Author’s Note: As mentioned in my Publisher’s Note, our next book History of the World from a Gambler’s Perspective by Mason Malmuth and Antonio Carrasco will be published next month. Many have been asking what exactly is this book about. To help answer that, here are two excerpts.
Definitions
Since this is not a statistics text book, we’re going to stay away from mathematical equations and mathematical rigor. However, we do need a few ideas from the world of statistics for what follows to make sense, and to lead us to the proper conclusions. But these definitions will be written so that (hopefully) anyone should be able to understand them.
Expectation
Expectation, sometimes written as EV for expected value, is exactly what you think it is. If you have a job that pays (before taxes) $1,000 per week, your expectation is to make $1,000 a week. If you need to cross a neighborhood street, your expectation is to get to the other side.
But expectation doesn’t always have to be positive as it is in the above two examples. For instance, instead of crossing a neighborhood street, if the task at hand was to cross a busy freeway while blindfolded, your expectation would be to get run over which is certainly a negative outcome.
As another example, suppose you’re someone who likes to go to a casino and play the standard slot machines. As with the last example, since the house has a built-in edge on these machines, your expectation is negative. And if you’re foolish enough to play them long enough, you can expect to lose all your money.
Variance and The Standard Deviation
Variance is a statistical measure of how much your result can vary from the expectation. You can also view it as a statistical measure of luck (which is, of course, important in gambling). Statisticians have specific formulas for calculating the variance or estimating the variance. However, those formulas are beyond what is needed for this book.
In addition, and this is an important idea, statisticians often look at the square root of the variance, which is known as the standard deviation. They do this because there are a number of well-studied properties associated with the standard deviation, and in this book, we’ll often use these two terms interchangeably.
To better understand variance, let’s look at a few examples. First, let’s go back to that job which paid $1,000 a week. Since you get your paycheck every week, and it’s always $1,000, the variance (and standard deviation) is zero.
Now let’s suppose you own a business where you average making $1,000 a week. Notice that the expectation for both the job and the business is $1,000 per week, but with the business, you don’t make exactly $1,000 every week. Thus, while you may average $1,000 per week, since you won’t make exactly that amount every week, these differences are measured by the variance which is now no longer zero but is instead a positive number. (Also notice that variance can’t be negative.)
Let’s look at one more example. Suppose you’re a poker player but not a very good one. Furthermore, let’s suppose your expectation is to lose $40 per hour and your standard deviation is $500 an hour — this can be typical results for a mid-stakes player who doesn’t play well but likes to sit in games with fairly tough opposition. What does it mean?
First, every hour that you play, expect to have $40 less than when the hour started. But a $500 per hour standard deviation can easily distort your results in the short run.
The reason for this is that most statisticians agree that your results for any given hour will be within 3 standard deviations of your expectation (which in this example was to lose $40). This means you can occasionally have an hour where you have done 3 standard deviations better than -$40, or $1,460, and you can occasionally have an hour where you do $1,500 worse than -$40, or -$1,540.
There’s also one other property of the standard deviation we want to mention. It’s the idea that the standard deviation is proportional to the square root of the number of events that occur while the expectation is proportional to the number of events that occur.
Putting this in simpler language, when looking at a small number of events where the standard deviation is large per each event relative to the expectation, then expect the standard deviation to dominate your results. However, over time, after enough events have occurred, since the standard deviation is proportional to the square root of the number of events and the expectation is proportional to the number of events, the expectation should dominate your results.
This means that if you’re that losing poker player we mentioned above, even though you’ll likely have some winning nights where you do quite well, eventually expect to be an overall loser. Put another way, while it’s nice to be lucky, it can’t be relied upon. Is this really true?
Gambling
Now we have the tools to define gambling and we can say that gambling occurs when the standard deviation is large relative to the absolute value of the expectation.* For instance, suppose there was an event which had an EV of 10 and a standard deviation of 100. We would conclude that gambling took place since it would be difficult to predict the outcome of the event with much certainty.
On the other hand, if these numbers were reversed and the expectation was 100 while the standard deviation was 10, we can conclude that gambling did not occur. That’s because the outcome can now be well predicted, except for a small variation, with much certainty.
This is a very important idea for understanding this book. If it’s not clear, please read the above two paragraphs again.
