Do you know the truth about "the law of averages"

[british bulldog]

Please take part the answers will be given tomorrow.


Right or Wrong?

It is a 50/50 chance that a tossed coin will come down heads, therefore if you go on tossing the coin long enough you will get exactly 50% heads and 50% tails.

If you toss the coin 200 times and it provides 108 heads, the next 200 are likely to provide 108 tails because things have to be evened up in the long run.

 

[Spock]

would throwing a coin 400 times in the air constitute a long run.

 

[Korn]

I'll say WRONG.... it doesn't matter if you flip the coin and it comes up heads 100 times in a row..... the next time you flip it, it still has a 50% chance of being heads again...

GL

 

[Skinar]

Re: Do you know the truth about "the law of averages"

Right or Wrong?

It is a 50/50 chance that a tossed coin will come down heads, therefore if you go on tossing the coin long enough you will get exactly 50% heads and 50% tails.

It's unlikely that you would get EXACTLY 50% on each side unless you have an infinite number of trials. Assuming you had a non-biased coin and have an infinite number of trials then the expectation of a 50/50 split would be 100%. In the case of non-infinite trials the longer you tossed the coin the closer you should be to a 50/50 split.

If you toss the coin 200 times and it provides 108 heads, the next 200 are likely to provide 108 tails because things have to be evened up in the long run.

WRONG. And this is a great point you're making here. The two separate 200 toss trials are unrelated therefore the outcome of the first trial has no impact whatsoever on the second trial.

Did I pass?

 

[OtroPex]

Skinar,

I'd say you passed!

Too bad for the life of me I couldn't remember how to explain
the statisitcs 'rules' - someone obviously remembered...

Now what was that they said about drinking and memory loss?

Ah chit - I forget...."Joven, mas tequila por favor"

 

[Kel]

What are the odds that my statistics class actually came in handy for once?? But yeah, I'm in good ol' Stats class this semester and we just covered this unit. It's 50/50 regardless of past trials. Now if only z-scores, t-scores, confidence intervals and normal approximation to the binomial distrubution would be this easy.

 

[acehistr8]

Please keep in mind this simple rule about dice, roullete, coin flipping etc.

Each event is a seperate and independent event unrelated to the event that came before it.

Just because it comes up red 7 times doesnt mean the next 7 will be black to even out the wheel.

 

[Skinar]

Hey Kel, I wish I was in stats class, or any other class for that matter. I took statistics in 1972. Damn, that's much too long ago. I would still like to lech around campus though and leer at all the pretty young girls, perhaps an Aqualung type just 'sitting on the park bench in shabby clothes' scaring the bejesus out of the nubile coeds. Perhaps I could conduct seminars on 'Sports Gaming and the Internet ' which is my true and only area of expertise - nah, I'm sure the administration would frown on such an idea.

 

[ferdville]

I agree with Korn. Each new toss is not in any way impacted by what happened prior.

 

[british bulldog]

Answers and reasons

Answers and reasons

The answers to both quotes are that each is WRONG.

I posted these same quotes on a UK forum site some six months ago and from 23 responses only 2 or 3 were correct. It makes you wonder why people bet when they dont understand the fundermentals.

In Quote #1 the word "exactly" makes the contention false. If it read the longer you go on tossing the coin the nearer you will get to 50% heads would be a perfectly true statement of fact.

In Quote #2 there is no such thing as a "law of averages" in mathmatics. There is only a "LAW OF GREAT NUMBERS".

In all forms of betting the bettor and the bookmaker deal / trade in odds. Odds are chances and chances are percentages.

If you toss a coin 100 times it is an even chance that you will get less than 56.75% of either heads or tails.
If you toss it 1,000 times it is an even chance that you will get less than 52.133% heads or tails.
If you toss it a million times the odds are that you will not get more than 50.0674% heads or tails. Thus it is perfectly true that the more trials you make of a chance event the nearer the result approaches to the true theoretical probability.

Let me make the difference clear. In 100 tosses it is evens that you will not get more than 56.75% heads or tails, ie: between 44 and 56 heads. In 1,000 tosses it is evens that you will not get more than 52.133% heads or tails, ie: between 479 and 521 heads. Thus on 100 tosses the chances are that you may be only 6 out either side of the theoretical 50/50, but on 1,000 tosses the chances are that you may be 21 out. The percentage probable error is smaller, but the actual numerical probable error is larger. If you go onto a million tosses the odds are that you will get a 50.0674% result, ie: only 0.0674% difference from the true result. But 0.0674% of a million is 674, so your actual numerical result may be as many as 674 out either way. Put these figures side by side and you will recognise the fallacy in the popular idea of the so called "law of averages".

It is actually true that the more tosses you make the more in number, not percentage you are likely to be out from the theoretical 50/50 figure.

JUST THE OPPOSITE OF WHAT MANY PEOPLE THINK.

 

[TheShrimp]

Re: Do you know the truth about "the law of averages"

Right or Wrong?

It is a 50/50 chance that a tossed coin will come down heads, therefore if you go on tossing the coin long enough you will get exactly 50% heads and 50% tails.

This isn't stated that well. As stated, I'd actually say its "RIGHT". In spirit, it's wrong.

If you consider an infinite sequence of coin flips, you actually will have exactly 50% heads and 50% tails an infinite number of times. If you call a head +1, and a tail -1, and keep a running total, you will have an infinite number of "zero crossings", points where you've had an equal number of heads and tails. So in short, it is true to say "if you go on tossing the coin long enough you will get exactly 50% heads and 50% tails". Once it gets there, it can "drift off" again, but it will return if you wait long enough.

The spirit of both questions, however, is that the percentage of heads will converge to 50% even though the absolute number of heads may not be close.

WHAT?

Well, like Bulldog said, you might get 540 heads out of 1000 flips, for a .54, but get 5100 heads out of 10000 for a .51. You've gotten closer percentage-wise in the 10000 flips, even though you're further away (40 vs. 100) from exactly half. And it definitely is an important concept in sports gambling.