Well, it figures. One final screw up in 2020. Most years, I use the last five days of the year to give y’all a recap of the most popular posts from the previous year. That means I should have started posting last Friday so that I would finish with #1 on December 31.
Oh well.
The #1 post from 2020 was the first one posted. I talk about statistics and degrees of precision, but not in a boring way.
Happy 2021 and good riddance to 2020.
Many thanks to all of you who put up with these scribblings every M-F. You have no idea how much I appreciate you all. (But, it’s a lot!)
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How I Guessed the Exact Amount Of Coins In The Jar
January 2, 2020
It’s a common raffle. There’s a jar full of stuff. Maybe it’s gumballs. Maybe it’s jellybeans, or guitar pics. Or, as in my case, coins. You have to guess how many. Or, again in my case, how much.
How much are the coins in the jar?
I like using cash. Despite our society’s continued push towards a cashless society, I actually like cash. I prefer to carry bills.
Maybe it’s a sense of nostalgia. After all, despite having a phone (with it’s ubiquitous clock) I also have a smartwatch, and yet I carry a pocket watch. I have for years. My car is a 1996 Toyota that includes manual transmission, manual door locks and manual windows. I write letters. And I write for a local newspaper that exists only in print edition. I work in IT, but my life is definitely not ruled by technology.
I like cash, but, I don’t like carrying coins. I have a jar that I keep coins in. I don’t collect them. Well, I do collect coins, but not every coin. So, I have this jar and every time I have coins I dump them in. Eventually the jar fills up, of course. It doesn’t fill up in a strictly linear manner. Occasionally, a child will need change for a dollar. Or during Chinese New Year when we give the kids money it typically comes out of the coin jar.
But, eventually, it gets too full to hold any more coins. I then take it to the bank and get it changed into cash. Bills this time. Plus, some remaining coins of course.
I try to guess how much money is in the jar. And this time I guessed it just right. Well, almost. But, really, really close.
Do you ever play the lottery? Maybe you’ve hit the numbers. Chances are you haven’t. But, I’ll bet you’ve been really, really close. Like maybe only off by a number or two.
Yeah, we all have. In fact, I was just as close to guessing the amount of money in my coin jar as you were to hitting the lottery. That is to say, very close and incredibly far off.
Yesterday’s powerball numbers were 49, 53, 57, 59, and 62, the Power Ball was 26 and the Power Play was X2. If you had known these numbers yesterday, you’d be $220M richer. (No one matched all the numbers, so you have still have a chance.)
Someone matched five numbers. They won a million dollars. (Oh, so close.)
Have you ever played the powerball lottery? I haven’t. It’s not just that Utah doesn’t participate in the lottery. To quote a disgraced actor from a good movie, “I believe in the power of large numbers.”
Ever wonder why no one picks the numbers 1, 2, 3, 4, 5, 6 as their powerball sequence? Stupid question, right? No one would ever pick those numbers. There’s virtually no chance those numbers would come up.
Actually, the odds are 1 in 292,201,338 that those numbers will come up. Do you know what the odds for yesterday’s winning numbers (49, 53, 57, 59, 62, 26) were?
They were 1 in 292,201,338.
Weird, huh? The exact same odds for both numbers. There’s a pattern here. By this time you can guess the odds of any number being the winning number. Yup, it’s 1 in 292,201,338.
It doesn’t make sense to us. We know that 49, 53, 57, 59, 62, 26 is more likely than 1, 2, 3, 4, 5, 6.
Don’t we?
I remember seeing a computer parlor trick one time. The website claimed it could read your mind using a set of cards. The website showed you a group of five face cards and asked you to mentally pick one. Once you had picked your card, you clicked NEXT. And it worked. Magically, the website managed to make only your card disappear.
I like puzzles. And this one had me stumped. I visited the website multiple times. And it absolutely worked each time. One clue was that the website didn’t allow the back button in the web browser.
I eventually figured out the trick, of course. The website didn’t just make the card you picked go away. It made all of them go away. It simply replaced them with a new set of four cards. The trick, like all good magic tricks was about misdirection. You, or rather I, was so focused on my own card, that I ignored the other cards. Later, when I was presented with a group of four face cards, which replaced a different group of four cards I didn’t notice.
The lottery is like that. We focused on our own numbers. We hardly pay attention to the winning numbers, except to note that our card isn’t there. All the rest of the numbers look the same.
If the computer had showed me a new group made up entirely of the cards Ace, two, three, and four, I would have immediately noticed that they were different. But, since the face cards all have a familiar pattern, I didn’t notice.
When I took my jar of coins to the bank, I guessed there was $65.00 in the jar. I got it right. Or nearly so. There was exactly $67.72. The distribution was
Pennies: 672 $6.72
Nickles: 158 $7.90
Dimes: 171 $17.10
Quarters: 132 $33.00
Dollars: 3 $3.00
Total: 1,136 $67.72
It’s remarkable, don’t you think, that the total value includes the same numbers that are in the pennies total, the numbers 6, 7 and 2?
No?
No, it’s not remarkable. It’s coincidental, but really that’s all it is. And when your powerball numbers seem oh, so close to the winning numbers, it’s not remarkable. It’s a coincidence. Because the odds of 1, 2, 3, 4, 5, 6 being the winning numbers are exactly the same as 49, 53, 57, 59, 62, 26.
When I guessed my total value of coins, I knew it was somewhere between $55 and $75. And since the distribution of coins was random, the odds that it was exactly $65 were the same as the odds the total would be $67.72.
I only missed it by that much.
Rodney M Bliss is an author, columnist and IT Consultant. His blog updates every weekday. He lives in Pleasant Grove, UT with his lovely wife, thirteen children and grandchildren.
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