> but around 20 I'm going to be suspicious.
There's a multiple-endpoints effect here. If there are 2^20 participants all doing that, one of them is going to flip 20 heads in a row. You only notice the one who did after the fact. Some participant has to be the most outlying result and that's the only one you notice.
(Not that that's necessarily the case for Buffett, but that's a general fallacy to be aware of.)
edit: With Buffet, he's not actually getting everything right, so I guess a better metaphor would be like 70% heads over 1000000 flips... more likely under random circumstances, but still pretty suspicious.