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Paradox of Kraitchik

dylancatlow
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6/9/2014 12:09:42 PM
Posted: 2 years ago
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...
slo1
Posts: 4,341
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6/17/2014 3:25:18 PM
Posted: 2 years ago
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.
dylancatlow
Posts: 12,245
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6/17/2014 3:35:39 PM
Posted: 2 years ago
At 6/17/2014 3:25:18 PM, slo1 wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

Think of it like this:
50 percent chance of losing your 10 dollars.
50 percent chance of winning 25 dollars.
The expected utility of betting is greater than not betting.

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.
dylancatlow
Posts: 12,245
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6/17/2014 3:37:13 PM
Posted: 2 years ago
At 6/17/2014 3:25:18 PM, slo1 wrote:
25 because 10 + their 15 (because if you win, they would necessarily have more money).
slo1
Posts: 4,341
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6/17/2014 3:39:00 PM
Posted: 2 years ago
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

Think of it like this:
50 percent chance of losing your 10 dollars.
50 percent chance of winning 25 dollars.
The expected utility of betting is greater than not betting.

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.

I didn't see anywhere, where it had stated amount in my wallet or the other person's wallet. The envelop creates the paradox because I see what is in my wallet and understand the possible options of what is in the other envelop. What happens in the wallet game if I have $1,000 in my wallet? I sure am not betting it against an average person's wallet.
slo1
Posts: 4,341
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6/17/2014 3:40:01 PM
Posted: 2 years ago
At 6/17/2014 3:39:00 PM, slo1 wrote:
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

Think of it like this:
50 percent chance of losing your 10 dollars.
50 percent chance of winning 25 dollars.
The expected utility of betting is greater than not betting.

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.

I didn't see anywhere, where it had stated amount in my wallet or the other person's wallet. The envelop creates the paradox because I see what is in my envelop and understand the possible options of what is in the other envelop. What happens in the wallet game if I have $1,000 in my wallet? I sure am not betting it against an average person's wallet.

Fix
dylancatlow
Posts: 12,245
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6/17/2014 3:41:07 PM
Posted: 2 years ago
At 6/17/2014 3:39:00 PM, slo1 wrote:
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

Think of it like this:
50 percent chance of losing your 10 dollars.
50 percent chance of winning 25 dollars.
The expected utility of betting is greater than not betting.

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.

I didn't see anywhere, where it had stated amount in my wallet or the other person's wallet.

That's not the point. Those numbers are just arbitrary. It's assumed that you don't have any reason to believe you have more or less money than the other person.

The envelop creates the paradox because I see what is in my wallet and understand the possible options of what is in the other envelop. What happens in the wallet game if I have $1,000 in my wallet? I sure am not betting it against an average person's wallet.
slo1
Posts: 4,341
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6/17/2014 3:45:11 PM
Posted: 2 years ago
At 6/17/2014 3:41:07 PM, dylancatlow wrote:
At 6/17/2014 3:39:00 PM, slo1 wrote:
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

Think of it like this:
50 percent chance of losing your 10 dollars.
50 percent chance of winning 25 dollars.
The expected utility of betting is greater than not betting.

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.

I didn't see anywhere, where it had stated amount in my wallet or the other person's wallet.

That's not the point. Those numbers are just arbitrary. It's assumed that you don't have any reason to believe you have more or less money than the other person.

The envelop creates the paradox because I see what is in my wallet and understand the possible options of what is in the other envelop. What happens in the wallet game if I have $1,000 in my wallet? I sure am not betting it against an average person's wallet.

If that is the case, they should stick with the envelop because the wallet game does not create the paradox. It is faulty logic from the get go.
dylancatlow
Posts: 12,245
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6/17/2014 3:48:20 PM
Posted: 2 years ago
At 6/17/2014 3:45:11 PM, slo1 wrote:
At 6/17/2014 3:41:07 PM, dylancatlow wrote:
At 6/17/2014 3:39:00 PM, slo1 wrote:
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

I just can't wrap my head around this:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

Think of it like this:
50 percent chance of losing your 10 dollars.
50 percent chance of winning 25 dollars.
The expected utility of betting is greater than not betting.

It is one thing to randomly get an amount handed to you in an envelop which could be exchanged for another envelop with either 1/2 the amount or double the amount where you did nothing to obtain the initial envelop. According to the logic of the wallet, i would be in the casino betting on black every paycheck.

I didn't see anywhere, where it had stated amount in my wallet or the other person's wallet.

That's not the point. Those numbers are just arbitrary. It's assumed that you don't have any reason to believe you have more or less money than the other person.

