Teaching an intelligent guy about a basic statistics concept

[Silent A]

Just to defend my number theory creds, my discussion with my friend was only in the context of how likely a set of numbers was to be the winning numbers, not the likelihood of having to split. I realized long ago that 1,2,3,4,5,6 could easily be a terrible choice.

I actually find this de-rail to be very interesting. But it's a de-rail so I'll stop there.

[RedManPlus]

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A friend of mine who has a decent understanding of statistics...

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This is not a case of "decent understanding"...
And it's hopeless...
Unless your friend choses to undertake serious study of statistics.

Statistics is not a candy store...
Where "your friends" pick up this or that.

It's a Hard Science...
With laws that seem to be counterintuitive for most people.

But then...
Zero Sum Games would not be immensely profitable for 5% of the players...
If otherwise intelligent people had a clue about statistics.

[Apocalypso]

If he doesn't understand any of the other explanations (which is unlikely), try explaining it in this way. It has worked for me in the past.

1) Ask "What are the odds of 2 heads in a row?" He should answer 0.25. (If he doesn't, just give up)

2) then say:

"You flip a coin. 50% of the time it will come heads. If 0.25 [his figure] is the total chance of two heads in a row, and if X is the chance of it coming heads again, X can be found by

0.25 = 0.5*X

X is 0.5, so the chance of it coming heads is 0.5 and so is the chance of it coming tails IE neither probability has been affected by the prior results. Therefore either the original 1/4 figure is wrong or your assumption that the odds will 'even out' are wrong."

That argument combined with some of the others will work.

[vhawk01]

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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?

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No, it is exactly breakeven.

EDIT: Although in a meaningless way, since infinity/inifinity-1 and so on.

[vhawk01]

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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.

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This is a good point. I had a very good friend who was well trained in math and statistics (he became a chartered accountant in the end). We were talking about lotteries (powerball, 6/49 type). I mentioned that one could just pick numbers 1, 2, 3, 4, 5, 6. His initial reaction was, "that's stupid, what are the chances of that happening?". To which I answered, "just as likely as any other numbers". He had to think about it for a while before he convinced himself that I was right.

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As it turns out, though, picking 1-2-3-4-5-6 is stupid, since you are punished for picking the same numbers as others.

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I would think the exact opposite is true.

[wtfsvi]

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Offer to bet him. Say you'll repeatedly. flip a coin, and every time it comes up five in a row heads or tails, you will bet on the same result for the sixth toss, as long as he gives you 11:10.

At least if you can't convince him you'll make some money.

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[Benholio]

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As it turns out, though, picking 1-2-3-4-5-6 is stupid, since you are punished for picking the same numbers as others.

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I would think the exact opposite is true.

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You think picking the same numbers as others is a benefit, or you think that less than 1 in 14 million numbers picked are 1-2-3-4-5-6? Sure, maybe 99% of people would never pick 1-2-3-4-5-6 for the wrong reason (they think it is not as likely to hit as some random group of numbers), but even so, as long as more than 1 in 14 million of chosen combos are 1-2-3-4-5-6 then you shouldn't play it.

Heck, if you knew that 1 person was playing 1-2-3-4-5-6 and 99 million people were playing random numbers, you are still better off picking a random number.

[Max Raker]

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Your friend is not intelligent.


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LOL. This might be the dumbest thing I have ever read on 2+2. Gauss wasn't 100% sure on this, the only reason you are is beacause somebody told you.

[BlueBear]

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LOL. This might be the dumbest thing I have ever read on 2+2. Gauss wasn't 100% sure on this, the only reason you are is beacause somebody told you.

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This strikes me as odd, was Gauss really uncertain on certain elementary principles of probability? I would very interested if you could elaborate.

[chezlaw]

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LOL. This might be the dumbest thing I have ever read on 2+2. Gauss wasn't 100% sure on this, the only reason you are is beacause somebody told you.

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This strikes me as odd, was Gauss really uncertain on certain elementary principles of probability? I would very interested if you could elaborate.

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Its not any principle of probability. That future coin tosses are independent of past ones is a fact about the world (and may not be true).

The statistical principle only applies once you assume that future coin tosses are independent of past ones.

chez