Mathematics of Betting: Odds vs Probability vs RRR

O

OddTrader

" http://en.wikipedia.org/wiki/Odds

A simple example is that the (statistical) Odds for rolling six with a fair die (one of a pair of dice) are 1 to 5. This is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 six event for every 5 times the die does not show six. For example, if we roll the fair die 600 times, we would very much expect something in the neighborhood of 100 sixes, and 500 of the other five possible outcomes. That is a ratio of 100 to 500, or simply 1 to 5. To express the (statistical) Odds against, the order of the pair is reversed. Hence the Odds against rolling a six with a fair die are 5 to 1. The probability of rolling a six with a fair die is the single number 1/6 or approximately 16.7%.
"
" http://en.wikipedia.org/wiki/Risk_return_ratio
The Risk-Return-Ratio is a measure of return in terms of risk for a specific time period.
"
 
The probability does not exclude a non-6 for the next 100 throws. In that case the curve fitter is wiped out.

The market is not a fair dice. The market maker needs to make his daily living. Therefore the market is biased to not give you a 6 if you were to put money on it. You'd have better luck with a demo account where the market maker doesn't care to win your demo cash.
 
ExperiencedJoe said:
The probability does not exclude a non-6 for the next 100 throws. In that case the curve fitter is wiped out.

The market is not a fair dice. The market maker needs to make his daily living. Therefore the market is biased to not give you a 6 if you were to put money on it. You'd have better luck with a demo account where the market maker doesn't care to win your demo cash.
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Agreed.

" http://en.wikipedia.org/wiki/Reflexivity_(social_theory)
In economics

Economic philosopher George Soros, influenced by ideas put forward by his tutor, Karl Popper (1957), has been an active promoter of the relevance of reflexivity to economics, first propounding it publicly in his 1987 book The Alchemy of Finance.[1] He regards his insights into market behaviour from applying the principle as a major factor in the success of his financial career.

Reflexivity is inconsistent with equilibrium theory, which stipulates that markets move towards equilibrium and that non-equilibrium fluctuations are merely random noise that will soon be corrected. In equilibrium theory, prices in the long run at equilibrium reflect the underlying fundamentals, which are unaffected by prices. Reflexivity asserts that prices do in fact influence the fundamentals and that these newly influenced set of fundamentals then proceed to change expectations, thus influencing prices; the process continues in a self-reinforcing pattern. Because the pattern is self-reinforcing, markets tend towards disequilibrium. Sooner or later they reach a point where the sentiment is reversed and negative expectations become self-reinforcing in the downward direction, thereby explaining the familiar pattern of boom and bust cycles [2] An example Soros cites is the procyclical nature of lending, that is, the willingness of banks to ease lending standards for real estate loans when prices are rising, then raising standards when real estate prices are falling, reinforcing the boom and bust cycle.

Soros has often claimed that his grasp of the principle of reflexivity is what has given him his "edge" and that it is the major factor contributing to his successes as a trader. Nevertheless, there is little sign of the principle being accepted in mainstream economic circles.
"
" http://en.wikipedia.org/wiki/Game_theory#Zero-sum_.2F_Non-zero-sum
Zero–sum game

Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others). Poker exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include matching pennies and most classical board games including Go and chess.

Many games studied by game theorists (including the infamous prisoner's dilemma) are non-zero-sum games, because the outcome has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.

Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential gains from trade. It is possible to transform any game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called "the board") whose losses compensate the players' net winnings.
"
 
OddTrader said:
Agreed.

" http://en.wikipedia.org/wiki/Reflexivity_(social_theory)
In economics

Economic philosopher George Soros, influenced by ideas put forward by his tutor, Karl Popper (1957), has been an active promoter of the relevance of reflexivity to economics, first propounding it publicly in his 1987 book The Alchemy of Finance.[1] He regards his insights into market behaviour from applying the principle as a major factor in the success of his financial career.

Reflexivity is inconsistent with equilibrium theory, which stipulates that markets move towards equilibrium and that non-equilibrium fluctuations are merely random noise that will soon be corrected. In equilibrium theory, prices in the long run at equilibrium reflect the underlying fundamentals, which are unaffected by prices. Reflexivity asserts that prices do in fact influence the fundamentals and that these newly influenced set of fundamentals then proceed to change expectations, thus influencing prices; the process continues in a self-reinforcing pattern. Because the pattern is self-reinforcing, markets tend towards disequilibrium. Sooner or later they reach a point where the sentiment is reversed and negative expectations become self-reinforcing in the downward direction, thereby explaining the familiar pattern of boom and bust cycles [2] An example Soros cites is the procyclical nature of lending, that is, the willingness of banks to ease lending standards for real estate loans when prices are rising, then raising standards when real estate prices are falling, reinforcing the boom and bust cycle.

