How much is a four-pair serial number worth?

If you're perusing the bills in your wallet or purse, you may run across a bill that has four pairs of digits together, like 22559977.

A term that has gained some traction is “four pair” or “quad pair” — an eight-digit serial number paired off into four pairs of identical digits.

What are the odds of finding a four-pair serial number?

(WARNING: Math ahead!)

Bills entering circulation in recent years have serial numbers 00000001 to 96000000.

We can “count” four-pair bills in a couple of different ways. The first way is to consider serial numbers that have a distinct pairing where no pair of adjacent digits is the same. (So 44664499 would qualify, but 44446699 would not.) The second way is to take this restriction away and allow successive pairs to be the same, as in 44446699.

Let's consider the first way first. The leftmost pair of digits can be anything except 99, so there are nine possibilities for the first two digits. The next pair has to be different than the first, so there are nine possibilities for the second pair. Similarly for the third and fourth pairs. This gives 9 x 9 x 9 x 9 = 6,561 four-pair bills.

The second way gives a few more. The leftmost pair again can be anything but 99, so nine choices. The next one can be any pair at all, so 10 choices. Similarly for the third and fourth pairs. The only one in this group that's not possible is 00000000. This gives 9 x 10 x 10 x 10 – 1 = 8,999 four-pair bills by this method.

Finally, we calculate the probabilities as 6,561 / 96,000,000 = 0.00006834375 and 8,999 / 96,000,000 = 0.000093739583, or 1 in 14,632 and 1 in 10,668 bills, respectively.

What kinds of four-pair bills are there?

The Green Guide of Fancy Serial Numbers (check on Amazon or eBay) talks about these kinds of bills in several places.

The first category is classified as a CS-Quad Pair if all of the pairs are different, as in 22779944.

If one of the pairs repeats, they classify this as a four-of-a-kind bill. If the repeating pair is at the front and back, this is a CS-Pairs In Quad type (like 44779944). If they're not, then this is a CS-Repeating Doubles type (like 44884477).

What are four-pair serial numbers worth?

The answer to this question depends on who you ask. Many currency dealers will consider these bills to be worth face value, or at best assign only a small premium to them if they're in great condition.

Let's limit the discussion here to an “ordinary” four-pair serial number, like 22669944. The reason is that a lot of the serial numbers counted above are more special and worth quite a bit more. Examples:

• Binary radar serial numbers like 22888822
• Binary repeater serial numbers like 22882288
• Ladder-like serial numbers like 11223344
• Double quad bills like 44447777
• Low serial numbers like 00000011
• True binary serial numbers like 11001111
• Even solid serial numbers like 55555555

Condition, age, and other factors also affect what a bill may be worth. If we consider only the serial number being a four-pair on a $1 bill, this is usually worth around $10 over face value on eBay.

Should you buy a four-pair serial number?

Four-pair serial numbers are actually harder to come by than other kinds of special serial numbers, like radars and repeaters. It might be a long while before you find one. Anything's possible, but if you really want an example and don't want to wait to find one, then there's of course nothing wrong with buying one. I would aim to buy one for between $5 and $10.

I would advise against buying too many of them for that price, though. They're on the rare side but for some reason, they don't get much the same interest as radars and repeaters, which are of similar difficulty to find. It might be a trick to get your money back, even if you get good deals on what you buy.

Can you sell a four-pair serial number?

If you can buy one, you certainly can sell one.

Just be sure to price it so that it makes money for you.

Remember to take into account the listing and final value fee, merchant fees, shipping fees, and the face value of the note of course!

If you can sell a $1 bill for $5 shipped and mail it in an envelope with some protection inside for the bill, you'll likely make a small profit.

(Photo by Kelly Sikkema on Unsplash)