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#1
06-03-2007, 12:35 AM
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Clarifying The Bent Coin Problem
I want to make sure I understand the other side. Am I right to assume they disagree with the following statement:
Someone is offering you 11-10 on a flip of a fair coin. Or alternatively 12-10 on the flip of a bent coin you can't see. You call the flip and your adversary is unaware of any bias on your part toward calling heads or tails. There is no justification for choosing to bet on the fair coin. 
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#3
06-03-2007, 01:33 AM
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Re: Clarifying The Bent Coin Problem
Bent coin with unknown bias =: shuffled deck with unknown stack.
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#6
06-03-2007, 12:24 PM
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Re: Clarifying The Bent Coin Problem
[ QUOTE ]
[ QUOTE ] Am I right to assume they disagree with the following statement [/ QUOTE ] No. [/ QUOTE ] Well as far as I'm concerned that is all I am saying. So I don't fully understand what you are arguing about. Neither does anyone else here. I would also like to ask again whether you think Persi Diaconis agrees with you.
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#7
06-03-2007, 01:35 PM
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Re: Clarifying The Bent Coin Problem
[ QUOTE ]
So I don't fully understand what you are arguing about. [/ QUOTE ] Obviously. [ QUOTE ] Neither does anyone else here. [/ QUOTE ] Wrong. [ QUOTE ] I would also like to ask again whether you think Persi Diaconis agrees with you. [/ QUOTE ] Not enough information. I would also like to ask something again: -------------------- QUOTE: -------------------- Okay, look, I just bent a real penny. It is sitting here on my desk. Here are two questions: (a) What is the probability the penny comes up heads? (b) What is the probability the penny comes up tails? Pick a question, either question, and answer it. You can answer with "not enough information" or you can answer with a number between 0 and 1. All of your posts seem to indicate that your answer to both questions is 0.5. Yet I do not think you have come right out and said that. Why? Am I misunderstanding you? --------------------
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#8
06-03-2007, 02:39 PM
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Re: Clarifying The Bent Coin Problem
My point is that there is no such thing as THE probability of an event. There is only a probability correlated with the information you have.
In the specific case where the only information is the number of choices than the probability associated with that information has historically been one over that number. And I assume that you would agree that if Diaconis disagreed with you, that would at the very least make it reasonable to disagree with you. (I have no idea if he does.)
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#9
06-03-2007, 03:13 PM
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Re: Clarifying The Bent Coin Problem
[ QUOTE ]
And I assume that you would agree that if Diaconis disagreed with you, that would at the very least make it reasonable to disagree with you. (I have no idea if he does.) [/ QUOTE ] Then why bring it up? I recognize he is a Super-Expert on Probability. Since neither of us have read him we can't know for sure what he says. Are you implying there is therefore a 50% chance he will disagree with me? That's exactly the kind of nonsense your Sklanksy-Probability-Logic can produce. The fact is that I've studed the mathematics of probability extensively. You haven't. I didn't study under Diaconis but I did study under people who are also Super-Experts in the Field. You haven't. jason1990 is a real expert and I'm saying nothing different than what he is saying. You on the other hand are an amateur probablist with a high IQ who knows enough probability to write good poker books. But on this question you are flying by the seat of your pants and beginning to look more and more like the person you described here, [ QUOTE ] DS - they think that because they have above average IQs they shouldn't be considered morons when they offer their opinions about stuff that isn't obviously highly mathematical. When they enounter a subject that is 20% mathematical they either deny that it percentage, or claim that they can overcome the 20%. Thus they are in fact morons. [/ QUOTE ] This situation is even worse. This is a question that is almost 100% mathematical yet you think your high IQ can make up for your lack of mathematical knowledge. PairTheBoard
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#10
06-03-2007, 03:37 PM
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Re: Clarifying The Bent Coin Problem
[ QUOTE ]
My point is that there is no such thing as THE probability of an event. [/ QUOTE ] Okay, great. Thank you for clarifying. You are not alone in this belief. Many philosophers agree with you. The idea that all probabilities are subjective and relative to an observer is possibly as old as probability itself. But I would like to firmly nail this down. How exactly does that translate into an answer to my question: [ QUOTE ] Okay, look, I just bent a real penny. It is sitting here on my desk. Here are two questions: (a) What is the probability the penny comes up heads? (b) What is the probability the penny comes up tails? Pick a question, either question, and answer it. [/ QUOTE ] Am I correct in assuming your response is: "There is no answer to question (a). THE probability of heads for your bent coin does not exist. Same for (b)." [ QUOTE ] And I assume that you would agree that if Diaconis disagreed with you, that would at the very least make it reasonable to disagree with you. (I have no idea if he does.) [/ QUOTE ] You do not need Persi in order to reasonably disagree with me. But you do need to understand me.
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Hybrid Mode
