Two branches of mathematics

The Greeks had a simple number system, but it was different from the Egyptian system. Egyptians used pictures to represent numbers. Greeks used the letters of their alphabet. The Greeks got the idea for an alphabet from the Phoenicians, a seafaring people who lived around 1500 BC along the coast of Syria. The Greek number system used units of 5 and 10. The Greek alphabet had twenty-seven letters, so the first nine letters represented the digits 1 through 9; the second nine letters represented the tens, and the last nine letters represented the hundreds. The highest Greek number was 900. The Greeks did not have a zero, and since they rarely needed numbers higher than hundreds, the system worked fairly well. Even though the Greeks were logical about numbers, they were surprisingly superstitious too. Some numbers were evil, while other numbers were friendly or even sacred. Number 10 was the number of harmony. Number 8 was the symbol of death. Odd numbers were female, and even numbers were male. Two branches of mathematics resulted with separation of whole numbers and geometry. Eudoxus used geometry to define lengths, angles, areas, and volumes with irrational numbers as lengths or line segments. Converting all mathematics except the theory of whole numbers into geometry had consequences. From Euclid until 1600, geometry was the basis of all rigorous mathematics. Mathematics begins intuitive or empirical and remained so until the 4th century BC. Babylonians used numbers without any understanding of decimal approximations. BC Pythagoras of the 5th century had linked whole numbers and ratios of whole numbers as the way to study nature and insisted the whole numbers were the measure of all things until Hippasus discovered a irrational number or incommensurable ratio. Pythagoreans and the classical Greeks rejected irrational numbers. Classical Greeks believed in the theory of whole numbers with a logical foundation. Deductive mathematic attempts led Euclid to define all his concepts to provide a logical treatment of the whole numbers. Geometric representation of numbers and of operations with numbers was not practical. The deductive orderly proof of the geometry of Euclid, Apollonius, and Archimedes was merged with the indeterminate class of problems in the works of Diophantus. Classical Greek civilization combined with Egyptian and Babylonian in the period of Alexandrian Greek civilization. Various types of undefined numbers continued to be used to provide empirically correct solutions. Heron translated much of the Greek geometrical algebra into arithmetical and algebraic processes and provided a formula for the area of a triangle. Hipparchus and Ptolemy created quantitative astronomy with the creation of trigonometry. Arithmetic and algebra emerged without logical structure since it could be used provide empirical results. Diophantus introduced symbolism in algebraic operations that was entirely arithmetical with no appeal to geometry. He introduced indeterminate equations as a branch of algebra but considered equations producing irrational negative or imaginary roots as unsolvable. Heron accepted irrational quantities; Archimedes put bounds around irrational numbers. Hindus and Arab advanced arithmetic and algebra empirically. They reasoned by analogy and introduced rules for manipulating irrational numbers without providing any logical foundation favored in classical Greek mathematics. The Hindus introduced separate symbols for the numbers 1 to 9, converted from positional notation in base 60 to base 10, recognized 0 as a number, and used negative numbers. Europeans of the Renaissance acquired its knowledge of mathematics via the Arabs and Greek manuscripts. They noticed a dilemma presented by the two disparate states of arithmetic and geometry. They realized the utility of arithmetic and algebra of ancient times lacked a logical foundation. Europeans of the 16th and 17th century considered the negative numbers in Arab texts as absurd. Girard and Harriot used the minus sign to describe negative numbers. A negative number is an independent concept, not the operation of subtraction. Using separate symbols would have been better.

Logarithms, complex numbers, mathematical induction, and the binomial theorem were added to the body of algebra without proofs. Algebra became a study of general types of forms and equations when Vieta introduced literal coefficients separating arithmetic and algebra, types from numbers. By the mid-18th century, algebra included many branches.

