There are two arguments being made that are both partially correct.
I agree that there will be roughly the same number of copper cents in the wild as people will keep cashing them in (minus the small percentage lost or destroyed). However, as each year passes and more cents are minted, the percentage of copper found will continue to go down as the total number of copper cents minted compared to the total number of all type of cents minted will be a smaller percentage.
The example that follows assumes:
a) No coins have been pulled from circulation, lost, or destroyed (though we all know some has been).
b) No coins before 1909 and no foreign coins are a percentage of the coins searched. Just to make the math simpler.
Example:
If you add up all cents minted starting at 1909 through 1981 (+50% of the 1982 mintage as I wasn't sure of the breakdown for 1982), the total number of copper cents minted is 175,611,234,077.
The total number of cents minted from 1983 through 2016 (+50% of the 1982 mintage) is 328,731,909,501.
So at the end of the 2016, at best one could expect to find approximately 34.82% would be copper as that is the percentage of copper ever minted. The equation is 175,611,234,077 / (175,611,234,077 + 328,731,909,501)
Taking those numbers forward one year and assume that in 2017 the United States mints the same number of cents as it did in 2016 (9,118,400,000). Then at the end of 2017, the max copper percentage drops to 34.20% as the total number of copper cents is a smaller percentage of the total cents minted even though the total number of copper cents in circulation didn't change.
Summary:
Assuming the mintage numbers stay the same as they were in 2016, each year the find rate of copper cents in circulation will be ~0.6% less even if no copper cents are pulled.
And just for more fun with math of what is really left out there, let's use wheat cents. From 1909-1958, there were 25,817,950,007 cents minted. If they were all in circulation and randomly distributed, one would expect to find on average that 5.12% of all cents searched were wheat cents. That would work out to roughly 128 wheat cents per $25 box. Obviously, many wheat cents have been pulled, lost, or destroyed, so the actual find percentage is considerably less. Although it varies based on location, the average number of wheat cents found per $25 box seems to be ~10 (or a find percentage of 0.4%). If that's true, it means 10 of every 128 wheat cents is still circulating, leaving only 2,017,027,344 wheat cents yet to be pulled from circulation. Still some work to do!
Another note:
Just subtracting the number of wheat cents no longer from circulation (based on the find rate), the maximum copper % find rate would drop from 34.8% at the end of 2016 to about 30.08%. Subtract the other copper cents that have been lost, destroyed or pulled from circulation already and that is the actual copper % in circulation.
If enough people had interest, you could do some analysis to figure out what percentage of copper is actually still in circulation. It's not a number I ever tracked, so I have no data on the subject to try to figure it out. It would be best to have find rates for a number of different locations in the country as well as multiple searches at each location across a period of time to make it statistically significant or at least close.
