The Lucky Donut

In his show The System, which aired on Channel 4 on Friday night, Derren Brown showed that winning (or, by implication, losing) ten coinflips in a row is quite a normal occurrence and really nothing to get excited about. 

If you haven't seen it and don't want me to spoil the surprise, go watch the full thing on YouTube.

The show centered on a system for winning at horse racing, except in fact it wasn't a system at all.  The woman featured in the show was the "winner" of a elaborate brute force attempt to whittle a starting field of over seven thousand runners down to one person who had inevitably backed five winners in a row.

Brown's crew had sent out every possible permutation of tips across five six-horse races to find the one unlikely winner, removing anyone with a losing bet from the pool after each race.  The number of participants required to do and produce one guaranteed winner is six times six times six times six times six, a total of 7,776.

The ten heads video is apparently just a small clip from a nine hour flipathon, although because it's Derren Brown I'm just not sure whether to really believe this.  Don't rule out some some magic coin shenanigans here, although the point he's making is definitely valid: anything can happen, and it will happen eventually.

Here's an example I made earlier.  Am I the luckiest blackjack player in the world because I got dealt this almost-impossible great trio of hands?  It should happen roughly every 85,000 deals.  I've lost count, but I must have played at least that number in the past six months, so it was bound to happen eventually.

The nine hour filming session suggest that their experiment ran a little behind expectation, although not too badly.  Because the outcome is not guaranteed, variance needed to go in their favour to make sure this shoot didn't last several days!

A streak of ten heads should appear once every 1024 flips.  One flip every ten seconds would be just over 3000 over 9 hours, but you have to figure the actual number would be much less than that, allowing for enough breaks to avoid insanity.  He probably tossed the coin 1500-2000 times.

Derren declinesd to mention whether or not they also experienced an equally likely streak of ten tails during this trial, and if so whether it put him and the crew on lifetilt.  I expect it would do.