Soul forever under contract, 666 credit score rating

For so remarkably perverse is the nature of man that he despises whoever courts him and admires whoever will not bend before him. --Thucydides As nineteenth century America traded liberty for ambition, financial circumstances evolved as categories of personal identity. Imperialism trumped freedom; capitalism made every soul a business. Failure, a language of business, was applied to the soul. Failure was made yet never born prior to capitalism. Now, more outrun failure than chase success as a low ambition offends more than a low achievement. With the Civil War failure grew to mean insolvent. Failure became a sin promoted by the idea that men who failed lacked ability and ambition. Men were always at fault for their failures even though honest dealings and hard work could fail under capitalism. Failure went from an incident to an identity. A man became nothing more than his occupation. Striving for success became a compulsory virtue and even a sacred duty within religious cultures. Perpetual ambition became self respect and self esteem, where every life was to be lived on the stretch and an easy life could never be good enough. Men publish the successes of their efforts but shy from sharing failures, a practice of concealment that causes the ruins of many a man as every success is followed by eight failures with a paper trail of common failure hidden within libraries and public archives. The basis of modern American law, economy, and society is contract theory. Contract became the framework of achieved identity in its supreme place in legal thought. Free man could make deals to advance him and nobody fails who ought not to fail. A contract was a promise to succeed, to uphold your end of a bargain. Any soul freely accepted or rejected contracts, which completely ignores the basic facts of poverty and power. Legal release from debt violates two rules of capitalism, keeping a promise and taking responsibility when a soul’s actions harm others. An entrepreneur who failed in the early nineteenth century faced inadequate laws, vengeful creditors, and forced idleness in debtor’s prison. Bankruptcy laws voided a debtor’s legal obligations, not a soul’s moral ones. During rampant failure, a contract came to signify obligation but not a promise. A moral obligation was at odds with legal and economic change, yet worth preserving. To enshrine moral obligations was to sequester it unenforceable or ordered from the court.

Bankroll vs Edge and Odds

For a positive expectation bet, you need an edge.
Edge is the amount you expect to win.

For a positive expectation bet, you need the odds.
Odds of 2 to 1 converts to 1/(2+1) fraction

Wagers of positive expectation have size limitations.
Bankroll must be a consideration for making a wager.

Kelly Formula relates 'bet to bankroll' as 'edge/odds'.
Edge/odds formula ignores the effect this wager has.

Arithmetic Mean vs. Geometric Mean

Arithmetic Mean = the sum of 'X' values divided by 'X' = Average.
Geometric Mean = the 'X' root of the product of 'X' values.

Geometric Mean < Arithmetic Mean, except when equal average values.
if Geometric Mean < Arithmetic Mean, then any risk is unfavorable

if an investor trades then zero sum game loses payments in trade
if a gambler makes a fair wager then risk makes wager unfavorable

if you wager or invest then you chose the highest Geometric Mean
if a Gemetric Mean = 0 then you can go to zero and will in time

Arithmetic Emprical not Truth

The problem in arithmetic is people use applications to physical phenomena without the necessary experience to understand if it even applies. Examples of arithmetic applications can be absurd. I like Grey Goose Vodka and if a quart of alcohol is mixed with a quart of water it will yield ~1.8 quarts of vodka, which is true of most mixtures of alcoholic liquids. I play basketball and if one night I hit 2 out of 3 shots and the next night I make 3 out of 4 shots and you compute my average over both games by adding the two fractions in the usual method of adding fractions, which is find the common denominator:
2/3 +3/4 = 8/12+9/12=17/12
So, I made 17 shots in 12 tries? The method of adding fractions does not give my shooting average over separate games.

A new way of adding fractions is add the numerators and add the denominators:
2/3 +3/4=5/7
Experience tells us this arithmetic method is correct.

Under normal rules 2/3=4/6 but not under this new method of adding fractions:
4/6+3/4=7/10, and 7/10 does NOT equal 5/7.

In normal arithmetic, fractions behave as integers. So consider the numerators 2 and 4. The numbers can be fractions: 2/1 and 4/1.

Now use our new arithmetic:
2/1+4/1=6/2 rather than the 6/1 obtained under normal rules.

