but what if the coin remembers?
February 15th, 2009If you flip a fair coin and it comes up heads twelve times, what is the probability of it coming up heads the thirteenth time?
Well, you’d tell me, it’s fifty fifty just like the previous twelve flips. And as statistics teachers say all the time, “the coin doesn’t remember that it came up heads twelve times before.” They say each flip is “independent” from one another, and from there on out we base a buttload of the statistics world. (Probably more than a single butt at that).
But what if the coin remembers?
Meaning what if there isn’t independence? What if each time the coin comes up heads the next time it is more likely to come up heads again? So if it comes up heads 99 times, it is very very likely to come up heads for the 100th flip. Doesn’t that change all the rules? And what if when the streak is broken, it goes back to 50-50? It means we can see huge streaks that simply flatten out and die. Or worse we can see several big streaks move in one direction and then precipitously drop. And all this volatility would be normal.
So, moving towards my point, one of the many buttloads reliant on ‘independence’ include to many “real world” situations such as finance, stock prices, economics and forecasting. And what happens to our models when things aren’t independent?
What happens when we have herding? What about network externalities? What about something being cool? For some period of place and time, for every person who buys an iPhone, the next person is slightly more likely to buy an iPhone?
It’s a good idea to diversify when you invest. But exactly how much diversification is there when Asia’s economy is largely dependent on the US economy? It’s really nice that everything is online and it makes life easier. So you keep betting heads and put everything you can online. But what happens when the internet is down or there is a power outage? Is it worth the everyday convenience only to be uber-screwed once in a while? Don’t we get lulled into this false sense of security? Yes, if the coin actually remembers, then every once in a while we get to be unpredicably uber-screwed.
Sounds a bit like what might be what might have happened before this market crash right? False sense of security and prosperity?
**I’m not suggesting this is the sole cause, but I do think a lot of people took hidden risks, or weren’t fully accountable for the risks they were taking.
