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I'm not 100% certain (in fact it is a coin flip lol) but isn't it (1/2)^9?

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This is correct if flipping coins.

If a 45% favorite, it is similarly .45^9.

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yes, that's correct!. i don't understand the wording. is 45% the favorite? unless there's a big push potential, you'd be an underdog.

but yes, .45^9.... i know 50% to the 9th is 1 in 512. yours would be even longer-shot