Law of Large Numbers, and being "due".

[peritonlogon]

[ QUOTE ]

This doesn't make any sense to me? In this scenario the gap between your work done and work remaining is continuously growing. In that case over an infinite time span wouldn't that gap approach infinity?

[/ QUOTE ]

Hence, I Hate it, hate it, hate it.

[peritonlogon]

I brought up Cantor sets because it seemed analagous to saying that a streak would reach infinity over an infinte time span. Cantor proves that there are more points between any two points on a line than there are rational integers, meaning some sort of order of infinity. I am drunk now and care not to rehash argument but it is googleable. However Cantor was not able to disprove (or prove) that there are 365 times as many days than years when a single quantity of time is dealt with while reaching infinity. However, when doing calculus one makes many leaps of infite space and logic in order to come out with intelligible results. (eg claiming that an integral is the sum of the "points" under a curve. Newtonians add "as the parallelograms APPROACH zero" to avioid this nonsensicallity(is that a word?)) These leaps of logic are made out of a faith in proportionality, Cantor's proof and many people's understanding of it, go on to "disprove" the same sort of thing that the same people are willing to gloss over for the sake of maintaining proportional areas under curves. No, the time that it would take our hero to write his autobiography and the time it would take to live his life are not equal; it merely, like zeno's paradoxes simply betrays our lack of understanding of infinite sets. We should really refrain from using the term until we understand the concept better, esspecialy since we now have computers that do astronomical calculations. Saying that streaks of a certain nature will go on infinitely if they are tested infinitely just doesn't get at the fact that at the same time there is also infinite number of predictable and acceptable streaks. Which really means that calling something infinite and making a case for something logical to come from it is talking nonsense. After studying Cantor and other theoretical mathematicians one realizes that "infinity" can be a way of saying X=not X and that when this happens one is simply talking nonsense. Which is cool.

[BeerMoney]

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Its not like youll approach even and never get to it.

Aicirt

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The expectation of the average will approach zero as you take a larger sample. Hence, like a limit.

The expectation of the sum will be 50.

(Do you disagree with E(X) = 0 and E(Y) = 0 for future events?)

[jon_1van]

[ QUOTE ]
Its not a limit. The probability that you get 1 fifty times in a row is the exact same as getting -1 fifty times in a row. While this highly unlikely (as is getting 1 fifty times in a row) given a large enough sample size you would expect to see a long string of -1 at some point. So yes, most likely it would take a long time before you got back to even, but it will happen given a large enough sample size. Its not like youll approach even and never get to it.

Aicirt

[/ QUOTE ]

What beer is saying is that once you get a -50 run you shouldn't ever "expect" to get zero. This is because any future experiment you run will have an expectation of 0 ie [(.5 * 1 + .5 *(-1)) * number of coin flips]. So once x = -50 we shouldn't expect to get even.

Now, given a long enough sequence of coin flips we probably will get even because of the ebb and flow of the -1 and 1's. But this is not the same as saying the expeected result of that long sequence of coin flips was positive (enough to make you even).

[BeerMoney]

[ QUOTE ]


2) Clearly, you do not drink enough.

[/ QUOTE ]

Clearly you weren't a witness to my consumption on friday night.

I was TANKED!

[zatoichi]

After 8 to 9 months of reading this forum, a few things are apparent...

You know beer.
You know statistics.
You know poker.
(presumably in that order, but maybe that's not the case)

Have you ever read Ben Crenshaw's book "A Feel For The Game"?

your friendly blind samurai masseuse
(not a thread-jack... off-topic but on topic, distraction with purpose)

[peritonlogon]

For some reason this idea reminds me of mountain climbing in dense forest. It seems like you have try to take two perspectives at once and try to reconcile them, the -50 where I am here and the approaching limit, where I am everywhere.

You're all forgetting that if I've read Ken Warren's new book on coin-tossing, and my opponent is on a bad run, I need to be careful because he's due.

[peritonlogon]

[ QUOTE ]
You're all forgetting that if I've read Ken Warren's new book on coin-tossing, and my opponent is on a bad run, I need to be careful because he's due.

[/ QUOTE ]

Good point, watch out for Beer next month.

[BeerMoney]

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[ QUOTE ]
You're all forgetting that if I've read Ken Warren's new book on coin-tossing, and my opponent is on a bad run, I need to be careful because he's due.

[/ QUOTE ]

Good point, watch out for Beer next month.

[/ QUOTE ]

Ya, since I've been playing like a maniac for the past year, look for me to play like rock next year!