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The probability of getting 6 heads is 1 / 2^6, or 1/64. Since there are 250 people, 250/64 or 3.90625 people will get 6 heads in a row.

As we can see for this example, every round on average half of the people will sit down. Since 2^8 = 256 which is close to 250, the most likely scenario is that the winner flips 8 heads in a row.

Since 2^10 is 1024, you could expect there to be someone standing after 10 flips if there are 1024 people.