14 Super Bowl Coin Tosses - Numberphile

The NFC's streak of 14 Super Bowl coin toss wins has come to an end... And they aren't likely to do it again for another 32,766 years.

Dr James Grime attempts to calculate how many years - on average - the NFC will wait to win another 14 in a row.

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Videos by Brady Haran

James Grime's website is http://singingbanana.com/

• Category

  Science & Technology

[chrissydude1]

I can tell you one thing without having to watch this video. I'll only have to wait, at most, 10^10^10^10^10^1.1 years to see this again.

[Taber McFarlin]

I trust numberphile's math of coarse, but I was bored so I made a program that "flipped a coin" (produced one of two values) until it got 14 wins in a row and kept track of how many tries it took. I had it run 10,000,000 times and find the average tries, it usually comes out relativity close to 32,776 :D yay math

[chrissydude1]

Still. That's the max I'll have to wait.

[Matteo Mcdonnell]

Not quite. That was for the very large universe. It will actually happen in

10^10^10^10^2.08

[Nick Malygin]

Well, after second look I realized that the phrase "the probability of winning under 14 occasions in a row in 45 games is equal to 1" is not correct. But I think, you've got the idea. Basically, if each time the team had approx. 87.3% chance to win, then this event would not be unlikely at all. (The future will tell :o) )

[Nick Malygin]

What's about considering the following issue (asymmetric coin?): assuming the probability of winning under 14 occasions in a row in 45 games is equal to 1, find the relation of forces between the two teams, given it is constant with time? In other words, t = 45, but the probability to win (p) is higher than the probability to loose (1-p). The equation would turn: 45 = 46*(1-p) + 47*p*(1-p) + 48*(p^2)*(1-p) +...+ 59*(p^13)*(1-p) + 14*p^14. It can be rewritten as a 14 order polynomial, p=0.87269..

[bugMASTER1337]

10^10^10^10^2.8 for our universe...

[SpringSamurai]

Wrong.

[GrayBlood1331]

I'm confused by the mathematics used by James to find the average time needed to get 3 heads in a row. Can someone point me to a video or something? Thanks.

[radiocativekitty]

This is just for one side. HHH would be winning for whoever called heads, losing for whoever got tails, and vice versa for TTT.

[Matthew Schmirler]

My mistake, I was wrong!

The answer is 2 + 4 + ... + 2 to the power of n