Some people say that when they switched to full synthetic oil it caused leaks.
I switched to all my vehicles over to royal purple and in the ten or more years since i haven`t had any leaks start after swapping.
My 116K mile baby Northstar (Olds Aurora) started leaking a bit when I switched to synthetic, prior to that it was only a seep that never formed drops. I've read that's pretty common.
My Escalade has some oil drops on the pan as well.
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I was sold on synthetic oil about 15 years ago when I pulled the intake and heads on my 88 IROC and found absolutely no sludge in a 120K mile engine. I had never seen clean internals on a high mileage engine before. Not one speck of sludge, not one flake of baked oil on a high mile, severely overheated engine.
Synthetics hold up much better to the sustained high temps the engines experience in prolonged idling and stop and go traffic.
The synthetics hold up so well to high temps (around 100F hotter if I remember correctly), that GM switched the Corvette to synthetic in 1992 on the LT1 engine so they could get rid of the external engine oil cooler of the previous L98 cars. They touted it as high tech engineering in the Corvette but it was really about cost savings of the oil cooler they had to use on previous models.
I think one reason that switching to synthetics causes oil leaks is because the sludge that might be present in your used vehicle might be what's keeping the oil from leaking out. Once that disappears there isn't anything to stop the oil from leaking out of where it was intending to.
I don't use anything but synthetics anymore, even on my winter beater. On that vehicle I will use the Walmart branded synthetic (it's made by Kendall) as its only about $1 a quart more than the Walmart branded conventional oil (also made by Kendall if I remember correctly), and about the same price as any recognized brand name conventional oil.