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

Limit Poker Parameters

♠♣ the parameters of limit poker ♥
β=bank roll
R=win rate
σ = standard deviation = √variance
T = time (hours)
τ = sample size
99.5% of the population is within 3 standard deviations = 3 σ
σ = √τ

β = R T - 3 σ √T
So, 0 = R T - 3 σ √T hours necessary to ensure a profit
(if you know your win rate)
dβ = R d(T - 3 σ √T )
0 = R dT – 3σ dT¹∕²
0 = R (1) – 3σ ½ (1/√T)
T = |3σ/2R|²

Effects of debt related fiat currency

'He who cannot draw on 3000 years of history is living merely from hand to mouth'-Goethe The US gross domestic product (GDP) is approximately $12,000,000,000,000 ($12 trillion). The federal government should borrow money on the global market based on its creditors believing they will be repaid in full with interest. However, it also prints new currency (M3) that dilutes the value of the currency.

Britain recovered from the highest recorded national debt of 250% of its GDP after World War II. Britain repaid its debts to about 50% of G.D.P.

Debt burdens of 150% of GDP have proven unsustainable. Smaller countries are not credit worthy anywhere near this level. Argentina lost its ability to borrow after its debt hit 65% of GDP. A borrowing limit for the United States using 150% of its $12 trillion GDP would be about $18 trillion.

The official Treasury debt equals $4.6 trillion but the government has also spent money borrowed from the trust funds. The government owes $3.2 trillion, of which, $2 trillion is to Social Security and Medicare trust funds. Count this and the US has a debt of $6.6 trillion. However, the Social Security trust fund requires an additional $4 trillion to cover its obligations. Add this $4 trillion and the current debt is $10.6 trillion. Medicare trustees states the fund faces a shortfall of $9 trillion in obligations. Now, the prescription drug benefit reflects another $21 trillion deficit that to cover its supplementary obligations. This debt must be borrowed as there is no trust fund from which it can be taken.

This aggregate debt is $40.6 trillion, which is well beyond the unsustainable 150% of GDP limit of $18 trillion.

Total U.S. obligations of $40.6 trillion are nearly 338% of the GDP.

Now the USA must remain an empire. An empire’s economic foundations, from Greek and Roman, to Ottoman and British, are based on its ability to tax other nations. An imperial ability to tax demands a better, stronger economy and military. Subject taxes go to improve the living standards of the empire and to strengthen the military dominance that is necessary to enforce the collection of such taxes. Nation-states tax its citizens but an empire can tax other nation-states.

America can tax the entire world indirectly via inflation. It does not need to enforce direct payment of taxes as the predecessor empires as it distribute a fiat currency to other nations in exchange for goods with the intended consequence of inflating and devaluing those dollars via M3 growth and paying back each dollar with less economic goods. This difference is an imperial tax.

The U.S. economy would not dominate the world economy if the U.S. dollar was tied to gold. The M3 currency could not increase if it was limited to a gold reserve. The Great Depression, with its preceding inflation from 1921 to 1929 and its subsequent ballooning government deficits, substantially increased the currency in circulation, and rendered the backing of U.S. dollars by gold impossible. President Roosevelt removed the dollar from gold in 1932. The U.S. dominated the world economy from an economic point of view but was not an empire as the fixed value of the dollar did not allow the extraction of economic benefits from countries since these dollars remained convertible to gold.

With William Jennings Bryan’s famous "Cross of Gold" speech, Keynesian monetary policies, and the historical record during the Gilded Age of depressions and bank panics represented by an onerous gold standard that most economists reject, no one is suggesting a return. Under the gold standard, the money supply was so limited with unprecedented economic, industrial, and population expansion that deflation resulted and ended the era with the Panic of 1873. However, deflation is not the problem with fiat currency.

The United States accumulated the world’s gold by supplying allies with provisions during WWII and receiving payment in gold, which allowed the dollar to become the world currency. However, the dollar supply is no longer limited to the availability of gold since the Bretton Woods arrangement. An Empire began when foreign governments could not exchange dollars for gold. The supply of dollars was increased to finance Vietnam and LBJ’s Great Society, where most of those dollars were given to foreigners in exchange for economic goods.

