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#121
07-18-2005, 08:06 PM
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Re: A Less Obvious Martingale Fallacy
[ QUOTE ]
drudman -- "Okay, so the pro-Martingalers are arguing that there cannot be an infinite series of losses. The anti-Martingalers are arguing that there can be." No. I think MMMMMMMMMMMM is getting off base with that argument. [/ QUOTE ] Maybe so; I worried about that; off main point at least. Yet can anyone tell me WHY (without just meaning 100% "for all practical intents and purposes") 
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#122
07-18-2005, 08:10 PM
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Re: A Less Obvious Martingale Fallacy
[ QUOTE ]
[ QUOTE ] Special relativity and quantum mechanics as we understand them today state that it is impossible to retrieve any matter from a black hole. Ergo, your chips will be lost forever. [/ QUOTE ] I don't think this is true. I saw something a couple of weeks ago about how Steven Hawking is advancing a theory that black holes actually emit some kind of particle. [/ QUOTE ] Yes, but not chips.
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#123
07-18-2005, 08:16 PM
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Re: A Less Obvious Martingale Fallacy
[ QUOTE ]
[ QUOTE ] Special relativity and quantum mechanics as we understand them today state that it is impossible to retrieve any matter from a black hole. Ergo, your chips will be lost forever. [/ QUOTE ] I don't think this is true. I saw something a couple of weeks ago about how Steven Hawking is advancing a theory that black holes actually emit some kind of particle. [/ QUOTE ] http://en.wikipedia.org/wiki/Black_h...mation_paradox
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#126
07-18-2005, 08:38 PM
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Re: A Less Obvious Martingale Fallacy
If I had an infinite bankroll, couldn't I just buy the casino and play for free?
The more important question is: Why bother playing Roulette if one has an infinite bankroll? If both the player and casino have infinite bankrolls, each finite win/loss no matter how large would be equivalent to zero. That means, neither the player nor the casino has an edge over each other because the bankrolls of either player will not change. However..... if you could lay infinite wagers in an infinite time, the finite wins/losses would become infinite so that at the end of infinite time, the summation of the infinite finite losses by the player would be larger than the summation of infinite finite wins by the player. i.e. the player would have lost infinity. Therefore, the final question is: Does infinity (player bankroll) - infinity (player's losses at the end of infinity if the end of infinity exists) = 0 ? [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] 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#127
07-18-2005, 08:48 PM
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Re: A Less Obvious Martingale Fallacy
[ QUOTE ]
If both the player and casino have infinite bankrolls, each finite win/loss no matter how large would be equivalent to zero. That means, neither the player nor the casino has an edge over each other because the bankrolls of either player will not change. [/ QUOTE ] I mentioned this before, but got no response. What I had said was that in this case, an infinite bankroll defeats all edges. [ QUOTE ] Does infinity (player bankroll) - infinity (player's losses at the end of infinity if the end of infinity exists) = 0 ? [/ QUOTE ] I asked this too. In the form of: Solve for x: infinty - infinity = x x = ?
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#128
07-18-2005, 09:08 PM
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Re: A Less Obvious Martingale Fallacy
[ QUOTE ]
If I had an infinite bankroll, couldn't I just buy the casino and play for free? The more important question is: Why bother playing Roulette if one has an infinite bankroll? If both the player and casino have infinite bankrolls, each finite win/loss no matter how large would be equivalent to zero. That means, neither the player nor the casino has an edge over each other because the bankrolls of either player will not change. However..... if you could lay infinite wagers in an infinite time, the finite wins/losses would become infinite so that at the end of infinite time, the summation of the infinite finite losses by the player would be larger than the summation of infinite finite wins by the player. i.e. the player would have lost infinity. Therefore, the final question is: Does infinity (player bankroll) - infinity (player's losses at the end of infinity if the end of infinity exists) = 0 ? [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] 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[img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [img]/images/graemlins/confused.gif[/img] [/ QUOTE ] This is not the question at hand. It would be a very simple problem if it were simply which value approaches infinity faster, wins or losses. The question is, is it possible for the player to begin a series that will never end in a win. And the answer is no, it is not. I'm officially no longer just playing Devil's Advocate.
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#129
07-18-2005, 09:08 PM
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Re: A Less Obvious Martingale Fallacy
[ QUOTE ]
It is a mathematical fact (which can be proven) that those probabilities are exactly equal to the number 1. So I guess that would be "true one." [/ QUOTE ] OK, well then: wouldn't the loss at the far convergence point also be infinite dollars? As the probability of never getting a win is halved each time as you project the trials into the future, so too is the loss doubled with each projected trial. So if you extend the sequence out far enough to equate the probability of a win to 1.00, you are also enlarging the corresponding loss at that point to infinite money. And that's with a fair coin, not a roulette wheel.
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#130
07-18-2005, 09:20 PM
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Re: A Less Obvious Martingale Fallacy
I really think everyone is starting to totally misunderstand the point.
Forget the betting. The betting doesn't matter. You are betting with funny money. It is just an inconvenience... irrelevant to your goal, which is to complete series. You always win when you complete a series, and every series completes NECESSARILY. Stop thinking about each individual bet, and the terrifically mind-boggling exponentially large amounts of money that are lost on many of them. Your probability of eventually winning a bet, and therefore recouping ALL of that lost money is 1. You can increase the house edge of the bet even. Play Pai Gow Poker if you like. Sic Bo. Let it Ride. Whatever your poison. So long as the house edge is less than 100%, your probability of completing a series is 1. You always complete a series. And you always win when you complete a series. Now that you are looking at it in terms of series, and not in terms of whatever individual bets comprise the series, you realize that you can never ever lose.
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Linear Mode
