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#31
10-25-2005, 10:25 PM
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Re: How do you explain Martingale to someone who doesn\'t understand EV
[ QUOTE ]
If you have to spin the wheel an infinite number of times to get the win, isnt that the same as an infinite number of losses? [/ QUOTE ] That's a good question, and I don't know the answer. Infinity is a very strange number. I think we need to get some of the hard-core math guys on this site to weigh in on this... 
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#32
10-25-2005, 10:29 PM
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Re: How do you explain Martingale to someone who doesn\'t understand EV
You will always hit in a finite time. It may be 2 tries it may be 20 trillion trillion tries, but it will be some finite number. You can't predict where it will stop, but it will be some finite number.
The real martingale fallacy is that it DOES work with all these infinite conditions. People think they can use a large amount of money to approximate infinity, but you can't approximate infinity. A point you may not have realized, but the infinite martingale works for any non-zero event. Even if you were betting on a 100,000 to 1 shot that only paid out 1 to 1 if you hit, it would still work, as the math would all be the same.
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#33
10-25-2005, 10:42 PM
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Another infintity conundrum , is there a math nerd to explain this?
This is something I have though about for years, and when I thought of it in junior high and asked my teacher to explain, she yelled at me for wasting class time.
Say you have a point on a 2 dimensional plane, for the sake of demonstration, let's say on the surface of a table. How many lines could one draw through that plane? Infinite, yes? Okay, now if you were to open it up to all three planes, how many lines could go through that point? An infinite amount. So both of them have a set of an infinite number of lines, BUT the three dimensional example definitely has more. It has all of the lines that the 2 dimensional plane has PLUS all possible lines by using the 3rd dimension. How can this be, where two things have a set of infinite possibilities, but one has more than the other??
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#35
10-28-2005, 06:31 AM
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Re: Another infintity conundrum , is there a math nerd to explain this
Flatline. Take a look at this thread: http://forumserver.twoplustwo.com/sh...&fpart=all
If you dont get it after this, i cant help you.
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#36
10-28-2005, 01:35 PM
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Re: Another infintity conundrum , is there a math nerd to explain this
[ QUOTE ]
Flatline. Take a look at this thread: http://forumserver.twoplustwo.com/sh...&fpart=all If you dont get it after this, i cant help you. [/ QUOTE ] First off, learn how to make a link. Second, in that thread they concede that infinite martingale would work. Did you even read it? For the fourth time, please find the flaw in the above proof or quit posting.
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#37
10-28-2005, 04:16 PM
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Re: Another infintity conundrum , is there a math nerd to explain this
[ QUOTE ]
This is something I have though about for years, and when I thought of it in junior high and asked my teacher to explain, she yelled at me for wasting class time. [/ QUOTE ] She likely didn't know the answer. You don't have to be very good at math to teach it in junior high. [ QUOTE ] How can this be, where two things have a set of infinite possibilities, but one has more than the other?? [/ QUOTE ] Because infinity is not a number, like "1000" is. There are different types of infinity. There are things that are "countably infinite" and things that are "uncountably infinite." For example, there is a countably infinite number of positive integers. There is an uncountably infinite number of real numbers. (Another example like yours: positive integers versus all integers.)
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#38
10-28-2005, 06:25 PM
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Re: Another infintity conundrum , is there a math nerd to explain this
Please explain how the concept of countably and uncountable infinite applies to the lines through the point example.
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#39
10-28-2005, 10:03 PM
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Re: How do you explain Martingale to someone who doesn\'t understand EV
[ QUOTE ]
[ QUOTE ] We can contine this by saying the posibility of infinite money and infinite spins are impossible. [/ QUOTE ] Of course infinite money or spins is impossible. This is all theoretical. [ QUOTE ] You cant make the assumption that infinity is possible on one side, but not by the other. [/ QUOTE ] Please rephrase. What sides are you talking about? [/ QUOTE ] I think he's saying you can't assume infinite money is possible, but then by the same token assume that infinite losses is impossible. They are both equally impossible.
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#40
10-29-2005, 12:41 PM
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Re: Another infintity conundrum , is there a math nerd to explain this
[ QUOTE ]
Please explain how the concept of countably and uncountable infinite applies to the lines through the point example. [/ QUOTE ] I agree it's not really an issue of countable and uncountable. It's just what happens when you square "infinity". Lines in the plane through a point can be definied by a single real number in (0,1] (The slope of the line.) This is equivalent to choosing a positive real number without bound. (If "a" was the % of 360, look at 1/a.) We call this set R+. Lines in space can be defined by 2 angles, we're looking at the size of (R+)^2. Squaring any transcendental number gives you the same transcendental number, so there's the same number of lines in the plane as lines in space. -Sam P.S. I think it's important to mention that the notation we use (which Cantor defined) for these transcendental numbers is that Aleph_0 = |integers|, Aleph_1= |reals|, and so forth. Aleph_i = Aleph_{i-1}^{Aleph_{i-1}}. In other words, when we need higher-order characters, we switch to hebrew. [img]/images/graemlins/smile.gif[/img] 
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