America was without prospect of buying these dollars back. The increase in dollar holdings of foreigners via persistent U.S. trade deficits was a classical inflation tax. A country normally imposes this tax on its own citizens but this time around an inflation tax was imposed on the entire world. In 1970-1971 foreign governments were demanding repayment for their dollars in gold, which caused the U.S. Government to default on August 15, 1971 by severing the link between the dollar and gold. This was an act of bankruptcy by the U.S. Government as it had extracted an enormous amount of economic goods from the rest of the world, with no intention or ability to return those goods, but the world was powerless to respond. The world had been taxed and it could not do anything about it. Therefore, the U.S. became an Empire.

Since, America sustains it Empire by continuing to tax the rest of the world. The United States must force the world to continue to accept ever-depreciating dollars in exchange for economic goods and to have the world hold more and more of those depreciating dollars. The economic reason to for the world to hold dollars since it could not buy back its dollars with gold was controlling the purchase of oil. Since 1972-73, the empire ensures the world only accepts U.S. dollars for oil. Because the world had to buy oil, it needs U.S. dollars. Since the world uses ever increasing quantities of oil at ever increasing oil prices, the worlds demand for dollars increases. Dollars are not exchangeable for gold but remain the only way to buy oil.

The economic essence is that the dollar is backed by oil. As long as that remains the case, the world has to accumulate increasing amounts of dollars because they needed dollars to buy oil. As long as the dollar is the only acceptable payment for oil, its dominance in the world is assured. The American Empire can continue to tax the rest of the world. If the dollar loses its oil backing our Empire may cease to exist. Imperial survival dictates oil is sold only for dollars. Oil reserves remain in sovereign states that are not strong enough, politically or militarily, to demand payment for oil in something else. Political or military means will be used to change any minds if a different payment is demanded.

A man who last demanded Euro for his oil was Saddam Hussein in 2000. At first, his demand was met with ridicule, later with neglect, but as it became clearer that he meant business, political pressure was exerted to change his mind. This caused the recession of March 2001. Countries, like Iran, wanted payment in other currencies, most notably Euro and Yen, the danger to the dollar was clear and present, and a punitive action was in order. We defended the dollar that supports the American Empire. We set an example, anyone who demanded payment in currencies other than U.S. Dollars will be punished. We went into Iraq to defend our Empire. Two months after the United States invaded Iraq, the Oil for Food Program was terminated, the Iraqi Euro accounts were switched back to dollars, and oil was sold only in U.S. dollars. No longer could the world buy oil from Iraq with Euro.

The current home values relative to inflation adjusted currency are the highest in history. Other housing booms have been an offshoot of excess profits during the roaring 20's, specifically Florida's growth and development, at the end of the World War II when property loans expanded to home loans, and then expanded to giving loans on mass produced items such as washers and dryers. The later increasing prices in the 70’s and 80’s were related to economic booms. However, the latest housing market value has no such foundation.

Increasing dollar circulation causes currency inflation reflective of the outstanding debt, as that is how the privately owned Federal Reserve Bank operates. The government quit providing the M3 numbers on the date that IRAN had planned to start using another currency to sell its oil and has not released it since.

Global inflation has been controlled by the government by allowing US consumers to borrow it so its circulation is taxable. First bankruptcy was overhauled then the rates were cut to entice internal borrowing. Cars had 0% interest t rates. Home lending was whatever amount you wanted (i.e. ads for 125% of value). Tons of currency entered the US market. Cars quit selling, and then houses quit increasing in price, now hedge funds, which are unregulated, are acquiring companies using debt. Solid companies have to borrow massive amounts internally or become takeover targets.

USA has spent $50,000,000,000.00 on rebuilding Iraq, not including costs of the war or troop support. Who is left to borrow next? Wars have always been won by the country that can best liquate its assets.

