Teaching an intelligent guy about a basic statistics concept

[chezlaw]

Its not really about statistics. Does your friend believe the coin or the universe keeps track of past results in a way that influences future results?

If he doesn't then he must immediately realise that he must be wrong. If he does believe the above then only experiments can hope to persuade him otherwise.

I'd guess his just confused about regressing to the mean. Pointing out to him that that doesn't mean 'making up' for the past but just means that the long term swamps the short term.

chez

[m_the0ry]

I read through your post and your arguments matched up almost exactly with what I would have said to your friend in your same position.

He does not understand statistics. Or probability, if this is actually how he feels.

[ncray]

Please. Your friend is wrong. If you flip a coin, get heads and flip it again, everybody knows you're more likely to get heads.

http://www-stat.stanford.edu/~susan/...headswithJ.pdf

[CrayZee]

That sounds like a classic example of what's known as the "Gambler's Fallacy". If s/he is smart, s/he should be able to figure that out on his/her own.

S/he basically doesn't understand independent random events. This is an elementary concept and sounds like s/he doesn't truly have a grasp of probability and statistics. So I'd be skeptical of the "decent understanding of statistics" assumption you're making of your friend. No biggie, this is the sort of thing where human intuition doesn't serve us very well.

[AquaSwing]

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http://www-stat.stanford.edu/~susan/...headswithJ.pdf

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To quote John McClane

"[censored] Calfornia"

Also, on the Martingale crap. Isn't it profitable- given no betting limit and an unlimited bankroll?

[Silent A]

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Also, on the Martingale crap. Isn't it profitable- given no betting limit and an unlimited bankroll?

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He was talking about using it in a real casino with a real bankroll. Actually, I don't think he had a concept of "bankroll" since he just assumed it couldn't fail.

[PantsOnFire]

I didn't read all the posts here so I apologize if this has already been brought up.

You are going to do a trial of 1000 coin flips of a fair coin. The statitiscal prediction is that there will be 500 each of heads and tails.

After 100 tosses, somehow heads has come up 100 times in a row. Using those results we now can recalculate that at the end of the trial, we now expect that there will be 450 tails and 550 heads.

The same concept can be applied to poker. Say you are a breakeven player and you start with a big bankroll. In the last year you have been very lucky and are up $5000. Even though you are a breakeven player, your total life winnings are now predicted to be $5000. You cannot expect bad luck over that time to bring you back to even since you are a breakeven player.

Your friend may be thinking along these lines in that over the course of those last 900 flips, we can't expect tails to "catch up" and reach the orginally predicted 500.

[blah_blah]

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S/he basically doesn't understand independent random events. This is an elementary concept and sounds like s/he doesn't truly have a grasp of probability and statistics. So I'd be skeptical of the "decent understanding of statistics" assumption you're making of your friend. No biggie, this is the sort of thing where human intuition doesn't serve us very well.

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imo the problem is that people don't understand what it means for events to even out in the long run. what the large law of numbers really says is that if you flip fair coins, the number of heads you get in n tosses is n/2 PLUS an error term that goes to infinity slower than sqrt(n).

[CrayZee]

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imo the problem is that people don't understand what it means for events to even out in the long run. what the large law of numbers really says is that if you flip fair coins, the number of heads you get in n tosses is n/2 PLUS an error term that goes to infinity slower than sqrt(n).

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I think a simpler explanation is that people naturally want things to "even out" in the short term rather than the long term. "Infinite discrete distributions" is kinduva hard thing to understand.

Usually, the explanation of "each individual coin flip is even money" for either heads or tails assuming an unbiased/fair coin...and that T-T-T-T-T-T-T-T-T-T is as likely for a "random walk" as, say, H-T-T-H-T-T-H-T-H-H. All tails just looks funny; we are pattern recognizing machines after all, oftentimes regardless of any value in meaning.

Now where's my grilled cheese w/ the Virgin Mary on it? I'm hungry.

[tshort]

Soon2bepro,

What math classes has this guy taken?

If you express the ratio of heads to tails as an infinite sequence you can show the addition or deletion of a any finite number of terms to the sequence won't change it's convergence (to .5).