Anything that can happen will happen?

[ QUOTE ]

3)Finally I present a paradox which might probably be the result of my lack of skill in mathematics. [img]/images/graemlins/tongue.gif[/img]

In a North America Roulette wheel the chance of hitting a Red is about 47.3%. This refers to 473 Reds out of 1000 spins IN THE LONG RUN. (100,000 spins?)

The chance of 100,000 Reds happening in 100,000 spins is a positive number still but very very very small. (0.473^100000) So this could happen.

But if 100,000 Reds occur in 100,000 spins...wouldn't the probability of Reds be 100% instead of 47.3%? The 47.3% dictates that 473 out of 1000 MUST be Red in the LONG RUN. Just like the ~5% house edge dictates that gamblers WILL lose ~5% of their bet in the long run.

Will the occurance of black swans not contradict probability theory?? [img]/images/graemlins/confused.gif[/img]

[/ QUOTE ]

"The 47.3% dictates that 473 out of 1000 MUST be Red in the LONG RUN.", this is only true if by "the long run" you mean an infinite number of spins. Given 100,000 spins, there is no "must" involved, it is only probable that about 473 out of 1000 will be red.

[ QUOTE ]
If there are 10,000,000 spins a day for 1 billion years, then we can expect 49 reds in a row once. Thus I think we can safely say that 60 reds in a row will never occur on this planet (on a fair wheel).

[/ QUOTE ]

anyone here seen one of those before? the look on gamblers betting black and losing all the way must be very amusing. [img]/images/graemlins/grin.gif[/img]

[ QUOTE ]
Thus I think we can safely say that 60 reds in a row will never occur on this planet (on a fair wheel)

[/ QUOTE ]

umm! fooled by randomness!

[see Nassim Nicholas Taleb]

[ QUOTE ]

umm! fooled by randomness!

[see Nassim Nicholas Taleb]

[/ QUOTE ]

60 reds in the row has the same probability as 60 red/black mixed in a row right?

[LetYouDown]

[ QUOTE ]
The 47.3% dictates that 473 out of 1000 MUST be Red in the LONG RUN.

[/ QUOTE ]
No, just that it's extremely likely to work out this way. It is not absolute.

[ QUOTE ]
60 reds in the row has the same probability as 60 red/black mixed in a row right?

[/ QUOTE ]
Any specific color pattern of red/black will have the same odds as another.

Probability tells you that 60 reds in a row is as likely as any other sequence you may posit.

[LetYouDown]

[ QUOTE ]
Probability tells you that 60 reds in a row is as likely as any other sequence you may posit.

[/ QUOTE ]
I posit 60 greens in a row.

nh [img]/images/graemlins/smile.gif[/img]

[magiluke]

[ QUOTE ]
Is it true in probability theory that "anything that can happen will happen"?

[/ QUOTE ]

No.

Let's start with a coin flip example:

You flip a coin until it comes up heads. Heads has a probablilty of .5.
You probably will get heads fairly quickly, but there is nothing that
states that you absolutely will get that heads. There is the possibility that
it could happen in a year. There is the possibility that you will never see it.
Of course these are improbable examples, but they could happen.

It's a little bit easier to understand if you look at the lottery:

Lets say you have a 1/5000000 chance of winning the lottery (I don't know
what the actual odds are, especially since lotteries vary, so I'm arbitrating
it somewhere above the actual chances, I think). You can win the
lottery 5 times in a row, but the chances are (1/5000000)^5, and
that's a very small number. I don't see that every happening, even though
it has the possibility to.

Of course, if you throw that up against infinite
trials, it will happen. But I'm not doing it infinite times. You aren't
doing it infinite times. No one is doing it infinite times. Infinity is
just a concept, and for the purposes of reality, doesn't exist. Only the
arbitrarily large exists.

[ QUOTE ]
Of course, if you throw that up against infinite
trials, it will happen. But I'm not doing it infinite times. You aren't
doing it infinite times. No one is doing it infinite times. Infinity is
just a concept, and for the purposes of reality, doesn't exist. Only the
arbitrarily large exists.

[/ QUOTE ]

Indeed, I am also really concerned with reality... I am just not sure about where it starts, or where I am on this infinite sequence. And to say that my experience will be neccessarily(!) unremarkable, is not taking the real for real [img]/images/graemlins/smile.gif[/img]