The envelop creates the paradox because I see what is in my wallet and understand the possible options of what is in the other envelop. What happens in the wallet game if I have $1,000 in my wallet? I sure am not betting it against an average person's wallet.

If that is the case, they should stick with the envelop because the wallet game does not create the paradox. It is faulty logic from the get go.

How is that faulty logic? Thought experiments don't have to be realistic.

Essentially, you are getting a random amount handed to you in an envelop which could be exchanged for another envelop with a random amount of money.
dylancatlow
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6/17/2014 3:57:46 PM
Posted: 2 years ago
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:

Actually, it makes more sense to think of it like this:
50 percent chance of losing 10 dollars.
50 percent chance of winning 15 dollars.
slo1
Posts: 4,341
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6/18/2014 10:32:21 AM
Posted: 2 years ago
At 6/17/2014 3:57:46 PM, dylancatlow wrote:
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:

Actually, it makes more sense to think of it like this:
50 percent chance of losing 10 dollars.
50 percent chance of winning 15 dollars.

Ok, you are going to have to help me out on this one if you have time. I would like to summarize this guys thesis and how he gets to his conclusion, but I need to understand it better first.

Let's just start with step 1.

1. Kraitechik's paradox produces a situation where both parties from their own subjective view point come to a conclusion where they have opportunity to win more than what they might loose.

A. The paradox exists because both parties have the subjective view point of a positive outcome. But.....

B. Using math it is demonstrated that n/2 + -n/2 =0, truly a "net zero" sum, meaning the rational position is that any one individual really does not have an true advantage because they might win more than what they loose.

C. The paradox is resolved when it is B is proven, showing the subjective view point in A is invalid.

Do I have this right thus far?
dylancatlow
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6/18/2014 10:43:10 AM
Posted: 2 years ago
At 6/18/2014 10:32:21 AM, slo1 wrote:
At 6/17/2014 3:57:46 PM, dylancatlow wrote:
At 6/17/2014 3:35:39 PM, dylancatlow wrote:
At 6/17/2014 3:25:18 PM, slo1 wrote:

Actually, it makes more sense to think of it like this:
50 percent chance of losing 10 dollars.
50 percent chance of winning 15 dollars.

Ok, you are going to have to help me out on this one if you have time. I would like to summarize this guys thesis and how he gets to his conclusion, but I need to understand it better first.

Let's just start with step 1.

1. Kraitechik's paradox produces a situation where both parties from their own subjective view point come to a conclusion where they have opportunity to win more than what they might loose.

A. The paradox exists because both parties have the subjective view point of a positive outcome. But.....

B. Using math it is demonstrated that n/2 + -n/2 =0, truly a "net zero" sum, meaning the rational position is that any one individual really does not have an true advantage because they might win more than what they loose.

C. The paradox is resolved when it is B is proven, showing the subjective view point in A is invalid.

Do I have this right thus far?

Essentially, the paradox is resolved by realizing that one's own stake can also be greater or less than the other person's.
slo1
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6/18/2014 1:17:00 PM
Posted: 2 years ago
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

It is all relative to the fact that if I win the amount I win is more money than what I have regardless of the amount of money I have.

"If I lose, then I lose just what I have, but if I win, I win more than what I have", which becomes

"If y1 < x, then gain1 = -x, but if y2 > x, then gain2 = y2 = x+n, n>0."
dylancatlow
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6/18/2014 1:21:39 PM
Posted: 2 years ago
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."
slo1
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6/18/2014 1:29:53 PM
Posted: 2 years ago
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.
dylancatlow
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6/18/2014 1:35:59 PM
Posted: 2 years ago
At 6/18/2014 1:29:53 PM, slo1 wrote:
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.

Yes, the amount of money in your wallet is completely irrelevant. Why did you need to say that?
slo1
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6/18/2014 1:59:35 PM
Posted: 2 years ago
At 6/18/2014 1:35:59 PM, dylancatlow wrote:
At 6/18/2014 1:29:53 PM, slo1 wrote:
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.

Yes, the amount of money in your wallet is completely irrelevant. Why did you need to say that?

Because you wrote this:

That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I just wanted to challenge that statement and make sure that I was not wrong when stating that this has nothing to do with the relative amount in your wallet and whether it is small amount or a large amount. The paradox is that you should really never bet regardless of the amount in your wallet.
dylancatlow
Posts: 12,245
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6/18/2014 2:02:01 PM
Posted: 2 years ago
At 6/18/2014 1:59:35 PM, slo1 wrote:
At 6/18/2014 1:35:59 PM, dylancatlow wrote:
At 6/18/2014 1:29:53 PM, slo1 wrote:
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.

