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#33
09-07-2005, 02:48 PM
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Re: Roulette
[ QUOTE ]
[ QUOTE ] put 9/9 and you get 1, which is the same thing as .999999999... I am not talking about rounding. You didn't do well in math class, did you? [/ QUOTE ] wow [/ QUOTE ] Dear god. If I took .9999 and called it 1, that would be rounding. If I take the number .9999999999...(with infinite 9s) and call it 1, I am not rounding because it is the same number. 
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#34
09-07-2005, 02:50 PM
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Re: Roulette
[ QUOTE ]
simply put YOURE WRONG! [/ QUOTE ] Joshman, I don't know if a mathematical proof will satisfy you, but 0.999999... is indeed equal to 1: Assign x the value of 0.99999...: x = 0.9999... Multiply each side of the equation by 10: 10x = 9.9999... Factor out 9.9999... as 9 + 0.9999... 10x = 9 + 0.9999... Since x= 0.9999..., replace 0.9999... in the right hand side of the equation: 10x = 9 + x Subtract x from each side: 9x = 9 Divide each side by 9: x = 1 Since x equals both 1 and 0.9999..., 1 does indeed equal 0.9999....
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#35
09-07-2005, 03:01 PM
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Re: Roulette
Yeah I'm the OP who sucked at math, and couldn't solve the original problem, and then had trouble witht eh answer I was given for a while and even I was taught in 7th grade that 0.99999..... is 1. Think about it, waht would you get if yuo tried to take away 0.000...forever....1 from the number? It just doesn't work because in your mind you are still thinking in finite terms if it worked.
Let this thread die.
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#36
09-07-2005, 05:26 PM
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Re: Roulette
[ QUOTE ]
Would they notice when the ball jumps out and sticks to my groin? [/ QUOTE ] The first couple of times, no one said anything, but after the third time they took me out back and killed me. <font color="white">I got better.</font>
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#37
09-07-2005, 05:43 PM
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Re: Roulette
[ QUOTE ]
if you assume an infinte bankroll you have to be willing to assume and infinte streak of losses. I dont care how small the chance of it happening is, fact is there is still a chance of it happening. Roulette is a game of individual trials meaning that every spin is independant of the last so it is completly possible for a never ending streak of one color to occur. It is an insanely small possiblity but then so is the possiblity of having an infinite bankroll or finding a casion willing to accept an infinite amount of action. [/ QUOTE ] 0.999... = 1. I'm telling you as a mathematician. You can also see the sci.math FAQ. The probability of an unending streak of one color is 0. It is not an insanely small number greater than 0. It is simply equal to 0. Any real number x greater than 0 has the property that 1/x is less than some integer. If you think the probability x is greater than 0, then you should be able to state an integer greater than 1/x, or you are inventing a new theory of probability where probabilities are not real numbers. What is happening is that the infinite bankroll and infinite sequence of bets is a very bad model for what can happen in the real world. Sometimes behaviors are continuous at infinity. Here, they are not. Even though the martingale will succeed with probability 1 with an infinite bankroll, it eventually fails catastrophically when you have any finite bankroll. There are additional conditions you need to satisfy to expect to find continuity at infinity, and those conditions are not satisfied here.
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#38
09-08-2005, 11:49 AM
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Re: Roulette
[ QUOTE ]
Dear god. If I took .9999 and called it 1, that would be rounding. If I take the number .9999999999...(with infinite 9s) and call it 1, I am not rounding because it is the same number. [/ QUOTE ] Correct.
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#39
09-08-2005, 11:56 AM
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Re: Roulette
[ QUOTE ]
The probability of an unending streak of one color is 0. It is not an insanely small number greater than 0. It is simply equal to 0. Any real number x greater than 0 has the property that 1/x is less than some integer. If you think the probability x is greater than 0, then you should be able to state an integer greater than 1/x, or you are inventing a new theory of probability where probabilities are not real numbers. [/ QUOTE ] Assuming you're correct (and as a mathematician, I'm sure you are), it quickly becomes apparent that the logical conclusion is pretty amusing for this discussion: 1)The probability of an endless streak of one color is 0. 2)The probability of an endless streak of one color is the same as the probability of any other specific sequence of colors (for this discussion, we'll ignore the green numbers). 3) Therefore, the probability of any endless sequence of colors is 0. 4) The Martingale will only work as a +EV enterprise with an infinite bankroll and an infinite (or endless) number of spins. 5) However, the endless number of spins can never produce any sequence of colors, as the probability of any such sequence is 0. 6) The probability of the Martingale working with an infinite bankroll is 0. It's been a while since I did this sort of thing in college, so my form is probably a bit off...but I found the conlusions amusing, even if they don't hold weight. [img]/images/graemlins/smile.gif[/img]
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#40
09-08-2005, 01:03 PM
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Re: Roulette
[ QUOTE ]
6) The probability of the Martingale working with an infinite bankroll is 0. [/ QUOTE ] Theory aside, even with a very large bankroll, a Martingale soon bumps up against the house bet limit.
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