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An obvious example is when the best hand shares a card with another hand, then you're often better off going with the third hand, even if it's weaker on average.

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Can you give an example of when this might occur?

Because the rules described originally are likely the rules that I will see when I show up next, I'd be interested to know what my strategy should be doubling pairs/aces (see my post a few above this one for my "theory" on how to play these). I know that you should for sure double when you are better than 50%, but I'm specifically curious as to how to alter this strategy with the extra payout system.

I suppose these are my questions:
a) If you hold a pair that is less than 50% to win, what are the odds that you will finish with a set and win (46 unknown cards)?
b) If you hold an A that is less than 50% to win, what are the odds that you will finish with a pair of aces and win (46 unknown cards)?