Yes, the amount of money in your wallet is completely irrelevant. Why did you need to say that?

Because you wrote this:

That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.


Those are both possibilities i.e. possible states of affairs.

The paradox is that you should really never bet regardless of the amount in your wallet.

That is not true. Betting = no loss or gain.
slo1
Posts: 4,341
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6/18/2014 2:06:52 PM
Posted: 2 years ago
At 6/18/2014 2:02:01 PM, dylancatlow wrote:
At 6/18/2014 1:59:35 PM, slo1 wrote:
At 6/18/2014 1:35:59 PM, dylancatlow wrote:
At 6/18/2014 1:29:53 PM, slo1 wrote:
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.

Yes, the amount of money in your wallet is completely irrelevant. Why did you need to say that?

Because you wrote this:

That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.


Those are both possibilities i.e. possible states of affairs.

The paradox is that you should really never bet regardless of the amount in your wallet.

That is not true. Betting = no loss or gain.

How do I rectify the dylancatlow paradox?

1. the amount of money in your wallet is completely irrelevant
2. If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

forgive me if I am being obtuse.
dylancatlow
Posts: 12,245
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6/18/2014 2:09:28 PM
Posted: 2 years ago
At 6/18/2014 2:06:52 PM, slo1 wrote:
At 6/18/2014 2:02:01 PM, dylancatlow wrote:
At 6/18/2014 1:59:35 PM, slo1 wrote:
At 6/18/2014 1:35:59 PM, dylancatlow wrote:
At 6/18/2014 1:29:53 PM, slo1 wrote:
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.

Yes, the amount of money in your wallet is completely irrelevant. Why did you need to say that?

Because you wrote this:

That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.


Those are both possibilities i.e. possible states of affairs.

The paradox is that you should really never bet regardless of the amount in your wallet.

That is not true. Betting = no loss or gain.

How do I rectify the dylancatlow paradox?

1. the amount of money in your wallet is completely irrelevant
2. If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

forgive me if I am being obtuse.

By "the amount of money in your wallet is completely irrelevant" I meant that the actual NUMBER OF DOLLARS in your wallet is irrelevant. You can have 5, 10, a million, it doesn't matter. That's not the point.
slo1
Posts: 4,341
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6/18/2014 2:14:23 PM
Posted: 2 years ago
At 6/18/2014 2:09:28 PM, dylancatlow wrote:
At 6/18/2014 2:06:52 PM, slo1 wrote:
At 6/18/2014 2:02:01 PM, dylancatlow wrote:
At 6/18/2014 1:59:35 PM, slo1 wrote:
At 6/18/2014 1:35:59 PM, dylancatlow wrote:
At 6/18/2014 1:29:53 PM, slo1 wrote:
At 6/18/2014 1:21:39 PM, dylancatlow wrote:
At 6/18/2014 1:17:00 PM, slo1 wrote:
At 6/18/2014 10:49:10 AM, dylancatlow wrote:
That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

I don't see that in the math. No where in the math does it make a statement that the perception of a positive outcome has anything to do with whether I have more or less money in my wallet.

Let the player's stake = x, his opponent's stake = y, "if I lose" = condition 1 (x1 > y1), and "if I win" = condition 2 (x2 < y2). Then the problem is simply this: each player lopsidedly treats x as fixed and independent (and therefore unindexed), and y as mutable and dependent (and therefore in need of an index 1 or 2)....In fact, y could just as well be the fixed quantity and x the conditionally dependent one. In this case, the player would reason:

"If x1 > y, then gain1 = -x1, but if x2 < y, then gain2 = y (< x1) = x1-n, n>0."

let the player's stake = x, his opponent's stake = y

Again the logic is pertaining to the value of what is in my wallet compared to the other guys wallet. There is no logical assumption that my perception changes based upon whether X is large or X is small. IE: If I have $1,000 I still perceive a positive outcome because if I win I get more than $1,000. That is the paradox because both me and the other guy have an expectation of a positive outcome when it really is no advantage.

Yes, the amount of money in your wallet is completely irrelevant. Why did you need to say that?

Because you wrote this:

That is: If I have more money, then I should not bet to the same extent that if I have less money, I should bet.


Those are both possibilities i.e. possible states of affairs.

The paradox is that you should really never bet regardless of the amount in your wallet.

That is not true. Betting = no loss or gain.

How do I rectify the dylancatlow paradox?

