jbusse -> RE: General Vikes Talk (10/18/2023 2:19:24 PM)
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ORIGINAL: jbusse quote:
ORIGINAL: Todd M If everyone in the world started flipping a coin and only those rolling heads or tails continually got to keep flipping how high of a number could we get to before the game is over? At some point there’s got to be a # you’d be willing to bet your life the next flip would be opposite. It's 33 flips on average. Taking the world population as 8,045,311,447, everyone stays in the game after the first flip (because you say either a string of heads or tails is OK). Thereafter, with each flip, the 8 billion number is cut in half, since there is a 50% probability that someone who had been flipping all heads gets another heads (similarly for the tails flippers): Flip # - # people remaining 1 - 8,045,311,447 2 - 4,022,655,724 3 - 2,011,327,862 4 - 1,005,663,931 5 - 502,831,965 6 - 251,415,983 7 - 125,707,991 8 - 62,853,996 9 - 31,426,998 10 - 15,713,499 11 - 7,856,749 12 - 3,928,375 13 - 1,964,187 14 - 982,094 15 - 491,047 16 - 245,523 17 - 122,762 18 - 61,381 19 - 30,690 20 - 15,345 21 - 7,673 22 - 3,836 23 - 1,918 24 - 959 25 - 480 26 - 240 27 - 120 28 - 60 29 - 30 30 - 15 31 - 7 32 - 4 33 - 2 After the 33rd flip, we would expect one to have flipped all heads and one to have flipped all tails. Correction, on the 34th flip, expect either the all heads flipper or the all tails flipper to drop out, leaving one remaining. So 34 flips.
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