goldy313 wrote:But that neglects statitiscal independance and therefore is proven false so it's not true odds. Because each flip is independant the previous 1 or 9 flips has no bearing on the next flip. Any gambler can tell you that the probability of of a roulette wheel hitting black or red 4 times in a row is only 5 times out of 100, yet it happens far beyond that probability. In fact after the 3rd red or black the odds that the fourth number will be the same color as the first 3 is 47%.
I'm losing faith in the Minnesota schools. Goldy, this is crazy talk.
neglects statistical independence
Um, no. The reason you take 2 to the whatever power (for the number of coin tosses) is because each event is independent of the others.
therefore is proven false so it's not true odds
The only thing proven here is that you semi paid attention in Statistics class. Your post dances around being correct by using some of the right ideas and jargon, but it's clear you don't understand probability very well.
Because each flip is independent...has no bearing
Ding Ding Ding - we have a winner. The explanation presented assumes the 10 coin tosses are independent of each other.
Any gambler can tell you the probability
Actually, you'll find most gamblers are horrible at calculating odds. If they could they wouldn't play games that have such a pronounced house advantage.
the probability of of a roulette wheel hitting black or red 4 times in a row is only 5 times out of 100, yet it happens far beyond that probability
I can answer this two ways depending on how I read this. #1 - No it doesn't, unless you have a weighted wheel. #2 - If you say black OR red, you've doubled the likelihood so it does in fact happen more than 5 out of 100.
The probability of a spin being black is 18/38 or .4737.
The probability of a spin being red is 18/38 or .4737.
The probability of neither (green) is 2/38 or .0526.
The probability of spinning two reds in a row is .4737^2 = .2244
The probability of spinning three reds in a row is .1063
The probability of spinning four reds in a row is .0504
Where I think you pick up that "it happens far beyond that" is that you will pretty regularly see runs of four of one color in a row. Why? Simple. The likelihood of getting four of one color in a row once you've had a spin double. After that spin to determine if the run we're looking for is red or black (forget green for now), you only need the next three spins to match the first.
If you are looking for the probability that the next four spins will be four of the same color - red OR black - the calculation is as follows:
36/38 * 18/38 * 18/38 * 18/38 = .1007
So you can see how easy it is to feel "it happens far beyond that". Also, let's say you watched 1,000 spin over several hours in a casino. Are their 250 chances for a run of four? No. There actually are 997, or nearly four times as many. There are all sorts of starting points for the next run, not just distinct four spin blocks.
Go to a casino, watch 1,000 spins, and you will see pretty close to 100 runs of four black or red in a row. (To count accurately, you'll need to count a run of five as TWO runs of four, a run of six as THREE runs of four, etc...)
This thread is intended to look at the AA teams in Minnesota and assess their chances of reaching the state tournament. I'm sorry it didn't turn out that way.
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