The enigmatic nature of probability

The concepts of chance and probability are so common in our everyday life that most people assume they understand them completely. This is far from the truth. Probability and chance are the most mystical concepts in science and fall far short of any rational explanation.

Yet, for all the mystery surrounding probability and chance, it has been the single most important concept to account for the rapid advance in science, technology and civilisation in general throughout the twentieth century.

My first serious encounter with probability came as a preliminary to lectures on the physics of semi conductors. It was explained to us that the flow of electrons over an energy gap was through a proportion of the electrons randomly acquiring sufficient energy to cross a voltage barrier. The higher the voltage the greater became the number that could randomly acquire sufficient energy to jump the gap.

To my student mind, what happened inside a transistor was far less interesting than the implications of the theory. It was telling me that I can could make sense out of apparent disorder and by so doing create my own luck.

It didn't take long for me to start applying this concept to everyday events. Straight from the lecture, I produced a pack of cards to create a simulated horse racing game. The idea, as I explained to my fellow students, was that this theory could be used to win money. I shuffled the deck and then started to deal out the cards, placing hearts in one row, spades in another and the diamonds and clubs in other rows. "The first suit to produce a line of ten cards would be the winner", I announced.

As the cards came out, the rows corresponding to the various suits changed in relative lengths. First the row of clubs was in the lead, then it was overtaken by the hearts, but, in a late spurt the spades suit produced ten spades to become the winners of the race.

Now came my cunning money-making plan. I'd understood that the way in which probability and chance worked was to even things out. It had been explained to us that if the chance of something happening was the same to all objects then after a sufficient number of chance happenings, the event would happen to all objects about the same number of times.

It seemed obvious to me that if spades had won the first race, all the other suits would catch up as eventually they would end up with an equal number of wins due to the law of probability. Logical reasoning then told me that the chances of the spades winning in subsequent races must be less than for the other suits. With this conviction in mind, I gave odds of four to one on spades and only three to one on the other suits: encouraging the students to place bets on the suit I saw as having the lesser chance of winning.

All the other students, going purely by the statistical probability of each suit having an equal one chance in four, placed their bets upon spades. Spades won.

Not particularly alarmed, I then invited the students to let their winnings ride and I increased the odds on spades to five to one. I chuckled when they all placed their money on spades again, but, the smile swiftly left my lips when spades won for a third time in a row.

Panicking, that all the students might want to cease playing and demand payment, I raised the odds on spades to twenty to one. Everyone stayed in the game and to my relief all of them staked their winnings on the spades.

To my absolute dismay, spades won for the fourth time in a row. "One more time", I cried, and raised the odds on spades to fifty to one. By this time, the students had realised that I owed everyone so much money that I wouldn't be able to pay them anyway so they let their winnings ride once more on the spades. To my discomfort, and to the merriment of the other students, spades came up for an unbelievable fifth time.

Fortunately, all the students took it in fun and didn't insist on being paid, otherwise I'd still be paying them off today.