Friday, June 17, 2005
12:14 PM — "If I had a quarter for every time..."
People keep using the phrase "If I had a nickel for every time someone did *blah*, then I'd be rich!" or "If I had a dime for every time someone did * blah'* then I could retire by now!" The example I read recently was "If I had a nickel for every restricted driver's license - a certain indicator of a DWI conviction in New York State - I see at the door, I could probably retire." (Club Life)

In my inimitable style of applying way too much math to everyday situations, I decided I'd analyze this in an order of magnitude approximation: make assumptions on how much money is "rich" or how much is needed per year to retire; determine how many nickels/dimes/quarters are in that amount of money and therefore how many times the event has to happen; estimate how often you'd need that to happen, or how long it'd take for *blah* to happen that many times; conclude whether the original statement was reasonable. Yes, this really does entertain me. Moreover, there's a chance I'll give a version of this on a physics exam in the Fall.

Intro:
I'm going to analyze the following: "If I had a dime for every restricted ID I saw, I'd be rich."

Definitions:
What does "rich" mean? If you win a lottery jackpot of \$1,000, that doesn't even buy you a decent used car. \$10k does, but it doesn't buy you a house. \$100k will net a house in some areas, but not most. \$500k is a reasonable estimate for "rich," but \$1M is definitely quite the pot of money, plus I want to make this an order of magnitude estimate (OME), meaning the first digit MUST be a 1, and all the others are 0's.

Since doing OME, let the coin in question be a dime (\$0.10). \$1 has 10 dimes. \$1M will have 10M dimes. Whatever event we're talking about has to happen 10 million times for the speaker to be rich.

Analysis:
The speaker of the "driver's license/I could retire" claim has been a bouncer for 6 months, or half a year. A year has 52 weeks, so 6 months is 26 weeks. (I will here dispense with the OME, since 10 weeks is drastically different from 100 weeks, but I'll later round results to OME.) Each week the club is open three nights a week, so he's worked 78 nights. If he worked the door checking ID's every night, then in order to "be rich" then each night he'd have to find 10M/78=.128M=128k = 128 thousand restricted driver's licenses per night. If the club's open from 10pm-4am (which seems to be the case from his posts), that makes 6 hours per night, or 128k/6= 21 thousand restricted driver's licenses per hour, or 360 per minute, or 6 per second.

While that's not FAR outside the realm of possibility, it is slightly so. Let's determine what is more realistic. Assume he worked the same 78 nights at the door, 6 hrs per night, or 468 hours or 1.68k seconds total. Assuming he can check an ID every 5 seconds, he's checked 340k IDs. It seems reasonable to further assume that at worst 1 in 5 IDs is restricted, so he has seen 67,000 restricted IDs.

At a dime each, he has earned a measly \$6,700 (or \$10,000 OME), which is probably enough to replace his free Oldsmobile with a purchased used car, or to instead maintain the free car for a few years, but is NOT enough to be considered "rich,"nor to retire comfortably. In all likelyhood, the speaker has not seen nearly as many IDs outside his bouncing job, so they can be safely ignored.

Conclusion:
The specific statement "If I had a dime for every restricted ID I saw, I'd be rich" is a gross exaggeration. Similar general statements "If I had a generic coin for every blah, I'd be rich/retired" are likely also overestimates. Better to keep working!

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