Anything that can happen will happen?

[LetYouDown]

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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.

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For a year? No. That wasn't the question. Add in the fact that we were referring to things that have a predetermined probability > 0, and there you have it.

Infinity is like...a totally big number.

[SheetWise]

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Add in the fact that we were referring to things that have a predetermined probability > 0, and there you have it.

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I don't understand. A player taking a shot at a golf hole has a probability > 0 of hitting the shot into the cup.

If you want another example that can be calculated -- I think the probability of you picking the six numbers (single pick) that win the Powerball Lottery in three consecutive draws is zero. (Actual 1:[147,107,962^3])

[Siegmund]

Our minds tend not to be well-equipped for the astronomical and the infinitesimal. Unusual things happen when both of these factors come into play.

Returning to the original question: yes, given a sufficiently large number of trials, anything that can happen with positive probability on one trial will eventually happen. On the other hand, given any fixed number of trials, you can find events so fantastically rare that it is almost impossible for them to occur within that time frame.

To take your golf example - at least on a short enough course that reaching the green in one shot is physically possible on every hole, there is some positive but small probability of a series of aces happening. (Say 1 in 1000 per hole, for the sake of argument - published estimates for pros on short holes range from 1500:1 to 4000:1. Less for amateurs or on long holes of course.)

Two consecutive holes in one is literally a one in a million (or one in a few million) chance, something you expect to make the news when it happens, but something you can expect to happen somewhere in the world reasonably often. A quick google search reveals it has indeed happened several times. There is argument about whether three in a row has ever happened. That's getting down to once in a lifetime or once in several lifetimes chances, but still not 'impossible'.

In real-life terms, bucking 1 in 10^54 or more odds to hit 18 in a row is getting up to the range where it takes an entire universe full of golfers playing for eons before it will ever happen. As long as you are talking about golf, you can call that "impossible" safely.

On the other hand, imagine you are interested in collisions between air molecules - interested in two particular types of collisions at very specific angles and speeds, so that collisions meeting your requirements happen exactly as often as winning Powerball 3 times in a row (1 in 3x10^24) or as hitting 18 holes in one (call it 1 in 10^54 for this example - but maybe really as bad as 1 in 10^70.)

At the pressures and temperatures at the surface of the earth, each molecule in the air bumps in to another one about 2 billion times a second. In just the bottom-most kilometer of the Earth's atmosphere, there are about 3.5x10^43 molecules bouncing around. The "as rare as eighteen consecutive holes in one" event, then, happens somewhere near the surface of the earth an average of once every couple minutes. The "3 in a row Powerball Winner" rare event happens about 10,000 times per second in every cubic centimeter of air, not so rare at all when compared with some of the things they build detectors for in particle physics.

I guess my point is that "rare" is a relative term. There are things you will see only a few times, things you are unlikely to ever see, things that noone is likely to ever see, things that are unlikely to have happened anywhere in the universe since the beginning of time.

[LetYouDown]

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I think the probability of you picking the six numbers (single pick) that win the Powerball Lottery in three consecutive draws is zero. (Actual 1:[147,107,962^3])

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But you're wrong. Infinity * (any number > 0) = Infinity. The golf course question is debatable, but only in that there are physical limitations. It's impossible to hit a golf ball 600+ yards with current physical standards.

[cwes]

The really funny thing is: If you spin a roulette wheel infinite times, there will be red streaks, black streaks and even green streaks of infinite length [img]/images/graemlins/crazy.gif[/img]

[SheetWise]

Excellent post. I'm really starting to hate these threads that contain the words "if" and "infinite".

[LetYouDown]

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Excellent post. I'm really starting to hate these threads that contain the words "if" and "infinite".

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Then don't debate them? LOL, in all likelihood, golf won't exist in its present form long enough for the stated example to even be a possibility. This entire thread revolves around infinity...if you're not a fan, there's no need to reply.

[Dan Mezick]

If you gamble, you dont need to know this.

If you gamble WITH the odds, however, you need to accept the axiom that "anything that can happen will happen".

Traders call these events "shock events". For example an accounting scandal news release results in a 35% haircut on share value, gapping the stock lower on the open. That's a shock event.

The only way to protect from shocks is to limit your maximum bet size, such that Risk of Ruin (which cannot be 100% eliminated,) is acceptable to the trader.

Accepting the risk that anything can happen and playing accordingly is taking responsibility for all your results.

[SheetWise]

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I'm really starting to hate these threads that contain the words "if" and "infinite".

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Then don't debate them? LOL ... This entire thread revolves around infinity...if you're not a fan, there's no need to reply.

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Actually, LetYouDown, the OP did not mention infinity ... you introduced it. The OP mentioned a color on a roulette wheel occuring 100, 500, 1000 times -- that's a question that can be put into perspective using lifetimes. The constant need of some posters to introduce infinity into every problem is amusing. The concept of infinity totally ignores risk tolerance.

[bobman0330]

Choosing .5 from the interval [0,1] can happen, but will not happen over an infinite number of trials. Correct?