Quoted from sparky672:More like 22 years.
You forgot all about the temperature rating - it's only 3,000 hours AT 105°C. Service life ratings are on a logarithmic temperature curve. The operating temperature of these caps is nowhere near 221°F, therefore 3,000 hours is really something like 100,000 hours at 131°F, which is 11 years 24/7, or 22 years using your 12-hr/day arcade example. And I doubt they ever see much of anything above 100-110°F, which adds even more years.
The DMD power supply in my X-Files ran in excess of 175F so cab temps could surprise you. I added a cooling fan to the cabinet, I didn't think those temps were conducive to good overall board health. Bally S&T 5v power regulators run hot too and that big honking heatsink on the power supply board isn't there for show.
And time drying the caps out is unavoidable and also shortens the life.
On Data East games the power supplies puke the caps all the time and rot out the traces and they are a decade newer than the stuff were discussing. The number of DE pins with replacement power boards is practically a running joke at this point. I rebuild the boards, Rottendog is dubious at best (I picked up a pin that had a bad RD board right out of the box and the owner sold it off in exasperation) and X-pin is a noisy board on some games.
Even at your best case, 22 years, anything older than 2000 is suspect.