Well I think my post makes my point clear. The terms of the game are not if AT ANY point they are even, it is if they are even at the END of some fixed number of trials. So we were in fact not talking about the same thing and it appears we don't disagree at all. Because I am not taking the bet you are offering and you are not taking the one I am offering.

Although I quoted Bugs, I was also referring to the OP's use of the term "even out" (both were posted in between my prior post, I just didn't quote them both).

I went to the doctor yesterday.

He told me "I've got good news and bad. The bad news is that nine out of ten people with your condition die. The good news is the last nine people I treated died, so you should be fine."

The good news is you should be able to make some money betting with that doctor before you die.

However, it's really good news if nine out of ten people with your condition die, because ten out of ten people without your condition die.

yes if we isolate each incident and put them in a sequence it is very possible this could happen. Odds are based on infinite attempts...any finite attempts will deviate somewhat from exact odds.

You are only basing that observation on the fact that everyone who previously died, has died. Remember, there are 6bn people on earth right now who may not die.

I'm betting on Aaron.

"Ha"

Nice one. I actually did audibly laugh somewhat, hence the "ha" above.

Perhaps if anyone is really stubborn and refuses to die Aaron intends to make sure that they do!
So am I - I wouldn't like to get on Aaron's bad side.

That's like when you ask the doctor if you will be able to dance after the operation. He says sure you will be able to dance. Then you say great because I can't dance now.

No human being alive today will live forever regardless of advancements because forever is as long as universe allows you and this is still finite time plus realistically even if you could extend past 115 easily we are far from full control of biological regeneration of everything including brain cells and you still would have had accidents as possibilities eventually.

It is however possible in the next 100 years not only to extend lifespan of anyone that is selected for this to over 200 years but to finally have a way to travel close to the speed of light with some amazing technology that exploits vacuum energy or something entirely creative like that which doesnt tax local resources to insane levels, enabling time travel forward that could be millions of years.

Oh what a paradox this is really for future. I mean nomatter what technology we create we could still do better soon thereafter so any such trip is still at the mercy of the others left behind to even stop it at some point lol...or alter its ...future.

Wow!

From a simple coin toss to biological regeneration to time travel to immortality.

Right! Next comes http://en.wikipedia.org/wiki/Doomsday_argument

Dooomsday Argument - "There is a 95% chance of extinction within 9,120 years."

That's not going to bother me as I only plan to live for another 9,100 years.

The side facing up during a coin toss has a 2% advantage. It's not 50/50.

In any case instances of probability are based on incredibly large sample sizes. So as n -iterations approach infinity AA will hold up ~80%. But infinity is a long time coming...

No, it doesn't take a large sample for your example to converge to expectation. With just 2300 trials, the chance for an 80% event to happen less than 78% or more than 82%, is less than 1% of the time.

With 4000 trials the chance is less than 1/10th of 1%. With 5750 trials the chance is less than 1/100th of 1%. With 7500 trials the chance is less than 1/1000th of 1%. It converges pretty rapidly.

This doesn't change the point I made in post #20 however, in answering the title question with No.

It converges pretty rapidly to within 2%. It doesn't converge very rapidly to within 0.5% or to within 0.1%. The convergence for a given probability slows down with the square of how close you want it. For 0.5%, it takes 57600 for 3 standard deviations (0.27%). For 0.1%, it takes 1.44 million. The number n you need for a given number of standard deviations s and accuracy a when your chance of winning is p is

n = p*(1-p)*(s/a)^2.

I simply did the below. I don't see anything wrong. It's the chance to get at most 78% (or at least 82%) on an 80% event.

binomdist(2300,.78*2300,.80,true) = .9%
binomdist(4000,.78*4000,.80,true) = .09%
binomdist(5750,.78*5750,.80,true) = .009%
binomdist(7600,.78*7600,.80,true) = .0009%

I was talking about getting 79.5% to 80.5% or 79.9% to 80.1%.

Understood, thanks.

Try this exercise for study. After a number of n flips how many visits to the origin do you expect (avg)? That will illuminate the process. In 3 dimensions its not even a given that it will happen eventually (eg random walk +-1 in each axis). In 2 and 1 it will eventually.

. It could if something acted on the coin otherwise there is no potiental