1. the amount of money in your wallet is completely irrelevant
2. If I have more money, then I should not bet to the same extent that if I have less money, I should bet.

forgive me if I am being obtuse.

By "the amount of money in your wallet is completely irrelevant" I meant that the actual NUMBER OF DOLLARS in your wallet is irrelevant. You can have 5, 10, a million, it doesn't matter. That's not the point.

I have got that and have said it is irrelevant. I'm trying figure out how the this proof shows that I should not bet to the same extent if is it 10 million versus a dollar in my wallet. You have two contradictory statements and again, no where in the math does it have logic where there are different amounts in my wallet.
R0b1Billion
Posts: 3,732
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6/18/2014 4:39:26 PM
Posted: 2 years ago
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

This makes no sense. There's no bet going on, all we do is compare wallets and hand over the cash...
Beliefs in a nutshell:
- The Ends never justify the Means.
- Objectivity is secondary to subjectivity.
- The War on Drugs is the worst policy in the U.S.
- Most people worship technology as a religion.
- Computers will never become sentient.
dylancatlow
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6/18/2014 5:01:50 PM
Posted: 2 years ago
At 6/18/2014 4:39:26 PM, R0b1Billion wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

This makes no sense. There's no bet going on, all we do is compare wallets and hand over the cash...

Bet: to risk something, usually a sum of money, against someone else's on the basis of the outcome of a future event, such as the result of a race or game.
R0b1Billion
Posts: 3,732
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6/18/2014 9:16:09 PM
Posted: 2 years ago
At 6/18/2014 5:01:50 PM, dylancatlow wrote:
At 6/18/2014 4:39:26 PM, R0b1Billion wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

This makes no sense. There's no bet going on, all we do is compare wallets and hand over the cash...

Bet: to risk something, usually a sum of money, against someone else's on the basis of the outcome of a future event, such as the result of a race or game.

OK but there has to be a decision to make. There's no decision here, you just compare and decide who's won. Am I not understanding it correctly?
Beliefs in a nutshell:
- The Ends never justify the Means.
- Objectivity is secondary to subjectivity.
- The War on Drugs is the worst policy in the U.S.
- Most people worship technology as a religion.
- Computers will never become sentient.
dylancatlow
Posts: 12,245
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6/19/2014 12:20:01 PM
Posted: 2 years ago
At 6/18/2014 9:16:09 PM, R0b1Billion wrote:
At 6/18/2014 5:01:50 PM, dylancatlow wrote:
At 6/18/2014 4:39:26 PM, R0b1Billion wrote:
At 6/9/2014 12:09:42 PM, dylancatlow wrote:
Two people are offered a chance to bet on whose wallet contains the lesser amount of money; the one with less gets all of the money in both wallets.

Both players reason as follows:

"If I lose, I lose just what I have, but if I win, I win more than I have [since if you win, the other person would be the one with more money]. Therefore, given that the win and loss probabilities are indifferent, my expectation is positive and I should bet."

First, note that the betting strategy is cyclic and cannot be completely executed; it applies iteratively to its own result, prescribing (if permitted) that the player bet over and over ad infinitum without ever realizing the promised "win". Since, within or without any one game, the switching strategy is cyclical and of period 2 - that is, since two iterations result in a return to the player's initial state, whatever that state may be - only one switching operation is meaningful. This is a signal that something is wrong with the strategy.

In fact, a paradox exists even where only one switch is allowed. This paradox resides in the application of the above rationale to both players, implying a positive expectation for each in a 0-sum game in which the total amount of money is fixed.

Solution: http://www.megafoundation.org...

This makes no sense. There's no bet going on, all we do is compare wallets and hand over the cash...

Bet: to risk something, usually a sum of money, against someone else's on the basis of the outcome of a future event, such as the result of a race or game.

OK but there has to be a decision to make. There's no decision here, you just compare and decide who's won. Am I not understanding it correctly?

You are betting on who has less money in their wallet...as was stated in the first sentence.
slo1
Posts: 4,341
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6/19/2014 4:06:38 PM
Posted: 2 years ago
http://www.jstor.org...

This explains it a bit better. From what I outlined the proof in the original link shows that it is a net zero and no person has an advantage thus solving the paradox where both players think they have an advantage. (They both can't).
dylancatlow
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6/19/2014 4:08:08 PM
Posted: 2 years ago
At 6/19/2014 4:06:38 PM, slo1 wrote:
http://www.jstor.org...

This explains it a bit better. From what I outlined the proof in the original link shows that it is a net zero and no person has an advantage thus solving the paradox where both players think they have an advantage. (They both can't).

That link doesn't work.