The Iranian government, which has over $53B dollars, is trying to use the Iranian Oil Bourse. This leads to the destruction of the financial system underpinning of our Empire as the Bourse is based on a euro-oil-trading mechanism that implies payment for oil in Euro. This circumvents the U.S. dollar by allowing oil to be bought or sold for the Euro. Europeans will not buy and hold dollars needed for oil if they pay with their own currencies. Adoption of the Euro for oil transactions provides the European currency with a reserve status that benefits Europeans at the expense of Americans. Chinese and Japanese will deplete dollar reserves and diversify with Euros that protect against the threat of depreciation of the dollar and spend remaining dollars without replenishing its holdings. Russia's economic interest is to adopt the Euro since the bulk of their trade is with European countries, oil-exporting countries, China, and Japan. Russians are buying gold with depreciating dollars. Arab oil-exporting countries will diversify its rising mountains of depreciating dollars with European countries who prefer the Euro for its stability and to avoid currency depreciation.

Britain has a strategic partnership with the U.S. The two leading oil exchanges are New York’s NYMEX and London’s (IPE) International Petroleum Exchange both of which has London IPE interests and it’s British Pound. The British did not adopt the Euro namely because the London IPE would have had to switch to Euros which would destroy the currency of a strategic partner. The Iranian Oil Bourse has the interests of the Europeans, Chinese, Japanese, Russians, and Arab who will adopt the Euro and seal the fate of the dollar. Americans cannot allow this to happen. The Iranian Oil Bourse would collapse the dollar, accelerate inflation, and increase U.S. long-term interest rates driving deflation or hyperinflation. If the Fed raises interest rates it will start a major economic depression, a collapse in real estate, and an implosion in bond, stock, and derivative markets, with a total financial collapse. Or, inflation where long-bond yield sinks the financial system in liquidity and hyperinflation destroys the economy.

The sinews of war are infinite money. – Cicero

First paper money issued in the Western world circulated in 1690 Massachusetts to pay for troops to fight against the French in King William's War (Nine Years' War, Europe). In 1729 Ben Franklin published, "A Modest Enquiry into the Nature and Necessity of Paper Currency". Ever hear the old quote, "Not worth a Colonial?"

Risk and Uncertainty

Uncertainty is measurable as a probability when all outcomes of certainty are defined. A probability of certainty is uncertainty, the entropy. Uncertainty is the randomness among certain outcomes.

Uncertainty is distinct from risk. If risk is a quantity susceptible of measurement, then risk is a measurable uncertainty. Risk that is un-measurable is not in effect an uncertainty at all but a result of any number of random unknowns.

Risk is defined as uncertainty only when it can be based on (quantitative) probability. It must by definable with an uncertainty, or variability of returns measured by a standard deviation of returns around a mean.

Risk can not assign such a probability if it can not be reduced significantly by attempts to gain all information about the phenomena in question and their causes or a defined uncertainty.

Risks of stock investments guess at immeasurable possibilities.
Risks of games of chance are uncertain at measurable probabilities.

Probabilities of measurable risks exactly predict every uncertainty in a game chance.
Randomness of real-world risks use mathematical models that attempt to predict immeasurable estimates of unknown situations as if it were a probability in a game of chance. The result is occasionally a good example of Feynman’s Cargo Cult Science.

