note has a unique serial number. The first letter of the serial number corresponds to the series year.

https://www.uscurrency.gov/denominations/bank-note-identifie...

It's not the whole story. In genuine currency, serial numbers are only unique within a series. Series 2017A and series 2021 notes can (and in fact do, since they start over at A00000001A) have identical serial numbers.

In 2014, the Bureau of Engraving and Printing (BEP) accidentally assigned overlapping sets of serial numbers for replacements notes to its currency-printing facilities in both Washington, D.C. and Fort Worth, Texas. The overlap occurred from serial numbers B00000001* to B00250000* and B03200001* to B09600000*. On the lower right-side of the front of the note, the letters “FW” with the face plate number indicate it was printed in Fort Worth.

https://www.pmgnotes.com/news/article/9321/Duplicate-serial-...

A significant quantity of those bills has probably been pulled from circulation. One of the things the Reserve does is swap damaged bills and look for counterfeits. Every bill they destroy is another crisp bill they can return to banks without fucking with inflation.

Notes prior to 1996, and $1 and $2 notes, use only a 10-digit serial number so there's repeats in new series.

You’re thinking of parallel numbers.

I can explain. But first, we have to talk about parallel universes and half-button-presses.

Great way to catch forgeries

That would be fraud by the radio station, wouldn't it? You can't run a contest that is impossible to win.

So? Who's gonna know?

Giveaways like that were far less regulated at times in the past.

Actually it's only 6 digits of the serial number that needs to match. According to [1] the game Michael Larson was trying to win was organized by $ale of the Century (SOTC), which was actually a TV show, not radio show. And as per [2] it was run for only 2 weeks in the fall of 1984, and the prize was indeed $30k as the Damn Interesting article claims. And there is a recording of an episode at [3] showing the six digits to match were "550085". Since Michael Larson had 100,000 bills, he basically had 10% chance of winning the $30k prize. If the game was run 14 times (over 2 weeks), he would have had a 77% chance of winning (1-.9^14)

I found another episode at [4] where the host even explains "according to the Treasury Department there as 3.7B one-dollar bills in circulation; that means [...] there are 3700 dollar bills with the winning number"

[1] https://www.gameshowforum.org/index.php?topic=5153.0

[2] https://tvtropes.org/pmwiki/pmwiki.php/Series/SaleOfTheCentu...

[3] https://www.youtube.com/watch?v=neCxKLjsow8&t=1510s

[4] https://www.youtube.com/watch?v=bnvSJZj3m0U&t=1296s

> Since Michael Larson had 100,000 bills, he basically had 10% chance of winning the $30k prize.

A bit less than 10%, since some bills would be functional duplicates.

Oh, you are right. It looks like it's around 9.5% according to a quick simulation I ran.

Looking at a dollar bill, I guess the serial-number space is 8 digits plus 2 letters. So naively the chance of any hit with 10^5 bills is 1 in 676000, yeah. (But maybe the serials were smaller then?)

Re the lookup problem, you could initially "hash" all the bills by say the two leading figures, in your first pass.

It's all way stupider than the game-show hack.

Other comments take the letters to not count, which would make the chance 1/1000 per trial -- not so ridiculous.

Yeah like, even if he somehow owned 10% of all dollar bills in existence and had a somewhat efficient way of looking them up, his expected value is still only $3,000! Does it really make sense to do all the work of taking your hard-earned, once in a lifetime windfall of $100000 (easily 4x the median annual income at the time, even for a person who had a steady professional job), out of the literal bank where it safely sits making ~10% interest in the mid 80s, and store it in your messy house in drawers and trash bags, for the opportunity to make 3% back? Not the thoughts of a rational person!

You mean the E[V] is 103,000. He still gets to keep the 100,000 he withdrew and re-deposit it.

I wouldn't consider the original 100K to be part of the expected value since that's money they already have, not money they're winning...

He should have just put it in a savings account and looked for something else.

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