Are You a Math Genius?
Consider the two flip sequences HH and TH. The three-flip sequences are HHH HHT HTH HTT THH THT TTH TTT. In these, HH appears first twice, while TH appears first four times. Already, TH has the advantage. The animation below shows how the four-flip sequences compare, with TTTT and HHHH left out, since neither is ever a good bet. Notice the counterclockwise ring of arrows on the outside - everything beats something. If you allow your victim to pick any sequence of 4, you can pick something better, due to nontransitivity. More details at the coin tossing page.
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