Today I witnessed the most extraordinary coincidence of my life.
I count myself lucky to have two amazing daughters, Sarah and Annalise. I also count myself lucky to have twins. Today, “lucky” took on a whole new meaning.
Annalise and Sarah are now ten-year-olds. They have both had piggy banks since they were about two years old. About a year ago, the piggies were full and so they each wanted to cash in their coinage for some folding dough. So we busted them open. Again, this was about a year ago.
Both girls dumped their respective hordes into heavy duty freezer bags. My guess is that each weighed about 8 pounds or so, but Sarah’s was just a little bit heavier; she must have had a higher concentration of pennies and nickels.
Sarah wanted to cash hers in at the Coinstar machine right away; Annalise wanted to hold on to her bag of booty a while. I totally understood Annalise’s choice… eight pounds of hard, cold cash is a pretty cool thing for a nine-year-old.
Sarah had a blast shuffling the coins into the machine. She even got to push all the buttons. A few minutes later, the noisy machine went silent. We decided that she’d get the Amazon certificate and avoid the 9.8% fee. I would buy the certificate from her for cash and then she could deposit the money in a savings account. A couple more button pushes the and out popped the Amazon voucher. The total: $100.30.
Fast forward to today. Annalise had completely lost track of her bag-o-coins. We decided to paint the girls’ bedroom this weekend and that meant sorting through (and purging) probably 200 pounds of accumulated kid debris. Well, I call it debris… they would call it treasures.
In the process, Annalise’s coins surfaced. She was very excited to have them in hand again; and this time she was eager to visit the Coinstar machine!
On the drive to the nearby supermarket where the Coinstar machine lives, Annalise hoped out loud that she had at least as much value in her bag as Sarah had a year earlier. She still knew Sarah’s number: $100.30.
“Dad, how much do you think there is in here?” She fondled the plastic pouch. “I hope I have as much as Sarah… do you think I do?”
There’s a twin thing. It’s like sibling rivalry… only much more refined. You see, each twin is always competing for the exact same resources all the time. If they were a year or two apart, the older one would outgrow the toys, activities and attention relevant to that age.
As the younger one reaches that age, the older one wouldn’t care much for those things because they would have outgrown them. Thus, less direct competition ALL THE TIME FOR EVERYTHING. But I digress.
Finally we reached the Coinstar machine. In go the coins. Of course, like Sarah before her, Annalise got to control all the buttons. Chugga chugga churn churn… ding! The total amount: $99.27. Remarkably close to Sarah’s $100.30.
Great result, I thought to myself; Annalise, though, was a little dissapointed. “Dad, you have any change in your pockets?” I didn’t. “Do you have a couple dollars I can have so that have the same amount as Sarah?”
I probably should have encouraged her that it wasn’t a contest and that $99.27 is an awesome number and close enough to Sarah’s number. But I didn’t. We figured out how much she’d need to feed into the machine to get her to Sarah’s number: $1.03.
I took two one-dollar bills from my wallet and walked 60 feet to the bank teller at the US Bank counter housed in the grocery store. “Could I get four seven quarters, two dimes and five pennies?” The teller shot back a brief, quizzical smile.
The entire walk and bank transaction only took at most 90 seconds.
But by the time I’d returned to the Coinstar machine, the screen was prompting us to confirm the Amazon certificate choice, with no way to go back and put more coins in! Oh no… the machine timed out! Foiled! Now the voucher would forever say $99.27.
As we reviewed the receipt, Annalise looked down at the coin return slot. Neither of us had noticed it till just then. “Wait, what’s this?”, Annalise said. “Oh, that must be the coins that the machine couldn’t figure out.
We counted it out. Holy crap! $1.03!!! I couldn’t believe. I counted it again… twice. Sure enough, exactly $1.03. Add that to the $99.27 and what do you get? Precisely $100.30.
What a tremendous coincidence. Annalise “got it”, at least in the way that a 10-year-old can. But I was reeling.
I’ve always been a geek about probabilities. In college, I used to count cards at blackjack, which is all about shaving fractions of a percentage off of the houses advantage until the advantage is yours. For the past decade I’ve been studying the odds and probabilities and odds of poker, to the point that I can calculate the percentage chance of making a flush or a full house out of my hole cards in a matter of seconds… and my expected long-term value of calling a bet based on that percentage and the amount of cash in the pot.
Roughly estimating about 17 random coins per dollar:
- 2 – Quarters
- 3 – Dimes
- 2 – Nickels
- 10 – Pennies
That makes about 1,700 coins collected randomly over about 8 years.
There was never any effort to achieve parity between piggies. Visually, Sarah’s piggy appeared to have about 20% more coins than Annalise’s piggy — Sarah was more diligent about stocking away change when you found it.
I don’t even know how to figure the odds that eight years of random coin collecting would yield the exact same dollar value. All I’m confident of is that the probability would be infinitesimal.
I’m also confident that I would have bet the farm if someone would have offered me a wager against.
I guess there really is a “twin thing”