Soros has often claimed that his grasp of the principle of reflexivity is what has given him his "edge" and that it is the major factor contributing to his successes as a trader. Nevertheless, there is little sign of the principle being accepted in mainstream economic circles.
"
" http://en.wikipedia.org/wiki/Game_theory#Zero-sum_.2F_Non-zero-sum
Zero–sum game

Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others). Poker exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include matching pennies and most classical board games including Go and chess.

Many games studied by game theorists (including the infamous prisoner's dilemma) are non-zero-sum games, because the outcome has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.

Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential gains from trade. It is possible to transform any game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called "the board") whose losses compensate the players' net winnings.
"
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Hi,
Thanks for the post, very interesting. My observations reflect the market constantly evolving where periods of both Reflexivity and Equilibrium occure for random periods. The trick to capitalizing is to know what phase the market is in and then act appropriately. On another note, I suspect that the Matching Pennies Game is actually what we call Two Up here in Australia, where the odds are 50-50 in it's purest form although often the house is taking a rake.
Cheers John
 
"Soros has often claimed that his grasp of the principle of reflexivity is what has given him his "edge""

Posteriori it cannot be accepted. he is looking for justification of his luck or trading boldness. he could have gone broke as well like many other have. He was just lucky.
 
OddTrader said:
" http://en.wikipedia.org/wiki/Odds

A simple example is that the (statistical) Odds for rolling six with a fair die (one of a pair of dice) are 1 to 5. This is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 six event for every 5 times the die does not show six. For example, if we roll the fair die 600 times, we would very much expect something in the neighborhood of 100 sixes, and 500 of the other five possible outcomes. That is a ratio of 100 to 500, or simply 1 to 5. To express the (statistical) Odds against, the order of the pair is reversed. Hence the Odds against rolling a six with a fair die are 5 to 1. The probability of rolling a six with a fair die is the single number 1/6 or approximately 16.7%.
"
" http://en.wikipedia.org/wiki/Risk_return_ratio
The Risk-Return-Ratio is a measure of return in terms of risk for a specific time period.
"
More...


Odds is what you expect to win for every unit of currency you bet. So the wiki article is stupid because we do not know the payoff. The article commits the fundamental error of confusing probabilities with values of random variables that are assigned to the probably events.Odds could be anything. If you make 1 unit for each number rolled than the odds are 1 to 1 because average winner is 1 no matter what. But if you say that 6 is assigned the value of 10, for example, then the odds are 10:1 because each time you win you make 10 units.

The odds as they say 5: 1 represent a game when 6 makes 5 units and the rest of the numbers make 1 units.

When you bet on a game of chance, the odds you get is how much you will win in the case your selection is correct, i.e. it is the average winner. It is not the probability of not winning or any other probability. How stupid one could get.
 
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" http://wiki.lesswrong.com/wiki/Log_odds

Log odds

Log odds are an alternate way of expressing probabilities, which simplifies the process of updating them with new evidence. Unfortunately, it is difficult to convert between probability and log odds. The log odds is the log of the odds ratio. Thus, the log odds of A are logit(P(A)) = log(P(A)/P(¬A)). "

" http://en.wikipedia.org/wiki/Logit

Log odds

When the function's parameter represents a probability p, the logit function gives the log-odds, or the logarithm of the odds p/(1 − p).
"

" http://wiki.lesswrong.com/wiki/Odds_ratio

Odds ratio

Odds ratios are an alternate way of expressing probabilities, which simplifies the process of updating them with new evidence. The odds ratio of A is P(A)/P(¬A). "
 
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OddTrader said:
" http://wiki.lesswrong.com/wiki/Log_odds

Log odds

Log odds are an alternate way of expressing probabilities, which simplifies the process of updating them with new evidence. Unfortunately, it is difficult to convert between probability and log odds. The log odds is the log of the odds ratio. Thus, the log odds of A are logit(P(A)) = log(P(A)/P(¬A)). "

" http://wiki.lesswrong.com/wiki/Odds_ratio

Odds ratio

Odds ratios are an alternate way of expressing probabilities, which simplifies the process of updating them with new evidence. The odds ratio of A is P(A)/P(¬A). "

" Log odd

http://en.wikipedia.org/wiki/Logit

When the function's parameter represents a probability p, the logit function gives the log-odds, or the logarithm of the odds p/(1 − p).
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how do I use this when sitting at the roulette table? Wasn't it enough just to look at the table and checking the odds to say, "There's no bet here."?
 
loyek590 said:
how do I use this when sitting at the roulette table? Wasn't it enough just to look at the table and checking the odds to say, "There's no bet here."?
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My guess is first at all, perhaps you are Not allowed to use any computers/calculators!

Now you understand your Odds! lol

PS: Read Chapter 7 The Trader's Edge - Thinking in Probabilities (Trading in the Zone by Douglas)
 
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