...just cite a number that's an even power of 2. The New York Times yesterday had a headline that did just that: 512 Paths to the White House. As any geek would instantly know, 512 is 2^9 (2 raised to the 9th power) – so the chances are that some set of binary choices was being examined.
In this case, the binary choice was Obama or Romney winning any one of the nine “swing” states. The New York Times counts nine states as possibly going either way on election day; other observers count as many as thirteen.
Two choices, nine states equals 512 (2^9) possible combinations of Obama/Romney wins in those states. The page linked above has a nice, interactive “tree” diagram that lets you explore all those possibilities. The subtitle points out that in 431 of those combinations, Obama wins the election; in 76 of them, Romney wins – and in 5 of them there's an electoral college tie (which means that the House chooses the president, and the Senate chooses the Vice President). The fact that more combinations lead to an Obama win tells you nothing at all about the probability of an Obama win; it's just the result of Obama having more electoral college votes in states like California or New York, where there's almost no chance of him losing.
That even power of two caught my eye, though. Without that, I'd never have clicked through to see that page :-)
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