Re: Number Due

On Thu, 08 Mar 2007 15:16:49 GMT, "Gregg Cattanach"
<rl3166pls@xxxxxxxxxx> wrote:

basicstrategy777 wrote:
The problem I have with you and your math is this.
If you flip a coin 100 times your math says you could toss 100 heads
in a row. And you would say
something like....'although somewhat remote it is possible to toss 100
heads in a row."

The chance of flipping 100 heads in a row is 1 in 1 followed by 30
zeros. Six billion people (every person on earth) tossing coins 24
hours a day at the rate of 100 tosses every 5 minutes......it would
take a million billion years until someone gets 100 heads in 100
tosses.

IT"S FRIGGIN IMPOSSIBLE...IT WON'T HAPPEN.

That is one of the differences between me and you when it comes to
this stuff.


I see no difference between the two descriptions other than the scale of
what 'somewhat remote' should mean.

Your problem is that when you see 10 heads in a row (wth a fair coin) you're
convinced the 11th toss must have a greater than 50% chance of being tails.

However, it's facinating that you can still calculate the chance of 100
heads in a row. In order to make that calculation you MUST assume the
chance of each toss is 50/50 regardless of the previous results.

Exactly. All of the calculations of probability theory are based on
constant probabilities of the outcomes. For example, the formula for
the standard deviation is:

(p * q * n)^1/2

or the square root of the product of the probability of "success", the
probability of "failure" and the number of trials.

Similarly, my computer program uses a constant probability or set of
probabilities, and it produced a distribution very, very close to the
theoretical one. It is impossible for my computer program to CHANGE
the probabilities. Even if I programmed it to do so, it couldn't
"compensate" across sequences, because as soon as the results of one
144-rolls sequence are output to the file, that memory is
re-initialized to zeros. The program CANNOT look back, any more than
the dice can look back.

How in the name of sense does 777 think that "compensation" occurs?
How are the probabilities, which are simply a function of dice being
manufactured to very, very exacting tolerances so that each side has
an equal chance of ending up on top, changed when some number is
"due"? There has to be some physical cause for this, right?

I will make one more attempt (probably doomed to failure) to explain
how "inundation" works in the long term to obviate the need for any
"compensation" in order for the PERCENTAGES to get very close to
expectation.

Suppose you are having a coin-flipping contest with a friend (assume a
perfectly balanced coin). You get quite lucky and win 15 of the first
20 throws, so you are plus 10. So, you think that your friend is "due"
to win back those 10. Of course, it's possible that will happen.
However, there is no expectation whatsoever that it will. For the next
100 throws, the most likely outcome is still 50-50. This is simply
because there are more ways to arrange 50 Ws and 50 Ls than to arrange
51 Ws and 49 Ls, 52 Ws and 48 Ls or any other. 50-50 is much less
likely than all the other possibilities combined, but more likely than
any other W-L record.

So, after 20 throws, we have:

777 friend 777 W-L
15 5 .750

If you split the next 100, which is the most likely result:

65 55 .542

You keep going for 1000 more, the most likely result being 500-500,
and we find:

565 555 .504

You keep going for another 1000, the most likely result being 500-500,
and we find:

1065 1055 .502

After a million more, 500K each, we find:

1,001,065 1,001,055 .5000024

Although absolutely NO COMPENSATION occurred, the difference in the
percentages is now many places to the right of the decimal point.

Get it?
Cheers,
Alan Shank
.

Relevant Pages

  • Re: Why the cards must have a memory
    ... Probability theory assumes uncertainty, ... This is why I used the "tiny universe" scenario, ... ***it assumes that the probability is heads half the time FROM NOW ... incident in this case being a coin toss). ...
    (rec.gambling.poker)
  • Re: Krigman article about sevens due
    ... You are tossing a fair coin. ... The probability is .5 for heads and .5 for tails. ...
    (rec.gambling.craps)
  • Re: Krigman article about sevens due
    ... You are tossing a fair coin. ... What are the chances of getting exactly what probability ... tails and half heads for this to be true. ...
    (rec.gambling.craps)
  • Re: WHY the cards have a memory
    ... If we keep flipping a coin over and ever, we expect that the ratio # of heads/# of tosses will approach 0.5. ... It never says if I flip a coin 10 times, it "must" come down heads 5 times. ... probability of exactly 5 heads and 5 tails is about .2461. ... As presently understood, the universe ...
    (rec.gambling.poker)
  • Re: WHY the cards have a memory
    ... assumption--- that if you flip a coin, ... up heads, half the time. ... It never says if I flip a coin 10 times, ... probability of exactly 5 heads and 5 tails is about .2461. ...
    (rec.gambling.poker)
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