Anything that can happen will happen?

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

Say you're playing Roulette even chances (red/black), the chance of red appearing in a spin is 47.368%.

The chance of getting 10 reds in a row is 0.0568% (0.47368 to the power of 10). The chance of not getting 10 reds in a row is 99.94%.

0.0568/100 x 2000 = 1.136
Therefore, in the long run around 1 string of 10 reds will appear in 2000 rounds of 10 spins each. (sorry martingale players hehe)

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? [img]/images/graemlins/shocked.gif[/img]

[LetYouDown]

Yes. Granted, for some things (100 red in a row), you'll need a huge timeline/# of spins, but it will happen on an infinite timescale. The odds of getting 100 red in a row in the span of a human life, spinning constantly every 30 seconds are still very small...but I assume you're talking about an infinite timescale.

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Does it mean that there is even a possibility of 100 reds in a row? Or even 1000 reds in a row? [img]/images/graemlins/shocked.gif[/img]

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Yes, or 10000, or 100000... etc.

It gets worse: there is as much chance to get such a sequence, beginning from your first observation, as any other specific sequence you may choose.

So you could really start out with a bad beat here [img]/images/graemlins/smile.gif[/img]

Enjoy

MidGe

"Our human race is affected with a chronic underestimation of the possibility of the future straying from the course initially envisioned" - Nassim Nicholas Taleb

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Yes, or 10000, or 100000... etc.

It gets worse: there is as much chance to get such a sequence, beginning from your first observation, as any other specific sequence you may choose.

So you could really start out with a bad beat here [img]/images/graemlins/smile.gif[/img]


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Yes its a perculiar how probability works. A BJ card counter might find the ultimate table that gives him an incredible 5% edge against the house. Yet he run the risk of being wiped out by a long chain of losers right from the start! If he restarts with a fresh pot after that, he still may get wipe out right from the first hand!

Gambling is indeed gambling. [img]/images/graemlins/shocked.gif[/img]

For a martingale player on Roulette even chances, his chances of getting 10 losers in a row is 100% - 99.83% or 0.17%. A 0.17% risk of ruin.

The question is...BJ card counters run about a 1% risk of ruin (just guessing, not sure kekeke) even with a positive edge. Does this mean a card counter is as likely to go broke as a martingale user? Is Professional Gambling a myth? With more than 0.17% risk of ruin we're better off doing martingale (which doesn't work by the way)?? [img]/images/graemlins/confused.gif[/img]

[donkeyradish]

And if a million people (who are immortal) repeatedly shuffle a deck of cards simultanously, eventually there will be a moment where all 1,000,000 of them by co-incidence manage to produce the same order of cards at the same time.

Infinity is not a real concept however - and I don't buy lottery tickets, either

[donkeyradish]

another thing

Suppose you are playing roulette and the numbers come up in this order:

4,12,8,34,12,30,19,5,20,15,7,22,9,3.

You wouldn't think this was anything out of the ordinary, right? It just looks like a typical random selection, doesn't it?

But now calculate how likely it is that this exact sequence shows up ...!!

[img]/images/graemlins/cool.gif[/img]

[LetYouDown]

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But now calculate how likely it is that this exact sequence shows up ...!!

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1/13090925539866773438464

What's your point? The question was answered.

[donkeyradish]

Point being that the questioner appears to believe that some very long sequence of all red numbers is much less likely than some equally long but specific sequence that contains a mixture of reds and blacks.

[OrangeKing]

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For a martingale player on Roulette even chances, his chances of getting 10 losers in a row is 100% - 99.83% or 0.17%. A 0.17% risk of ruin.

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You've way oversimplified risk of ruin. You only have a 0.17% ROR on any 10 spins in a row...but presumably, your goal isn't just to win one unit or go bust. However, when you keep doing this over and over again, you only need to hit that rare event once to go bust..and that "rare" event becomes more and more likely to happen somewhere along the line the more spins you are going to play.

[SheetWise]

I don't believe that anything that can happen will happen. In all games you can define a sequence of events whose probability is so close to zero, the probability can be substituted with zero.

On a regulation PGA golf course, it is possible that a player can shoot an 18. I put that probability at zero. I will offer any odds you want, and include every game played in the world for the next year.