Non-transitive dice and where your intuition fails you

The universe has an infinite number of facts. We can’t learn and process them all, so we compensate. We learn about the universe by analogy, and by inference, and by reference:

Analogy: A comparison of two otherwise unlike things based on the resemblance of a particular aspect.
Inference: If two or more things agree with one another in some respects they will probably agree in others
Reference: The words of trusted people.

Think of the factual statement: Dogs have four legs and teeth. Spot is my dog. Therefore Spot has four legs and teeth.

Image result for crocodile

Knowing that Spot is a dog, you infer a picture of him.

You visualize details about Spot without ever having to see or hear him.

Often though, what we think of as analogy and inference can deceive us:

Dogs have four legs and teeth. Spot has four legs and teeth. Therefore Spot is a dog.


Your inference threw you off because it wasn’t a true analogy. It was a misleading “intuition.”

Because the universe is so big, the vast majority of what you “know” is based on your intuition.

Here is another example of where your intuition fails you. As you “know,” when

  • “A” is bigger than “B” and
  • “B” is bigger than “C” and
  • “C” is bigger than “D” then
  • “A” must be bigger than “D”

Right? Do you know any exceptions to this? Actually, there are many exceptions.

Here is one example. It’s called “non-transitive dice.”

Non-Transitive Dice by MathArtFun

These are not ordinary dice. As you can see that they are numbered differently.

The numbers are:

A. Blue Die: 6 6 6 6 5 5

B. Black Die: 4 4 4 4 12 12

C. Red Die: 10 10 3 3 2 2

D. Green Die: 7 7 7 7 1 0

When rolled, die “A” will beat die “B” 2/3 of the time. “B” will beat “C” 2/3 of the time. “C” will beat “D” 2/3 of the time.

And counter-intuitively, “D” will beat “A” 2/3 of the time. No one die is the greatest.

We often see non-transitiveness in sports, where the winningest teams do not always have winning records against the poorest teams. Your favorite team may win the World Series in the same season as they have a losing record against a last-place team.

Politicians repeatedly create false analogies and false inferences. President Barack Obama, in his weekly radio address, July 2, 2011, said, “Government has to start living within its means, just like families do. We have to cut the spending we can’t afford so we can put the economy on a sounder footing.”

This is misleading on multiple levels.

The federal government is Monetarily Sovereign. It has a sovereign currency, the U.S. dollar, of which it can create an infinite supply. By contrast, you and your family are monetarily non-sovereign. You do not have a sovereign currency nor can you create an infinite supply of dollars.

The federal government can pay any debt denominated in dollars. You cannot. The federal government never unintentionally can run short of dollars. You can. The federal government needs no income to pay its bills. You need income to pay your bills.

Although you have a “means,” within which you must live, the federal government does not. And, unlike you, the federal government does not need to cut spending so it can afford to spend. Even if the federal government collected zero taxes, it could continue spending, forever.

And finally, it is federal spending, not spending cuts, that grow the U.S. economy and “put it on a sounder footing.”

Obama’s two short sentences were 100% wrong, and the inferences they were meant to draw were 100% misleading.

But to the average person, they sound logical, reasonable and prudent.

Because so much of what you know is based on what seems logical, reasonable, and prudent, you have learned to trust your intuition. You will fight mightily against anything that violates your intuition, despite powerful facts supporting the opposition.

You will believe your intuition especially if it supported by comments from a leader. You might more readily believe that vaccination causes autism, and immigrants cause disproportionate crime, and global warming is a Chinese hoax, if these ideas are supported by the President of the United States.

You have been primed for these beliefs by the knowledge that many medicines cause unpublicized problems, strangers are more responsible for crime than are friends, and China is an economic foe.

Nearly every politician, economist, and media writer tells you that federal financing is just like your personal financing (so debt is a danger and living within one’s means is prudent). The brainwashing comes at you from all sides.

Add such retorts as, “There’s no such thing as a free lunch,” and “Why are you the only one who knows this,” and you have created a powerful belief system that cannot be shaken by facts.

The federal government has increased its debt almost every year for the past 80 years, yet still, you are told that federal debt is a “ticking time bomb.”

Belief is less logical than emotional. You believe what you feel comfortable believing.

If, to help you visualize Monetary Sovereignty, I show you why federal finances are very much like those of the Bank in the game of Monopoly, you may dismiss that as being unrealistic, and “just a game.”

But by rule, the financial parallels between the Monopoly Bank and the federal government nearly are perfect. In the Monopoly rules, you will find this:

“The Bank never goes ‘broke.’ If the Bank runs out of money, the Banker may issue as much more as may be needed by merely writing on any ordinary paper.”

You didn’t question that rule in Monopoly, yet the vast majority of people’s intuition questions exactly the same rule for our Monetarily Sovereign federal government.

Finally, we come to inflation and the brainwashed belief that federal money “printing” causes inflation.

Let’s say you go to the store, and you find that the price of apples has gone up. Do you immediately think, “The government is printing more money,” or more likely do you think, “There must be a shortage of apples”?

In any capitalist economy, supply responds to demand, and prices result from an imbalance between supply and demand.

