As the pit boss staggers off the floor and before a replacement can stand in, a well-dressed young woman sits down at the table and places all her chips on "red." It later turns out this is the croupier's wife. The wheel spins; she wins and doubles her money. (The chances of a roulette wheel hitting either red or black is actually slightly LESS than 50 percent, since there are either one or two green slots to give the house an edge. But it's CLOSE ENOUGH to fifty-fifty for purposes of our example, here.) She leaves her chips on red. The wheel spins; she wins again.
In fact, she leaves her rapidly growing pile of chips on "red" and wins seventeen spins in a row, before she stands up, hauls her large-denomination chips to the cashier in a couple of plastic buckets, and leaves the premises with well over a million dollars of the casino's money.
Wow! The odds against that happening are, like 17-to-one, right? Actually, no. The odds of your flipping a fair coin 17 times in a row — starting with your first flip and flipping a fair coin 17 times — and having it come up "heads" 17 times are one in two to the seventeenth power, which I believe works out to one in 131,072.