Matching $10 And $20 Serial Numbers

Very interesting!

I just came across them randomly, wasn't specifically trying to match anything. I've been able to search for and find two $1 bills that match, but always thought it'd be impossible to find two non-$1, just extremely fortunate to have the right handful of bills at the right time.

Not directly related, when you guys reply on here, how do you copy a quote from an earlier post and then paste it so your reply is aimed at the specific quote and not the entire thread?

the FAQ has quoting instructions

Agree!

Odds on finding a match depend on how many bills you have.
--If I have only one $10 and one $20 odds are 1/96 million that the serial numbers match.
--I actually had a strap (100 bills) of each denomination, the chances that there would be a match was 1/9600, so again I was incredibly fortunate to find it, especially not looking for it.
--re: the referee's coin flip: If I had ~7000 of each denomination bill, there would be a 50-50 chance there is a match...half the time yes, half the time no.

@tavi888, I may not know much about combinations but let me take a stab.

What you learned in eighth grade math is correct. If you buy 5000 tickets against a 1/10,000 drawing, the chances are indeed 50-50 of finding a ticket that matches the drawing.

In ninth grade math we learned about sets. A set of 6928 $10s and a set of 6928 $20s, multiplied together, creates 48 million combinations out of 96 million possible serial numbers, and there's your 50% chance of finding a match. In the lottery, you need so many lottery tickets because you only have a single winning drawing in your second set.

5000 tickets x 1 drawing = 5000 combinations out of 10,000 possible outcomes = 50% chance winning.half the time yes, half the time no.
6928 $10s x 6928 $20s = 48M combinations out of 96M possible outcomes = 50% chance finding a matching $10 and $20. half the time yes, half the time no.

I'm not sure exactly what was your critique or what was your your better answer, but my math is right and I hope this helps. If you have a different answer or don't understand something, there's a respectful way to ask or to challenge someone. Having said that, welcome to the CCF!

What you're talking about @nss-52 is 'expected value', which is the value of all possible outcomes times the probability of each. Lotteries are notoriously low expected value. As you suggest, the concept isn't really relevant for matching serial numbers. The reward here (if you're into such stuff) is just finding matches given how unlikely and labor-intensive it is, not really worth anything from a payout perspective.