If supply is less than demand, there will be shortages and price increases, upon which producers will respond by creating more product, alleviating the shortages and lowering prices.

Here is the normal sequence leading to low amounts of inflation, and then inflation moderating:

  1. Shortages develop —>
  2. Prices rise —>
  3. Production increases to meet demand —>
  4. Shortages are eliminated —>
  5. Prices fall.

This process creates the average low inflation that has been the norm for decades.

Here is the process leading to large inflations and hyperinflations:

  1. Shortages develop —>
  2. Prices rise —>
  3. Production is unable to increase sufficiently to meet demand—>
  4. Shortages continue to grow —>
  5. Prices continue to rise into hyperinflation —>

All inflations and hyperinflations are caused by shortages, usually shortages of food or energy, never by federal money “printing.”

In the following graph, note how peaks and valleys of inflation do not match peaks and valleys of federal money “printing.”

In summary, the universe contains more facts than you can absorb. You are forced to develop shortcuts that allow you to bypass the vast majority of facts and to come to conclusions about the reality around you.

These shortcuts include analogy, inference, and reference, the guidance of other people.

Despite common belief, the federal government cannot run short of dollars with which to pay its debts, and federal money creation does not cause excessive inflation (which is caused by shortages.)

And yes, the federal government easily can pay for the Ten Steps to Prosperity (below), without causing inflation.

So why not?

Rodger Malcolm Mitchell
Monetary Sovereignty
Twitter: @rodgermitchell
Search #monetarysovereigntyFacebook: Rodger Malcolm Mitchell


The most important problems in economics involve the excessive income/wealth/power Gaps between the richer and the poorer.

Wide Gaps negatively affect poverty, health and longevity, education, housing, law and crime, war, leadership, ownership, bigotry, supply and demand, taxation, GDP, international relations, scientific advancement, the environment, human motivation and well-being, and virtually every other issue in economics.

Implementation of The Ten Steps To Prosperity can narrow the Gaps:

Ten Steps To Prosperity:

1. Eliminate FICA

2. Federally funded Medicare — parts a, b & d, plus long-term care — for everyone

3. Provide a monthly economic bonus to every man, woman and child in America (similar to social security for all)

4. Free education (including post-grad) for everyone

5. Salary for attending school

6. Eliminate federal taxes on business

7. Increase the standard income tax deduction, annually. 

8. Tax the very rich (the “.1%”) more, with higher progressive tax rates on all forms of income.

9. Federal ownership of all banks

10. Increase federal spending on the myriad initiatives that benefit America’s 99.9% 

The Ten Steps will grow the economy, and narrow the income/wealth/power Gap between the rich and you.



3 thoughts on “Non-transitive dice and where your intuition fails you

  1. Excellent article as usual, Rodger! I was wondering, have you ever heard of the Louis Kelso-inspired idea known as the Capital Homestead Act? What do you think if (a modified version of) it were to be implemented in addition to the Ten Steps to Prosperity? The idea is to effectively democratize capital ownership.

    Interestingly, Louis Kelso himself opposed the idea of a UBI, while supporting this idea. Though his “usufruct” argument against UBI/EB does not really hold water if it is not funded by taxes at all (like your idea) and/or is funded by Georgist-style land value taxes and severance taxes on natural resources such as oil in Alaska (gotta applaud anyone who can squeeze the word “usufruct” into a sentence).

    Meanwhile, Milton Friedman, the godfather of neoliberalism (to use the British term for Reaganomics and Thatcherism), supported a from of UBI called “negative income tax”, while at the same time denouncing the Capital Homestead Act as “dangerous”.

    Dangerous to whom, exactly? Perhaps he feared that capitalism would fatally overdose on too much capital, and we would end up with post-capitalism.

    Personally, I think we should have BOTH the CHA and the Ten Steps. It is most likely what the late, great Buckminster Fuller would have wanted. But if I had to choose only one of these two options, I would pick the latter.


    1. Some good ideas. Not so sure about “Balanced Budget (why?),” “Zero Inflation (how?),” health care vouchers (how big?), Democratize Ownership of the Federal Reserve (counterproductive), and I really, really hate “asset-backed currency.” On balance, I don’t like it.


      1. The parts about the “balanced budget” (bad) “asset-backed currency” (a Trojan horse, if it is what I think it is), and “zero-inflation” (an impossible holy grail in the long run in a growing economy) can all be nixed IMHO, and the more nebulous parts can be clarified, of course.

        And the vouchers would of course be unnecessary if the Ten Steps were followed. I was really mainly talking about the core idea of the Capital Homestead Accounts themselves, which are modeled on the Kelsonian idea of ESOP. And that core can stand alone, and mesh well the Ten Steps, especially when the second half of the CHA dealing with taxes is also nixed as well.

        As for the Federal Reserve (which I like to call call the FERAL Reserve since it is currently effectively owned by the big private banks), step 9 of the Ten Steps would by definition fully nationalize it as well along with the private banks themselves. “Democratize” is a nebulous concept as far as banks go, of course, but banks can certainly be nationalized without overly politicizing them.


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