Comments on: Super Bowl coin toss rigged like online poker

By: luckydonut

luckydonut — Wed, 10 Feb 2010 14:17:21 +0000

I get a similar answer an easier way The streak could have started (or ended) on 32 possible Super Bowls (this year’s was XLIV = 44), 4096/32 is 128 so that’s 127-1. Powers of 2 are nice. Would be 131-1 with 31 games, LOL rounding error-aments.

By: Geoff

Geoff — Wed, 10 Feb 2010 13:28:05 +0000

Then again, the question should really be, what are the chances of there being a sequence of 13 in 43 tosses (the number of superbowls). I’m pretty sure that that’s significantly less than 2000:1

Given odds of a particular event = 1/2, odds of a run of 13 events is (1/2)^12, or 1/4096; however, given 31 sequences of 13 flips, that means you have odds of (4095/4096)^31, or just under 99.25%, of the sequence _not_ occurring in the 43 flips.

So I make that just over .75%, or about 132:1.

Does that sound right?

By: Geoff

Geoff — Wed, 10 Feb 2010 13:09:18 +0000

It’s human nature to spot patterns in random events. AIUI that’s because we evolved to connect causes and effects as a survival mechanism – there’s a big rumbling sound getting louder and coming from that mountain -> run away fast &c &c.

There’s something similar in the treatment of anxiety attacks, ISTR they call it something like negative reinforcement theory – “today I got out of the left side of the bed and cracked my head on the door, and I didn’t have an attack” becomes the ritualistic “if I don’t bash my head against the door after getting out of bed on the left side I’ll have a panic attack”.

Of course consciously it’s a ridiculous notion but this stuff is all hardwired deep into the subconscious. And the worst thing is it becomes self-fulfilling so in a way it’s true.

I won’t get started on religion or alternative medicines….