[M.B.E.]

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I was just trying to find an example where a lesser than 50% chance at 999,997 would still be worth re-raising. Obviously I did it incorrectly and put the number too low.

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Okay, but 50% is the wrong number entirely to be looking at.

Consider this example. Playing limit holdem, heads-up on the river the board is Qh-Js-9h-6h-2h. You have Kh-7s, the second nuts. Your opponent bets into you, and based on the action so far, you figure there is about a 45% he has the Ah. Hence you probably have the better hand. Do you raise there? If so you are making a mistake (your correct play is to call).

EDIT: Actually, in that example you could raise IF you knew your opponent will never threebet without the Ah, and he will never fold to your raise. Then it would be correct to raise and fold to a threebet.