From what I can tell, they're tossing coins until the last 3 match Blue's choice (HHH) or Red's choice (THH), then starting again with a new round of coin tosses. Now think about how Red and Blue can win. The only way Blue can win a round is if the first three coins are HHH. They can't get a HHH any other way, since that means a THH happens first and so Red wins. Therefore, Blue's odds are 1 in 8, and Red's are 7 in 8.
Nice coin trick, Derren Brown
From what I can tell, they're tossing coins until the last 3 match Blue's choice (HHH) or Red's choice (THH), then starting again with a new round of coin tosses. Now think about how Red and Blue can win. The only way Blue can win a round is if the first three coins are HHH. They can't get a HHH any other way, since that means a THH happens first and so Red wins. Therefore, Blue's odds are 1 in 8, and Red's are 7 in 8.
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