Statistics 101

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Maybe if we knew more about life and the unviverse and everything (42) we might understand how playing the lotto can result in a 1-1 chance of winning, before we play.

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We know that there ISN'T - unless you cheat and rig the game somehow. Unless you knwo the number in advance the only 1:1 odds is the probability that you have the right number given that you have the right number. A trivial result of no significance.So my answers still stand. Unless you are claiming that the game was rigged in your favour you are wrong.

Make it up?Isn't obvious that time must pass in order to have a second choice?I understand what your saying, that time is not part of the equation in figuring out probabilities, but I am telling you the whole thing doesn't happen at the same time. Sort of if, then statement.

Are you saying that if we knew all the factors, and forces involved in a coin toss, that we couldn't predict which side it will land on?Doesn't knowing that information increase your odds, and it no longer is 50-50?Just like monty hall, if we knew all the factors that went into deciding which door the car might be behind, we might find out, that it is not truely random.After all, ask yourself, just why do certain lotto balls come up more than others?Say your to predict the outcome of a 100 coin tosses. Crash said there was a 7.5% chance that you might actually get 50-50, after 100 tosses. So you start betting heads. After 50 coin tosses, Tails comes up 30 times, should you then stay on heads, or switch to tails?
If your probability is always 1-2, then why even bother?

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Isn't obvious that time must pass in order to have a second choice?

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Isn't it obvious that the important thing is getting a second choice AND THE INFORMATION needed to make a better choice ?Time IN ITSELF is not a factor. Just as I said.Do you agree that waiting any length of time - no matter how long -would make no difference if there was no second choice ? Or if the information available to you didn't change ?If you agree you're wasting time repeating a trivial and irrelevant point.If you disagree you're wasting time by not actually saying so.So stop wasting time and say something relevant.

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Are you saying that if we knew all the factors, and forces involved in a coin toss, that we couldn't predict which side it will land on?

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If you knew them all to a very unlikely - practically impossible - degree of precision you coudl redict it.But of course that isn't the issue, is it ? You're not claiming to have calculated the lottery result in advance.

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After all, ask yourself, just why do certain lotto balls come up more than others?

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I don't need to. Probabiltiy theory says that that is expected to happen. If it didn't happen - if every ball came up exactly the same number of times - then I would be very suspicious. It would indicate that there was a non-chance factor at work.

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you start betting heads. After 50 coin tosses, Tails comes up 30 times, should you then stay on heads, or switch to tails?

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Without doing the maths it sounds like there is a significant bias there. But it's more likely to be a bias against you - i.e. the guy tossing the coin is cheating. In which case switching to tails will just make heads come up more often.

I did back in post in post 182, I guess you choose to ignore it, and still try to explain to me what I already understand.

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I understand what your saying, that time is not part of the equation in figuring out probabilities,

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Practically, but not impossible. One day it may be simple to do. No, I am not saying, or have I said that. If you win the lotto, your odds were 1-1, it's a proven fact. You or I just do not know the formula for calculating those odds before the fact. But it happened, so there must be some way of detecting it.Let me ask you this, is there anything truely random?Even the balls in the lotto machine, if we knew enough (or if we were God) we could predict the outcome based on the weight of the balls, the wind turbulence, the fluxuation in hertz dictating motor speed of the blower, the paint on the balls, the time in which the button was pressed, etc.There are whole web-sites, and programs that you can buy that dedicate themselves to try and figure out what number will come up, or which numbers are most likely to come up. Is it all poppy-cock? Many people play the lotto by looking at old numbers, and trying to figure out the new number.For instance, would you play the combination 1-2-3-4-5-6 ?
No because you can look at all the old numbers, and see that that many numbers in succesion have never came out. Sure the way you calculate odds will tell you that there is an equal probability that they can come out like that, yet, you (most normal people) would never go and play that combination. Are you denying that after 50 tosses, that tails could come up 30 out of the 50? How can that be considered bias? Maybe you mis-understood the problem.Ask you another question, is there anyway to program a computer to flip a coin, and have the outcome be 100% genuinly random?Edited by riVeRraT, : No reason given.

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I did back in post in post 182, I guess you choose to ignore it, and still try to explain to me what I already understand.

