Understanding Math of Expectations Differentiates Gambling from Calculated play

``Think of how stupid the average person is, and realize half of them are stupider than that.” George Carlin, US Comedian and Actor

Last week, I’d been posed a wily question at my blogsite on whether, given my present outlook, what constitutes a calculated play and a gamble?

I’d like to share to you my response. We are living in a statistical world of frequencies and probabilities such that the impacts or effects of our choices could be actually be measured by certain available variables during the time of reckoning. This is known as the concept of the mean (also called average or expectations).

Because of the complexity of the structural makeup of the financial markets, in most circumstances the profusion of variables could lead a participant to overlook certain variables or to overemphasize on some, given one’s innate biases. And this leads to what we may call as asymmetry.

In the financial playing field there is what you call an asymmetry of odds and the asymmetry of outcomes. Asymmetry in odds suggests that the distribution of probabilities is not a level 50-50% but with one aspect of the probability higher or greater than the other, while asymmetric outcomes mean that the payoffs are not the equal.

Let me ‘frame’ you a case which I lifted from mathematician Nicolas Taleb ``Fooled by Randomness”...

``Assume I engage in a gambling strategy that has 999 chances in 1,000 of making $1 (event A) and 1 chance in 1,000 of losing $10,000 (event B).

Event Probability Outcome Expectation

A 999/1000 $1 $.999

B 1/1000 -$10,000 -$10

Total -9.001

``My expectation is a loss of close to $9 (obtained by multiplying the probabilities by the corresponding outcomes). The frequency or probability of the loss, in and by itself, is totally irrelevant; it needs to be judged in connection with the magnitude of the outcome. Odds are that we would make money by betting for event A, but it is not a good idea to do so."

What Mr. Taleb suggests is that most people (including those with advanced degrees or MBAs) would be enticed to act on the winning odds (Event A) due to the inordinate focus on the frequency despite the understanding that an occurrence of a low probability event may affect a greater deal relative to the outcome than the combined wins. This blatant omission, despite the mathematical fact, is likely to lead to the decimation of one’s portfolio.

In other words, the difference between a calculated play and a gamble is matter of understanding the ‘concept of mean’ or of knowing one’s profit or loss expectations arising from the mathematical computation of events as determined by its probabilities and its potential outcome.

Edward Lefévre who wrote on behalf of legendary trader Jesse Livermore, in Reminiscences of A Stock Operator, notes of the importance of understanding probabilities even as a trader, quoting Mr. Lefévre at length,

``Observation, experience, memory and mathematics—these are what the successful trader must depend on. He must not only observe accurately but remember at all times what he has observed. He cannot bet on the unreasonable or on the unexpected, however strong his personal convictions may be about man’s unreasonableness or however certain he may feel that the unexpected happens frequently. He must bet always on probabilities—that is, try to anticipate them. Years of practice at the game, of constant study, of always remembering, enable the trader to act on an instant when the unexpected happens as well as when the expected comes to pass.”

Applied to the present risk environment, this is where, in my view, the probabilities of an outsized returns are greatly less than the potential losses until mitigating signs say otherwise.