Teaching an intelligent guy about a basic statistics concept

[soon2bepro]

A friend of mine who has a decent understanding of statistics believes that since random results will average out in the long run, when there's a variation from the standard, it will tend to go the other way in the future.

For example, he believes that if you flip a coin 10 times and get 10 heads, you're slightly more likely to get a tails next time since 11 heads in a row is very unlikely.

This is an intelligent guy, but I can't get to him on this. I'm not a good teacher.

What approach do you reccomend?

I've tried the "you're adjudicating a mystical power to the coin", the "the past doesn't influence the future in this way", and the "new information about the way things went affects how you project the long term result, so you can't expect to go 100 heads and 100 tails on average for 200 flips after you've gotten 10 heads in a row"; but none of these seem to work.

[tshort]

Your friend is not intelligent.

Edit: So, you take a fair coin and 10 flips in a row are heads. He now can have one of three assumptions:

1) Heads is more likely on the next flip
2) Tails is more likely on the next flip
3) They are equally likely

Ask him why he doesn't think heads is more likely?

[Silent A]

Intelligent people can believe pretty silly things (like the medical doctor I met who insisted that Martingale betting was risk free easy money). The problem is that they tend to have too much of an ego about such things to admit that they're wrong about something so simple.

Some ideas though:
1) ask him to calculate the odds of a fair coin coming up heads once
2) ask him to calculate the odds of it coming up heads twice
3) ask him to calculate the odds of it coming up heads 10 times in a row
4) ask him to calculate the odds of it coming up heads one more time after it has come up heads 10 times in a row
5) ask him to calculate the odds of it coming up heads 11 times in a row

Now see if he applies probability theory consistently as he does this.

[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

[Wyman]

If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.

[Justin A]

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.

[wtfsvi]

[ QUOTE ]
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.

[/ QUOTE ] This is the right answer.

[Phil153]

Bring it down to simple physics, and ask him if the movement of your fingers or the air currents in the room are going to change depending on whether the last throw was heads or tails.