It would be interesting to hear what "run a patch through it until clean" means. Its a subjective saying , to me as close to a white patch as possible. I'm curious because is it necessary to get a rifle bore how clean, using the stains on the patch as a guide. I am a bit OCD, or so I'm told............lol
It usually takes 10 - 12 patches to get there and its still not "brand new" white. I use a brass jag and wipe-out foam copper cleaner after I run a soaked patch with Birchwood bore cleaner (I've used shooters choice, Hoppes 9, CLP before), then a brass brush both ways for 30 or so times, followed by another soaked patch, then another round with the brass brush. Follow that up with a couple dry patches to clean that out.
When I'm running the jag I will pass the jag back and forth the length of the barrel, removing it from the chamber and to the end each stroke. I scrub the bore with the jag as opposed to pushing it all the way through once and replacing it with a new one. The first 5-6 patches come out dark purple. Each patch getting lighter. I start seeing a lighter purple color until about the 9-10 patch then a couple patches after that that are slightly discolored. I will clean my bore this way after 20 rounds but have gone as long as 40-50 rounds.
When I go shoot after a cleaning, I will put 3-5 rounds down range to foul and heat the barrel, let it cool then shoot for the day. These rifles are regular stock rifles off the shelf. I like my rifles to group, each touching or close. I'm a hunter and don't shoot competitively. I may or may not be overcleaning, its just my routine.