Law of Large Numbers, and being "due".

[BeerMoney]

Our experiment will be that we flip a FAIR coin N times, and on one side it has -1 and on the other it has a 1. Let x be the sum of the N flips... Let Y be the average of those flips... Both E(x) = 0 , and E(Y) = 0.. That is, in the long run, we expect both to be zero..

Consider if we flip the coin 50 times and all 50 times it is a one! Now, X = 50, and Y = 1. Well, what if we flip the coin another 50 times.. Now, what is E(X) and E(Y)? For those next 50 flips, we still expect both the totaland the average to be zero.. So, When we finish those fifty flips, we still "expect" the total will be 50+0 =50, but we would expect the average to be (50+0)/100 = .5. Same logic, consider if we flipped 999,950 more times... We would expect the total to be x = 50 + 0= 50, and y = (50+0)/1,000,000= .00005.

Point: The average is going to zero AS A LIMIT. However, we don't expect to experience a -50 downswing at somepoint, just because we had a strang occurence of a +50 upswing.

I hope this made sense..

[beta1607]

This is related to you losing for two months right?

Maybe you are not fliping the coin in a way to produce equal results?

[BeerMoney]

[ QUOTE ]
This is related to you losing for two months right?



[/ QUOTE ]

No, not at all. Where did I imply that?

The point is that if you lose, you lose, if you win, you win.. If you have a killer session, you shouldn't expect to get smoked in the next one, or vise versa. I see posts all over the place implying a notion of being due. MEbenhoe made a magazine article talking about earning theoretical $$. Two players with equal rates play for the same time, they both made the same theoretical $$, blah blah blah. No, one made money, the other lost.

With my example, we still expect our total to be 50 over the long hall.. That crazy streak of 50 never goes away, and we expect the total to still be fifty after 1 million trials, although the average will approach zero.

[ QUOTE ]

Maybe you are not fliping the coin in a way to produce equal results?

[/ QUOTE ]

That wasn't the point. The example could have stated that you flip the coin once and observe a "1". The example still holds.

[Bartholow]

What about it?

If this has to do with your downswing, it's true that you shouldn't expect that streaks will come to even each other out. On the other hand, with an infinite amount of time you should expect infinitely long streaks, as strange as that sounds. Or put another way, the best thing for you to do is figure out your observed win rate and standard dev, and use the math to figure out the A)likelihood that you are a winning player B) if you are a winning player, the likelihood that you'd have a streak of this length. It might require some stats work.

[peritonlogon]

[ QUOTE ]
On the other hand, with an infinite amount of time you should expect infinitely long streaks, as strange as that sounds.

[/ QUOTE ]

I hate this argument.... I hate it, I hate it, I hate it.
And I hate Cantor sets too. Like the number of all possitive integers is equal to all prime integers or, for that matter, all perfect integers. (this is not original) so if I start writing my autobiography, and it takes me it takes me a year to write about one day of my life assuming I live forever, at some point I'll finish it. Even though I think I'd get further and further from completion.

I'm trying to believe it, but I can't.

[Bartholow]

I'm not sure I follow you here. I'm somewhat familiar with Cantor sets, but I was really just trying to be practical and mention that streaks in poker can go beyond our ability to measure, but the likelihood decreases very quickly.

[Kaeser]

[ QUOTE ]

I hate this argument.... I hate it, I hate it, I hate it.
And I hate Cantor sets too. Like the number of all possitive integers is equal to all prime integers or, for that matter, all perfect integers. (this is not original) so if I start writing my autobiography, and it takes me it takes me a year to write about one day of my life assuming I live forever, at some point I'll finish it. Even though I think I'd get further and further from completion.

I'm trying to believe it, but I can't.

[/ 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?

A related problem is the race between a rabbit and tortoise where the rabbit runs 10X as fast as the tortoise but the tortoise is given a 1000 yard head start. In the time it takes the rabbit to run 1000 yds. the tortoise has run 100. Then as the rabbit runs 100 the tortoise travels ten. In this case the gap is growing smaller.

[ 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 ]
There are EXACTLY as many days in an infinite period of time as there are years (sounds weird but it's true). So you would "finish" it at the "end" of inifinty. Except infinity never ends, so you never finish.

[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.

[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.