Anything that can happen will happen?

[LetYouDown]

How can you not factor in infinity when reading the initial post? That's assuming you've read it, however. To say that the probability of winning 3 powerball lotteries in a row is equal to 0 is ignorant. I assume you've never taken calculus or covered any course material dealing with limits?

[SheetWise]

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From OP:Is this correct? Since the probability cannot be reduced 0%, even with 0.0000276% chance of getting 20 reds in a row we will and do get 20 reds in a row. Does it mean that there is even a possibility of 100 reds in a row? Or even 1000 reds in a row?

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How can you not factor in infinity when reading the initial post? That's assuming you've read it, however. To say that the probability of winning 3 powerball lotteries in a row is equal to 0 is ignorant. I assume you've never taken calculus or covered any course material dealing with limits?

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When I read about the probability of unusual and unfortunate events in a "gamblers" forum, I assume it is related to risk tolerance. When you introduce "infinite" trials, you can show that any finite bankroll will come to ruin even in +EV games. This is then "corrected" by introducing the concept of the "infinite bankroll" ...

Siegmund hit the nail on the head.

You think that it makes sense to factor infinity into this problem of 1000 red spins in a series, in a game that at best can produce 100 trials per hour, in an effort to prove that it can and will happen. You then say that it is ignorant to disregard a 1:147,107,962^3 event in a game that provides two trials per week.

I can appreciate the comments in the thread that note these unusual events might happen in the first series of play, but so what? People take risks of greater magnitude all the time, flying, pressing a brake pedal, walking on a sidewalk, etc. Put in perspective, are you suggesting that what we consider to be acceptable risk with our life on a moment to moment basis would be an unacceptable risk with our fortune? Because "it can and will happen"?

Even casinos recognize how unusual the events are from the OP -- that's why they've set limits. They recognize that even their substantial, yet "finite" bankrolls may not survive the non-occurrence of these events.

[LetYouDown]

We're not disagreeing on the likelihood. I interpreted the question literally, as "can and will happen". On a long enough time frame, it will happen. Is it likely? Absolutely not. Will it happen in my lifetime? Probably not. Siegmund, as usual, provided a real life example and interesting/intelligent explanations. It is unfortuante that he doesn't post more often. Probability is often theoretical, and I don't think that discussing the concept of infinity, which factors into every statistics/probability course, is unreasonable. I know where you're coming from with the risk tolerance assessment, but I didn't necessarily infer that from the OP.

[SheetWise]

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Is it likely? Absolutely not. Will it happen in my lifetime? Probably not.

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I suggest that the 2+2 forum coin a term representing a unit to use in describing unusual events. Many lay people use "... as likely as being hit by lightening" as a comparison -- which I find meaningless (I have no reference). Maybe if we used something like a unique nanosecond in an average lifespan or a unique minute in a century. We then call it Big, we can reduce large numbers to X number of Big's. Maybe it would make sense to use a number of game trials (B&M) that a person could experience in a lifetime. I think lifetimes would be something everyone could relate to. Has this been done? Any ideas?

[SheetWise]

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I think lifetimes would be something everyone could relate to. Has this been done? Any ideas?

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I'm reponding to myself. As an example, for a coin flip to come up heads 100 times in a row, we would get 1:1,267,650,600,228,229,401,496,703,205,376. If we defined a roulette lifetime as 60 years of play, 12 hours a day at 100 trials per hour, a roulette lifetime would equal 26,280,000 trials. The 100 in a row sequence could then be reduced to 48,236,324,209,597,770,224,379 lifetimes. I think we would need a bigger number.

Black Swan = term for highly unusual events in finance. coined by Prof Nassim Taleb who wrote the book "Fooled by Randomness".

Hmmmm....

1) According to some who replied, the probability of a black swan occurring can be so low that it doesn't happen in a lifetime.

EXAMPLE:
30 reds in a row in Roulette = 0.000000000176. The chance of this not happening is 99.99999998%. For a trial of 2000 spins, this will probably not happen. For a trail of 10,000,000 spins however, this might happen.

2)On the other hand, some who replied says it is as likely to happen!

EXAMPLE:
30 reds in a row happening = 0.000000000176 and 30 random mixture of reds/blacks happening in a row = 0.000000000176 too! Since the random mixture happens, why not 30 reds in a row when they have the same probability? This tendency to see long strings of identical outcome as "unique" is known as Leptokurtosis i think.

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]

[SheetWise]

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Will the occurance of black swans not contradict probability theory??

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Dear remiraz,

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Will the occurance of black swans not contradict probability theory??

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You are distorting the work of Nassim Taleb [img]/images/graemlins/smile.gif[/img]

Black swan events are a particularity of non-finite (or not completely known) sets. It doesn't apply to poker which is a game with, a large, but finite number of states (its set).

Unless you would consider being dealt AA 100 time in a row, a back swan event. I would not, it is a distinct possibility. In fact, it is AS possible as ANY arbitrary sequences of hole cards being.

[irchans]

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).

[SheetWise]

It's a manageable risk. [img]/images/graemlins/wink.gif[/img]