First, we have to look at the game. Let's say I'm one of the participants, and we are all told there are 1000 of us which will play a winner takes all coin toss game. There is one coin and each pair of players walks up to the coin, decides who will be the caller then watches for the result of the flip. We must all play until one person holds all the money. The first thing I'm going to do is casually head to the very back; that way I don't get eliminated until I reach the last person holding everyone's money, minus mine. At that point, if the coin was fair at 50/50 I would be happy to allow fate to decide whether I won very big, or lost my small stake. However, if the coin was biased at 60/40 favoring heads, and me being the astute observer I am noticed this tendency while awaiting my turn, when I reached the coin I would be sure to be the caller and firmly call heads. If I won, yes, I would give myself substantial credit for knowingly tipping the results in my favor.

The shorter answer to your question boils down to whether or not the winning caller used known information about the bias to his advantage. If he did, yes, he deserves some amount less than full credit -- fate will ultimately decide -- but more than zero credit, which would be in the case of a non-biased 50/50 choice. Also, I feel compelled to say I do believe Warren Buffet made the majority of his investment decisions on a mental certainty of far greater than 60% (unless the stake was quite small). One of the things about Warren Buffet's strategy is he buys for the long term, so, even if he's wrong in the short term, he won't sell. The company would practically have to go out of business for him to lose. The chance of that for companies he invests in is very slim.