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No, I didn't choose to ignore it. If you really understand that the passage of time in itself is not relevant then why do you keep repeating the same irrelevant and trivial resposne that nobody disagrees with ?

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Practically, but not impossible. One day it may be simple to do.

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I'd say that it isn't simple at all.

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No, I am not saying, or have I said that. If you win the lotto, your odds were 1-1, it's a proven fact. You or I just do not know the formula for calculating those odds before the fact. But it happened, so there must be some way of detecting it.

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But you're wrong, we do know the odds - and they AREN'T 1:1. In the lottery Crash referred to it is 146 million to one. The only way for the odds to be 1:1 is if the game is rigged in your favour.

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Even the balls in the lotto machine, if we knew enough (or if we were God) we could predict the outcome based on the weight of the balls, the wind turbulence, the fluxuation in hertz dictating motor speed of the blower, the paint on the balls, the time in which the button was pressed, etc.

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In principle, but in reality it isn't possible and a probabilistic model is the best practical description.

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For instance, would you play the combination 1-2-3-4-5-6 ?

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The only sensible way to choose a combination is to pick one that other people won't. If you do get lucky you're less liekly to have to share. Anything else is junk - it won't improve your odds at all.

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Are you denying that after 50 tosses, that tails could come up 30 out of the 50? How can that be considered bias? Maybe you mis-understood the problem.

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If there is any factor causing the coin to come up tails more often than heads then that IS bias. That is the DEFINITION of statistical bias. It could happen by chance and I'd have to do the math to work out the odds. Maybe my guess is wrong and it is quite likely.

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Ask you another question, is there anyway to program a computer to flip a coin, and have the outcome be 100% genuinly random?

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Not in the sense you seem to mean. Computers are MEANT to behave deterministically. YOu'd need special hardware to get it truly random.

This is a good question because this is the kind of thing statisticians deal with on a regular basis.When we say that a fair coin, flipped fairly, returns 50/50 odds on average, it's just that - an average. A given set of flips will deviate from that average, just based on random chance. The more you flip, the less deviation. (Obviously the trivial case is a single flip, which has to come up either heads or tails, in which case the ratio is 100% to 0%. And it wouldn't be unusual for two or even three flips to come up heads every time.)Statistics allows us to perform a "chi-square" test that compares the outcome we've measured against the outcome we would expect from chance. More than that, it tells us the odds of seeing our results if we assumed the results are determined by chance. If those odds are below a certain value we reasonably conclude that the results are most likely not due to chance.In your example? 30 tails out of 50 flips? I calculate that there's less than a 5% chance that you're dealing with a biased or unfair coin. (Check my math - chi-square value ~1.0101, significance threshold at 5% level and 1 degree of freedom would be ~3.84, 1.01 < 3.84, thus the null hypothesis is not rejected.)

The only reason to not play that combination is because so many people already play those numbers and you would end up splitting the prize-money, should you win, with thousands of others.If you think there is any other reason not to play those numbers, you do not understand probability - neither theoretically nor practically.

Another great question. This has consequences in cryptography, for instance.As you might have guessed it's very difficult to get truly random output from a deterministic computer. While all computers have routines to develop pseudorandom sequences (which are statistically indistinguishable from random output, but are deterministically generated by algorithm) computer scientists have to get... creative to generate truly random output.One memorable technique I remember, used at (I think) SGI, was to point a simple webcam at a lava lamp and hash the data a couple of times. But every technique I've heard relies on some external physical source of chaotic activity - bubbling wax in a lava lamp, boiling water, Geiger counter activity, etc. It's not possible to develop truly random output by pure algorithm. This is true by definition.

Hi Riverrat,I think you're confused about statistics. Even if you won the lotto, your a priori probability of winning does not change to 1. It's still 1 in some large number.Also, there is no reason that the sequence 1-2-3-4-5-6 has any less odds of coming out than any other 6-digit sequence. Do you think that after 1-2-3-4-5 come out, ball number 6 says to itself "Hey, 1-2-3-4-5 just came out, and since that sequence means something to humans, I better try my best not to be picked?" Of course not.

Because time is a factor. The amount of time is not. Both events cannot happen at the same time. They are two different events, the first choice, and the second one. Pretty simple, do deny it, is to deny life.