Quantum Bias

[Boz]

Deleted

[bigplayer]

So I conjecture after about 100 consecutive roulette spins landing on red, there is a 100% chance the next is black or green. Can anyone disprove my theory?

Sure, the fact that a wheel has no memory means that your previous spins of the honest wheel have zero influence on the next spin. If anything 100 consecutive spins of Red on a Roulette Wheel would rule out Green or Black possibly hitting because it would mean your Roulette Wheel is fixed and all of the red and green slots are blocked off.

[Three]

The law of large numbers basically says that 50% of an infinite number of coin flips will be tails. But when is a number 'large'?

You are not understanding the law of large numbers. It doesn't mean that the number of heads and tails will be the same as the number gets excessively large, it means that the difference between the number of heads and tails will become more and more insignificant even if the actual difference gets larger. It is the difference between percentages and actual numbers. Like 4 heads and 6 tails has a 40%/60% distribution but an actual difference of 2 between the two possibilities. If after 1,000,000 tosses you have a difference of 2 it will be 50%/50%. If the difference is 50,000 you have 475,000 heads and 525,000 tails for a 47.5%/52.5% distribution. As you can see the law of large numbers is not driven by the difference between the 2 but by the denominator of the total number of tosses. As the denominator gets large even large differences seem small relative to the denominator.

[Three]

Suppose you flip a coin a million times, and it lands on heads each time. Is there REALLY a 50% chance the next coin flip will be heads?

Yes, if it is a fair coin.

One might argue that before the first flip, it was just as unlikely to get a million heads then a tail than it was to get a million and one heads. But wouldn't that same person have said it was completely impossible to get one million heads in a row?

Not impossible just extremely unlikely 0.5^1,000,000 is such a small number that it is essentially 0 but it is ever so slightly positive.

So I conjecture after about 100 consecutive roulette spins landing on red, there is a 100% chance the next is black or green. Can anyone disprove my theory?

If the wheel has no bias and the guy spinning the ball is random the next spin will be totally independent of previous results.

[DSchles]

"So I conjecture after about 100 consecutive roulette spins landing on red, there is a 100% chance the next is black or green. Can anyone disprove my theory?"

There are three conclusions one could draw about the next decision after 100 consecutive red spins of a roulette wheel: 1) 50-50 chance for red; 2) much greater chance for red: 3) much greater chance for black. The only one of the three that is totally insane is number 3. Placed in this situation, I would bet a fortune on red. Betting black would be patently ridiculous.

Don

[Norm]

Flip a fair coin one trillion times and record the one trillion results. The odds that that particular string of results can occur is exactly the same as the odds that one trillion heads will occur. All possible strings of results have equal probability. And yet, as absurdly unlikely that that particular string could occur, it happened. Because one of the absurdly unlikely strings has to occur.

Unbelievably odd things occur all the time because an unbelievably large number of events occur in the universe every trillionth of a second.

[Freightman]

Flip a fair coin one trillion times and record the one trillion results. The odds that that particular string of results can occur is exactly the same as the odds that one trillion heads will occur. All possible strings of results have equal probability. And yet, as absurdly unlikely that that particular string could occur, it happened. Because one of the absurdly unlikely strings has to occur.

Unbelievably odd things occur all the time because an unbelievably large number of events occur in the universe every trillionth of a second.

And, in our alternate Universe as well.

[Norm]

Maybe in your alternate universe. In mine, I always win.

Wait for my upcoming book: So you want to build an alternate universe.

[Three]

I understand the law, but what is 'large'? The difference between red and black can be 'large', but they can't tend to diverge. Everyone, at some point, wants to add in outside physical bias to explain, but eliminate it--it's not part of the idea. I know what physical bias is--I'm not planning on hitting the roulette tables with my new system. Probability says although it's infinitesimally small, there is a chance a FAIR coin could land on tails 1 trillion times in a row. The law of large numbers says, no, it's going to be a roughly uniform distribution of heads and tails. I see a gap. I object that is even possible to land on one side a trillion times in a row because to observe such an event would cause physical laws, like the law of large numbers, to start breaking down.

To illustrate what I am talking about. If you had a string of 1,000 heads to start with you would still expect the long run to be about 50%. That doesn't mean you are going to get 1,000 excess tails in the next 1,000,000 tosses. It means after enough tosses that initial bias would become insignificant. Let's say in the next 999,000 rounds you get another 1,000 extra heads so you are not correcting the initial bias by the results. But you went from 100% heads after 1,000 rounds and in the next 999,000 rounds you has another 1,000 extra heads for 500,000 heads and 499,000 tails thus doubling the number of excess heads from when you had 1,000 heads in a row to start but the LARGE DENOMINATOR of 1,000,000 made the 2,000 excess heads far less significant. The 1,000,000 trials has 501,000 heads and 499,000 tails for a 50.1%/49.9% distribution despite never having any excess tails to correct the 1,000 straight heads.

How large is large? That depends on variance. The denominator has to be large enough to overcome the variance for the trial.

[Norm]

then we found out about non-local effects that were instantaneous that appear to violate the rules.

IANAP, but I'm not sure that quantum entanglement is actually an example of exceeding the speed of light -- although it's often phrased that way.

[Freightman]

I have lunch every 4-6 weeks with an AP friend of mine. At the end of every lunch, we flip a coin to see who picks up the tab. He got off to a fast start - I then caught up, and the lead has gone back and forth, I would say several times. The momentum has shifted back to me as my friend has now paid the last several tabs. I'm pribably at plus 4 or 5.

Despite this pleasing trend, it would be foolish of me to gloat, for at least several centuries. Despite my superior coin prediction technique, we just simply have not, nor will we ever arrive at the long run. Now, I suppose I could manipulate the outcome by calling heads on a double headed coin - but I won't, since I like the challenge if the unbiased con toss.

[Norm]

As an aside, there was a funny thread years back by a guy that claimed you couldn't trust math because quantum mechanics disproved everything Einstein theorized and proved that math didn't work.

[Norm]

unbiased con toss

Freudian slip?