The Science of Luck – How Probability and Quantum Mechanics Shape Gambling

Luck helps us make sense of life’s seemingly unaccountable events; yet can we influence or create our own good fortune?

Researchers have long studied the science of luck. They’ve discovered that how people frame their experiences–whether looking back on what went right or wrong–can profoundly impact their own luck.


Probability can be defined in scientific terms as an expression of how likely an event will take place; typically expressed as a percentage. The higher its probability value is, the more likely that event is. Probability plays an important role in many gambling games but has many different interpretations both subjectively and mathematically.

Blaise Pascal and Pierre de Fermat began exchanging letters regarding gambling issues around 1500, which eventually formed the basis of probability theory. But prior to their correspondence on this subject matter, researchers such as Gerolamo Cardano published his book entitled Games of Chance in 1470 – this subject had already been explored for over 100 years before this.

His classic definition of probability describes a ratio of favorable cases to all possible cases; while this definition can be useful and generalized, it has some shortcomings; thus a popular alternative definition refers to frequentist probability whereby probability is defined as the relative frequency with which outcomes have occurred in numerous trials of an experiment.

Quantum Mechanics

Quantum mechanics is a field that explores matter and light on an atomic level, yet its foundations contain unexplained features; such as being impossible to measure a quantum system without disturbing it. It has proven highly useful in practical applications but its foundations remain mysterious – for instance it seems impossible to accurately measure quantum systems without disturbing them!

But that is exactly what researchers at MIT and Caltech have accomplished, showing through experiments that quantumly entangled systems may give blackjack players a small edge against dealers.

Scientists used a machine that produced photons with either vertical or horizontal polarization state. After passing through a half wave plate that modulated vertical and horizontal states simultaneously, this photon landed either in Bob’s box (his detector; B) or Alice’s box (her detector; A).

As long as both parties are honest and adhere to the rules, they can create an impartial gaming machine (GM). By selecting appropriate parameters for this GM, they can ensure their average gain exceeds certain thresholds.


Randomness is a cornerstone of casino games and any process in which an outcome cannot be predicted from previous events. Randomness also provides the basis for algorithms used to protect passwords against hackers and software that checks whether slot machine games are fair.

Chance and randomness may seem distinct concepts; however, their definitions can often blur in real life.

Randomness can be defined simply as any event or set of events which does not influence future outcomes in any systematic manner, such as with a standard six-sided die roll or coin toss. Furthermore, computer simulation results do not “remember” previous trials and alter them each time new trials start up – an essential quality for systems which need to be fair like politics, military draft lotteries and lottery-style allotment of seats on governing committees. This kind of randomness should be valued as it allows systems like these in an objective manner.

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