"Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails, to balance out."

anomalous events become insignificant because normal events overwhelm them. If heads come up 20 times in a row, heads might continue to be favored in the next 10000 trials. But the percentage of time it is heads will still get lowered to the expected percentage.

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We all know that the trails is independeant (a 50/50 siutution) and all patterns has the same probability.

This means that you can pick any 10 random outcomes and compare them with 10 future outcomes.

Then using the benchmark O for "oppisite" and S for "same" and observe the results.

Simple as that.

Quote:odiousgambitthe statement could lead you to believe it is offering a "valid reason to base your gambling upon" some nonsense, because it simultaneously poo-poos gambler's fallacy but also hints there is something to it. To see that phrase, "average out", too many gamblers imagine that indeed the dice or coins must take action!

anomalous events become insignificant because normal events overwhelm them. If heads come up 20 times in a row, heads might continue to be favored in the next 10000 trials. But the percentage of time it is heads will still get lowered to the expected percentage.

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Quote Mike from other gambling forum:

Regression to the mean does not somehow mean that spins are not independent under some circumstances, so if you have observed an extreme event it does not make it any more likely that the next event will be less extreme. That is, there is no cause and effect operating. The next event, regardless of what has happened previously is unlikely to be extreme only because all extreme events are relatively unlikely, by definition, and that is the only thing that regression to the mean says.

So it is a fallacy, just as much as the gambler's fallacy, to use some extreme event as a trigger, believing that the following event will be less extreme than the first. No computer simulation is necessary to show that using a trigger in this way won't work. Ten reds in the next 10 spins is no more or less likely given that in the previous ten spins there were also ten reds, or ten blacks, or anything in between.

If you look for extreme events in a larger number of spins, say 100 or 200, these will occur as frequently as the normal or binomial distribution says they will, again regardless of what has gone before. So in 100 spins you will get between 45 and 55 reds in 68% of sessions, between 40 and 60 reds in 95% , and between 35 and 65 reds in 99.7%.

Qoute from other gambling forum.

"If a number has appeared 2131 times less than chance would have dictated after 100,000 spins, then it is on target to be still 2131 short of expectation after 1,000,000 spins, or any other huge number of future spins. Fate doesn't dictate that it will regress to the norm in terms of absolute count, only in percentage terms. eg, in your example, instead of appearing 1/38th of the time, or 2.631578947368421%, it instead came out 500/100,000 = 0.5%: It's 2.131578947368421% short, which is way out.But if after 1,000,000 spins it is still 2131 appearances short, then it will have appeared (1,000,000/38 - 2131) = 24184 times: It will have appeared 2.418478947368421% of the time. At 2.418478947368421% It will be closer to the expected 2.63158% and so can be said to be regressing to the mean.Now lets say we spin 1,000,000,000,000 times starting out 2131 appearances short and ending at 2131 short. It would then have appeared (1,000,000,000,000/38 -2131) times = 26315787342 times or 2.6315787342% : It has pretty much regressed almost exactly to the expected appearance frequency, but it is still numerically just as far away.Purely and simply, regressing to the mean does not mean any short term variation gets cancelled out, only that it becomes statistically insignificant in percentage terms.Oh, and just to be controversial 400/infinity = 0 EXACTLY. Not close to, but exactly: That's the nature of infinity." -Wizardofvegas forum

In the end, regression toward the mean appears to happen because the sum of all spins yet to happen dwarf the number of spins that you have collected.

What is described early in the thread is simply part of the gambler's fallacy.

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"Purely and simply, regressing to the mean does not mean any short term variation gets cancelled out, only that it becomes statistically insignificant in percentage terms.[/qoute]

No, that's not correct. Regression to the mean does not mean that - he's talking about the law of large numbers here; that the ratio will approach the mean as you take more samples. Regression to the mean says that if an extreme event occurs, the next event will not be so extreme, it doesn't lump together the two events and say that the combined event will be closer to the mean than the first, although that is a consequence.

If the first event is 10 reds in 50 spins, and the next 50 spins produces 20 reds, then the ratio of reds is 0.2 in the first event and 0.3 for the combined events (20 + 10)/(50 + 50), but it is 0.4 for the 2nd event taken alone.

It is incorrectly applied to independent trials where skill has no effect. There is no regression to the mean in independent trials of games like Roulette. Instead, there is the law of large numbers, which says that the long-term results of a game will tend towards it's mean. But this is only relatively (%), not in magnitude.

So I bet black waiting for the regression to the mean.

It landed on 00.

The next spin which I didn't take landed on black.

Still thinking the ball would regress on me I put my money on black hoping for a streak to compensate for all the reds.

But then at the last second, I figured the ball hates me and would try to fuck me over so I switched it to red.

I had indeed outsmarted the ball. It landed on red the next six times and I made some money adding more and more till I lost on the seventh bet.

BTW - all this is true although deep down I know the ball doesn't think or do anything on purpose.

Like the guy that doesn't double on a 9 because he "always" gets a 2.

Take a picture of the number display next time.Quote:darkozJust yesterday (this is true) I saw a table with 19 reds in a row. On the 20th spin it was black.

So I bet black waiting for the regression to the mean.

It landed on 00.

The next spin which I didn't take landed on black.

Still thinking the ball would regress on me I put my money on black hoping for a streak to compensate for all the reds.

But then at the last second, I figured the ball hates me and would try to fuck me over so I switched it to red.

I had indeed outsmarted the ball. It landed on red the next six times and I made some money adding more and more till I lost on the seventh bet.

BTW - all this is true although deep down I know the ball doesn't think or do anything on purpose.