This isn't as good as the Monty Hall Paradox, but I learned a new one today.

in numbers •  last year 

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In a random list of digits, which of these sequences would you expect to find first, or are the odds equal? 12345 vs 33333.

Would you believe that 12345 is favored by about 11%? Likewise 24680, and 87453 are both favored over 33333 or 11111.

Why? Because when a potential hit fails, say "123" is followed by a digit that isn't 4, there's a 1 in 9 chance that the digit is a one, immediately starting a new potential hit. When "333" is followed by a non-3, there is no chance that the new digit is the start of a hit.

Yet, if you examine a trillion random digits, the total number of 12345s should be roughly equal to the number of 33333s. (3333333 contains three sets of 33333, the overlap makes up for apparent deficit.)

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