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Using some simple probability tricks, I found that the expected number of years it will take for all 30 teams to win the World Series is 119.8.
In doing the math, we assume that each year's winner is independent of the next (definitely not true) and that each franchise is equally likely to win a championship in any given year (almost certainly not true). So, if anything, I'd expect the *actual* expected value to be a good deal *larger* than 120.
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