[ExI] psi yet again.
Damien Broderick
thespike at satx.rr.com
Tue Jun 29 21:38:03 UTC 2010
On 6/29/2010 4:02 PM, Mike Dougherty wrote:
> I think this is modified the same way 'predictive' analysis of the
> stock market by machines exacerbates instabilities. If the rate is
> 1/1000 and there are 3 psychics the effect may be accumulate to
> 1/(1000^3)
NOT what I'm saying.
Blimey, how hard is this to follow?
You buy a Lotto ticket (I use Australian data from 20 years ago, that's
all I know about) and you cross off 6 of the 45 numbers. (Here I
understand it's typically 6/44 or 6/49, and there are usually extra
supplementary numbers that allow for smaller prizes--but let's ignore
those for the moment).
You mark your first guess. Let us imagine (think of it as a science
fiction story if that steadies your nerves) that there's one chance in
1000 that a psi flash will cross your mind, either confirming your guess
or tempting you to change your guess. You do this five more times, and
submit your entry.
166 of your friends mark their own entries.
One of those 167 entries will contain one extra correct number than it
would without psi.
Does this mean (as I suspect John Clark would have us believe, since he
thinks psi would destroy Lotto) that 1 in 167 bettors will share in the
major prize? Well, no.
Here is the mean chance expectation of the distribution of guesses in
the Tattslotto game I studied:
All 6 correct 1.223 by 10^-7
5 of 6 2.726 by 10^-5
4 of 6 1.365 by 10^-3
Imagine an idealized 6/45 Lotto game in which exactly 8,145,060 people
enter, but each person chooses a different pattern of six numbers. Note
that LOW-scoring Lotto entries win NO prizes, and are therefore
invisible. It's simple to calculate how many people should fail to pick
any winning numbers, how many will get only one right, and so on.
It's all too easy for players to slip to the bottom of the probability
bucket. There's a little less than even money odds of choosing only a
single winning number. Indeed, it turns out that it's slightly easier to
guess one right than none at all, for the chances of getting all your
guesses wrong drops a little, to two in five!
Number right Mean chance expectation Probability - one chance in...
out of 6
6 1 8,145,060.00
5 234 34,807.95
4 11,115 732.80
3 182,780 44.56
2 1,233,765 6.60
1 3,454,542 2.36
0 3,262,623 2.50
Due to the pyramid structure shown above, the great majority of players
will select either 0, 1 or 2 of the 6 winning numbers. Forty percent
will be wrong on every guess; another 42.4 percent will get only one of
the 6 right; and a little over 15 percent will identify two of the 6
right. Added together, these worst outcomes make up nearly 98 percent of
all bets.
And there's very little chance that anyone in those categories could
jump up to the top category when the chance of getting an extra guess
right is only 1 in 1000, even if 10 million or even 100 million entries
are made in a draw.
I leave the rest for your exploration and entertainment.
Damien Broderick
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