This has a major significance since it concludes that there is no truth in mathematics but simply a tool developed by man. Only experience can show where ordinary arithmetic applies to any given physical phenomena. The theorems of mathematics are not truths but man's tool to model aspects about the physical world. As far as the study of the physical world is concerned, mathematics merely offers theories. Mathematics is based on man's intuition whereas axioms of logic or truth is an art where man is allowed to paint his better wrong answer with confidence.

Fractions and Odds

To convert odds to fractions: a to b is b/ (a+b)
To convert fractions to odds: a/b is (b-a) to a

Odds are a ratio of non occurrences to occurrences (losses to wins).
Ratios reduce to lower terms [i.e. (9 to 6) = (3 to 2)].

Think of things in terms of fractions or percentages not odds.
3 to 1 shot: 1/ (1+3) = 1/4: 0.25 = 25%
hence 3 to 2 shot = 40%
4 to 1 shot: 1/ (1+4) = 1/5: 0.20 = 20%

Odds need to be converted to fractions to do any arithmetic. Change odds to percentages, add the percentages, and revert that to odds. (i.e. to parlay 3 to shot and 4 to 1 shot):
3 to 2: 2/5
4 to 1: 1/5
1/5 x 2/5 = 2/25, which reverts to 23 to 2 shot.

Percentage advantage is not the same as percentage disadvantage. If you know either then you can tell if your expectation is positive or negative. Your average profit per game is your expectations. With 9 to 1 odds, the house has a 1% advantage, for example each $110 bet makes them $1, yet the player disadvantage is to lose $1 for each $11 bet, which is 9.1% when he bets $1 per roll for eleven rolls where he wins once ($9) and they win $10.

Mutually Exclusive vs Independent Events

Mutually exclusive or independent events must be considered before calculating the probability of two or more events occurring.

Two events "I am here" or "I am not here" are mutually exclusive. If ‘event A’ occurs, then ‘event B’ cannot, or vice-versa. To calculate the probabilities for exclusive events ADD the probabilities.

Two events "I am here" and "You are here" are independent. If ‘event A’, then if ‘event B’. To calculate the probabilities for independent events MULTIPLY the probabilities of two unrelated events.

The throw of a single die, outcomes are equally probable. Each throw is a mutually exclusive event. That is, if a die rolls A then it cannot roll B. The probability of rolling A or B with the first die is the sum of the equal probabilities, 1/6 + 1/6 = 1/3.
Independent events are multiplied. The probability of throwing two dice resulting in A and A is the probability of each roll times itself: (1/6) * (1/6) = 1/36th or 2.77%.

The probability of rolling A and B in either order with one dice is 1/3 x 1/6 = 1/18 (2/36). Add or multiply probabilities based on whether mutually exclusive or independent.

The different numbers obtained by the throw of two dice offer a good introduction to the ideas of probability. Possible outcomes for the total of two dice are not equal. Seven is a possible outcome with every throw of two dice. Two and 12 rolls only 1/36 (A and A) or (B and B). The "odds" of three (A or B) are two times greater 2/36. Rolling a 7 is six times greater 6/36, which raises the idea of distinguishable states. With two dice, the first dice throw does not matter as there remains a chance of rolling 7. If you throw one dice and it rolls a 3 then the next dice roll must be a 4 or vise-versa. Outcomes are exclusive if a result directly affects the other. The order does not matter (i.e. rolling a 3 is twice as likely as rolling a 2 since there are two distinguishable ways to get a 3). The probability of rolling a 7 with two dice is 1/6, rolled 6 of a total of 36 possible outcomes.

Standard Deviation Winner

The standard deviation is inversely proportional to the square root of the sample size. Success may be the result of a positive expectation but can be the result of a standard deviation, where many live in the variance.

if each possible outcome is not equally likely then each must be weighted according to its probability or element of change
if mean vs volatility then mean-variance analysis offers criteria for earning best combination of compound return on investment

The mean-variance analysis is static for given what you know now.
The mean-variance analysis is a theory over time at present frame.

Variance increases along with the arithmetic mean.
Variance goes to zero along with a geometric mean.

if zero is a chance of any outcome then the geometric mean is zero
if a geometric mean is zero then variance does not matter as there is a zero outcome with time