Finally, for completeness, there’s one other aspect of gambling we want to cover here. It’s the idea that lots of gambling events, when combined, are no longer gambling. Remember, we already mentioned that the standard deviation is proportional to the square root of the number of events and that the expectation is proportional to the number of events, and after enough time (or events) have passed the expectation will begin to dominate the standard deviation, and when this happens gambling is no longer taking place.
Here’s an example. Suppose you’re a poker player and your hourly standard deviation is much larger than (the absolute value) of your hourly expectation — typical for most poker players. This means that when you go to your favorite poker room for a playing session, you’re gambling.
But if you’re a regular poker player and over the course of time have lots of playing sessions, which means lots of hours playing poker, expect your results to dominate your fluctuations, and you won’t be gambling anymore.
This sure seems like a strange conclusion that you can gamble most every night and eventually not be gambling. But that’s the way the probabilistic world of gambling works and is an example of how probability theory can be counterintuitive.
However, again, this is only included for completeness, with one possible exception. In this book, we’ll mainly be looking at events that only happen once. Also, we won’t be putting values on the expectation and the standard deviation. So, you won’t have to worry about that. But we’ll be looking for situations where it was clear that the standard deviation was much larger than the absolute value of the expectation, meaning that gambling took place.
Trotsky to the Rescue
Gambling that Pragmatism was Superior to Bolshevik Ideology
Two – 12: Leon Trotsky
In Oct. 1917, after the failure of the Kerensky Offensive, the Bolsheviks take over the Russian government. Their leader is Vladimir Lenin with second in command being Leon Trotsky, whose real name was Lev Davidovich Bronstein.
But shortly after the Bolshevik takeover, civil war starts and it’s the White Russian (Democratic forces) versus the Red Russians (Bolshevik / Communist forces). And to lead Soviet Russia in the Civil War, Trotsky becomes the People’s Commissar of Military and Naval Affairs in March 1918.
But there was a problem. “Many Bolsheviks (according to Marx) assumed there would be no need for an army under socialism.” In fact, “‘Orthodox Bolsheviks’ thought the Red Army should rely on volunteers — conscription was a detested relic of the czarist past.”
But after four years of World War I, where the Russian people had suffered greatly, very few of them wanted to volunteer for the army. So, Trotsky knew that this wouldn’t work.
To help counter the problems in the army, Trotsky gambled on conscription to take advantage of the Soviet overwhelming superiority in manpower. And, as just mentioned, conscription was an idea that the original Bolsheviks objected to since they felt that Bolshevism should have a voluntary component.
But Trotsky did more than this since he needed to quickly create an effective fighting force and he went ahead and used former Czarist officers. This went against what the Bolsheviks wanted which was to have the workers elect their own officers since veteran officers were often politically unreliable. In addition, the use of Czarist officers also attracted fervent opposition from within the party. But to counter this, political commissars were brought into the army, and their purpose was to ensure “the loyalty of military experts (mostly former officers in the imperial army).”
Next, Trotsky reintroduced military discipline (back into the army), including execution when it was felt that extreme examples of discipline were needed. Of course, this also went against Bolshevik ideology, but it was necessary to defeat the White Russians and Lenin backed Trotsky.
And the result was that the Red Army became much better organized as well as a competent fighting force. Stated a different way, what Trotsky did was to proclaim workers “liberty and self-determination” while subjecting them to corporal discipline, including execution, at the hands of Czarist officers.
The gamble here should be obvious. Trotsky gambled that to win the Russian Civil War, the Bolsheviks would have to accept non-Marxist ways inside the army and that they would accept the idea that a “democratic army” was something for the future. Notice that the use of military specialists (former officers from the Czar’s old army), harsh discipline, and conscription were not Bolshevik ways, but they were necessary to win a difficult war and to preserve socialist power.
Thus, Trotsky was gambling that the more extreme Bolsheviks would accept an army that had similar characteristics to that of the Czar’s army (except that it would be a far superior fighting force), and at the 8th Congress in Moscow, on March 18, 1919, a compromise was reached which was essentially a victory for Trotsky’s position. It was understood that non-Bolshevik ways would be needed to make sure that the Bolsheviks and their form of government would be there for the future.
Trotsky now had won his gamble and Soviet Russia survived as the Red Army was able to defeat the different White Army forces. And the result was that when the Russian Civil War ended in 1922, the Soviet Union was formed, and it lasted until 1991.
* The absolute value of a number is the distance that number is from zero. So, the absolute value of negative 10 is positive 10.
