Just a couple comments and follow-up as I've received a couple emails about this thread. To answer the original question, I believe the survival rate is less than 1%. We seem to agree that there are no more than 50k N172s with us today and I believe there may have been more than 5 million originally produced from 1886-1890 (yes, this is a SWAG but based on some known information from 1889).
Some of the largest collections are not private collections, but instead housed in museums. The Burdick collection, for example, is extremely close to 2000 N172s. We then have Sir Edward Wharton-Tigar and others that fall in the #6-#25 such as LOC (476), BB HOF (400), etc. This is based on strictly N172s; the BB HOF has a very impressive N173 collection (250 cabinets) to boot.
To summarize, I believe the top five collections account for less than 10k cards and the next 20 fall even further from 10k. If we really did a deep dive, I suspect the top 25 collections are closer to 15k than 20k. I do realize there are a good number of small collections out there with active collectors and dealers but of the 3 groups (1-5 largest, 6-25 largest, and the rest), the smallest collections enjoy the highest collector/dealer head count but account for the smallest total population. So we might be able to arrive at 20-25k cards in known private and public collections but doubling this to cover the unknown cards seems excessive. I think the safe range remains at 30-50k.
For those who haven't read Dave Jamieson's reasearch on Old Judge card popularity when they were produced and distributed . . .
Read It Here!
Many adults and kids smoked heavily to build sizeable collections. Consider all the albums and cabinets that were ordered. At least 200-350 cigarettes (20-35 N172s accumulated) for every cabinet (depending on when it was ordered) or at least 750 cigarettes (75 N172s accumulated) in order to collect enough coupons for a Round Album (assumes all 10 count packs). Old Judge cigarettes were consumed at a scary rate by some individuals and families to be able to redeem their favorite player or team cabinets and albums.