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Wednesday, October 05, 2011

Things go to hell together

I'm re-reading (listening to) one of my favorite books, The Lost World by Michael Crichton. I've come to a part in the book where the gambler's ruin is mentioned, and I always find the idea just counter-intuitive. Here's a bit from the book ....


Gambler's Ruin was a notorious and much-debated statistical phenomenon that had major consequences both for evolution, and for everyday life. "Let's say you're a gambler," he said. "And you're playing a coin-toss game. Every time the coin comes up heads, you win a dollar. Every time it comes up tails you lose a dollar."


"What happens over time?"

Harding shrugged. "The chances of getting either heads of tails is even. So maybe you win, maybe you lose. But in the end, you'll come out at zero."

"Unfortunately, you don't," Malcolm said. "If you gamble long enough, you'll always lose -- the gambler is always ruined. That's why casinos stay in business. But the question is, what happens over time? What happens in the period before the gambler is finally ruined?"

"Okay," she said. "What happens?"

"If you chart the gambler's fortunes over time, what you find is the gambler wins for a period, or loses for a period. In other words, everything in the world goes in streaks. It's a real phenomenon, and you see it everywhere: in weather, in river flooding, in baseball, in heart rhythms, in stock markets. Once things go bad, they tend to stay bad. Like the old folk saying that bad things come in threes. Complexity theory tells us the folk wisdom is right. Bad things cluster. Things go to hell together. That's the real world."


Why do things go in streaks when there's supposed to be an even chance for them going either way, and if things go to hell together, do they also go to heaven together? :)


Blogger Matthew said...

You're right, and Crichton is wrong, or at least misrepresenting. Sure, in the case where things are truly random (50/50) bad things happen in streaks, but good things happen in streaks too, and furthermore, results alternate in streaks!

The point of the gambler's ruin is not that things go to hell together. It's that the wealth of the gambler will be exhausted long before the wealth of the house. Or put another way, the likelihood of the gambler hitting a streak that bankrupts the house is far higher than the likelihood of the house hitting a streak that bankrupts the gambler.

Crichton grabs the idea of streaks and pins it on his pessimist, but you might as well pin it on an optimist, especially given the complexity of the real world. =)

1:48 PM  
Blogger crystal said...

Hi Matthew,

So, things go in streaks both ways and the casino ultimately wins because it has more resources and can outlast the gambler, but if they had equal resources and could keep playing, it would really be still 50/50?

I like his books because they have a lot of science in them but I have to remind myself that he's the guy who didn't believe in global warming ... he tends to have a bias.

1:59 PM  
Blogger Matthew said...

Yeah, if the odds of the game are 50/50 then that's what should happen /by definition/. Silly Crichton.

7:28 PM  
Blogger Mike L said...

Try this thought: The first toss randomly comes up heads. If 50/50 results follow heads is always one up.

If over some number of tosses tails manage to take the lead, then it will stay in the lead until a sequence with more heads comes about.

Over time the number of heads and tails come closer and closer to being even, but one or the other will be ahead for "streaks".

And even though they tend to even out, over billions of tosses the absolute difference can be quite large.

Wow, I'm am impressed that I can figure that out after being away from statistics for so long.


Mike L

7:45 PM  
Blogger crystal said...

Hi Mike,

Statistics - I believe I failed that in college. This may explain why I still have hopes for the lottery :)

10:35 PM  

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