Investing vs Speculation vs Gambling

Investing is an attempt to forecast the yield of assets in the market Speculating is an attempt to forecast the psychology of the market Investor is a name given to passive investors Speculation is the name of an active investor >Investment is a name given to a successful speculation Speculation is the name given to a failed investment Investment infers an attempt toward a preservation of capital Speculation infers an attempt toward enhancement of fortune Investment attempts to prevent a lot of money from becoming a little Speculation is an effort to turn a little money into a large fortune Investment gone badly is called a speculation Speculation gone badly is called a gamble Investment involves less risk but is a form of a speculation Speculation involves more risk but is a form of investment Gambling involves the deliberate creation of new risks Speculation involves the assumption of the inevitable risks Uncertainty can describe risk that can be exactly measured >Risk is an uncertainty only when it can be exactly measured Investment or speculation involves immeasurable risk Gambling involves risk with a measurable uncertainty Psychologies of speculation and gambling are indistinguishable Psychology with an appeal to fortune is considered a dangerously addictive habit Financial risk can be uncertainty only with inside information Gmax = R suggests inside information equals the rate of return Law of large numbers is misunderstood by gamblers and investors Investment < speculation < reckless gambling Investment with borrowed money is always speculative Speculation is considered riskier than investment Gamblers create a risk Speculators assume a risk Average Return of investors = Average Return of stock market Subtract one from the other and you get Ave Ret of active investors Active Investor Average gains = Active Investor Average losses Average Return of Passive investors = Average Return of Active Investing is a zero sum - (mgt expenses + brokerage fees + taxes) Prediction of risk = immeasurable certainty = any and all gain Gamblers uncertainty can be measured risk with a positive expectation Investor’s risk has an empirical evidence of positive expectation A bet on stocks shows empirical evidence of a higher average return A bet in an attempt to take advantage of those with less information Favorable bets will be called investing Unfavorable bets constitutes gambling Investing, speculating, and gambling each represent bets that attempt to gain advantage of or take from one another. A positive expectation outcome is proportional to a difference in information. However, money is easily lost with a mathematical advantage due to the randomness of these outcomes. Investing is a positive expectation attempt to gain an empirically evident higher ‘than guaranteed savings’ average return. Speculating is an attempt to defy odds in order to gain an amount greater than the average return of the market. Gambling is an attempt to defy odds of outcomes with negative expectations. Speculating and gambling can have a positive expectation that is proportional to insider or privately held information.

People can't multitask

People can't multitask. Some mind's thought processes differ when people are thinking about the same thing. If he uses his brain to count to himself, he can not talk. However someone may visualize a tape with numbers on it going by and talk. He either can’t count to himself and talk or he can’t watch a metal tape and read. In summary, you can externally and objectively test how a persons brain works by observing what a person can and can’t do while he counts.

Basketball and Gambling

A basketball player's chance of making his shot is based on his athletic skill. His percentages increase with his advantage but has nothing to do with the results of his or her previous shots. Randomness-challenged minds give real-world errors of judgment that lead to the widespread belief that a basketball player has a hot hand when he makes a random number of consecutive shots yet the frequency or duration of the streaks never exceed chance fluctuations. Of course, give a large enough sample size it is likely that some unspecified player somewhere does have an inordinately lengthy lucky streak via a chance manifestation of regression to the mean. In any case, an inference engine such as one's mind does not necessarily result in the most acurate results. Man has a number of misleading beliefs about random events that are applicable to his assumptions of randomness. Randomness is neither clearly defined nor understood. Even random number generators merely use some belief system to create an array of events random. People take incredible amounts of risk in the stock market full of uncertainties and cheating opportunities but call it investing but consider gambling risk. Mathematically speaking, gambling should be easier to tolerate as risk numbers are known within a high degree of confidence and losses correspond to a well-defined chance where skill actually matters. An allusion is to treat small samples of information drawn at random from a large population similar to one another and representative of the entire population. Statistically significant relationships between two variables that emerge from 20 individuals may not reappear from an additional 10 individuals, as the odds of this happening are less than 50-50. A mind thinks on a small random sequence where extended runs of one value or another inevitably cancels each other out. The gambler's fallacy reveals one will assume that a run of heads in a sequence of random coin flips will give way to a corrective series of tails to result in roughly equal numbers of heads and tails overall. Random sequences of two values alternate frequently from one value to another may contain extended runs of a single value. A sequence of "HHTTHTHTTH" as no better example of randomness than "THHHHHHHT," as the chances of observing either sequence is the same as any other of equal length.