Naked Science Forum
General Science => General Science => Topic started by: Don_1 on 03/09/2008 11:23:48
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Can anyone explain why the lottery seems to defy the rules of ‘chance’?
Given that there is no difference between the weight of each ball or the surface friction, of the 49 balls there should (if the rules of chance are applied) be roughly the same frequency of being drawn.
So why is ball number 12 (the top hot number) showing a frequency of 22% while, and coincidentally, the same figure in reverse, ball number 21 (the least picked) showing a frequency of 8%?
Other examples of this are:
Ball # 6 = 13%
Ball # 9 = 19%
Ball # 13 = 15%
Ball # 31 = 12%
Ball # 14 = 17%
Ball # 41 = 10%
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Low number statistics gives high error margins.
If the lottery had been played millions of times, instead of a few thousand times, there would be much less variation in these percentages.
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That's right - small sample.
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The only rule of chance is that any result is possible. Although chance predicts equal probability for all balls before the event, an actual result after the event where that occurred would be suspect as it wouldn't be very random at all.
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It's perfectly normal, the deviation of the percentages form a symmetric bell curve. You also expect there to be as many at the high end as at the low end, so the fact that they have the same percentage is not unexpected, but not guaranteed.
The variations will shrink over time though. It's a standard statistical result that if the number of lotteries go up by four, the range of variations will shrink by two (it's a square root law).
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Here I was thinking 7 would be the most picked, why is that designated as the luckiest number anyway?
Then again, 7 has no reverse number.
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Then again, 7 has no reverse number.
What's one of them?
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Why do 'Mugs' buy tickets where on average you get 25% of your money back!
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The interesting fact is that while the balls obey the rules of chance the people that pick which numbers to select do not. Note that the big prizes are based on the total pot of money while the small prizes are fixed values of money. Many years ago there was a lottery where all the prizes were based on a proportion of the pool of money including the small ones so when "unpopular" numbers came up the small prizes were bigger. The mathematics department of a univertsity in the country where the lottery was held worked out that if they did a spread bet on all the unpopular numnbers they could win enough good value small prizes to make a profit in the long run. They worked the lottery and made a profit for quite some time until the organisers realised what was going on and changed the lottery to prevent people from winning this way.
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Don_1
The national lotto does not defy probability chance, take a game of chess the are an almost unbelieving number of outcomes rillions and trillions in fact
The reason the Lotto appears to defy chance is simply due the enormous possible outcomes
C(n, k) = --------------
k! (n – k)!
or
n*(n-1)*(n-2)*(n-3)*...(n-k+1)
C(n, k) = -------------------------------------
1*2*3*...k
n! represents the factorial and is calculated as 1*2*3*4*...*n. For example, the lotto 6/49 game has a total of [49 * 48 * 47 * 46 * 45 * 44] / [1 * 2 * 3 * 4 * 5 * 6] = 13,983,816 combinations
Alan