Re: Question for Alan Shank...or others

On Sun, 2 Apr 2006 23:34:47 -0500, jbkbub@xxxxxxxxx (John Kerr) wrote:


Re: Question for Alan Shank...or others

Group: rec.gambling.craps Date: Sun, Apr 2, 2006, 4:54pm (CDT-2) From:
ACDOCACDOC@xxxxxxxxx (ACDOC)
That's easy, you usually use a confidence interval of 2 Standard
deviations, or the 95% confidence range. p=q=1/2, n= # of trials.
So if your difference in the # of wins vs losses is within 2X (Sqr root
of p x q x n) or 2 standard deviations, then you have no issues. So for
1000 trials, that's within a difference of 31.6. For 2000 trials that's
within a difference of 44.7.
For both your examples, the results are suspicious. If it was a coin, it
is possibly biased.
Why are we examining "coin flips" on a craps site?
=======
Thanks, I was getting close to that conclusion, just didn't know the
confidence level. I am not talking about a coin flip in this particular
instance....and for my purposes, it is related to craps. Thanks
again.....

ACDOC's answer is rather simplistic, not surprisingly. The confidence
level to use if UP TO YOU. You have to decide for yourself what
probability of reaching an erroneous conclusion you are willing to
accept. How sure do you have to be before you challenge the honesty of
the other player, or the "fairness" of the coin or dice?

The whole idea of "confidence level" is based on the probability,
given a theoretical probability and a number of trials, that the
observed result could result from chance. This is the same way they
evaluated the ESP experiments at Duke University.

So, once you have the standard deviation, you can calculate the
probability of the actual result occurring by chance.

Here's your original situation:

"Example: after 1,000 trials, betting one unit per trial, they were up
+40 units, after 2,000, they were up +80, and so on. Where does
suspicion enter ? Where does something's wrong enter? Where does, that
ain't Right enter?"

If they were up 40 units, that would be 520 wins vs. 480, so the
difference between expectation and actual would be 20. The SD is (.5 *
..5 * 1000)^.5, or 15.8, so the difference is really only 1.26 SD,
which is associated with a probability of about .11.

For 2000, up 80 (difference of 40 from expectation), the SD is 22.36,
so the result is 1.79 SD from expectation, associated with a
probability of .0367, or odds of about 26-1 against. This means that
if you examined 27 parallel universes, you would expect these results
in one of them.

Finally, the 2 SD = 95% confidence level ACDOC quotes is for a
"two-tailed" test, because +2 SD has a probability of .0228 and -2 SD
has a probability of .0228, summing to .0456, so it's really a
confidence level of 95.44% However, since you suspect the probability
of your opponent winning is HIGHER than yours, you are really
interested in a one-tailed test, i.e. you are interested in the
probability of your opponent winning MORE than you, not LESS.
Cheers,
Alan Shank

.

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