Our resident expert on probability based attacks is Dr Tristan Barnett, who discusses various ways to win using mathematical techniques in his Probability Based Attacks section of Smartgambler. The page you are on gives an introductory overview of probability theory.

Probability theory is an important area of mathematics, with many applications to real life. It is absolutely central to gambling. It is not necessary to learn the math, provided you can accept the simple facts presented in this segment.

Probability will not dance to your tune. In Zen, the practitioner learns not to go against the flow. Probability too is a great ally but a terrible foe. Don't fight it. It is an area of ignorance for a surprisingly large number of people and is rife with popularly accepted myths and fallacies.

A smart gambler understands that blind chance does not play favourites, does not recognize 'lucky numbers', has no memory and no personality. It doesn't care whether you tap a card before looking at it or what amount you have placed on an outcome.

Everyone should know that if you toss ten heads in a row it is still 50/50 whether it will be another head, but many punters still allow irrational thoughts that something must be 'due to happen' to affect their gaming. The smart gambler, seeing ten heads in a row, would back heads again just in case there is a bias that is not apparent!

Confusion sometimes arises because of the different likelihoods of a given event occurring before it starts, compared to part of the way through the event.

Take the example above. Before you toss a coin you can say with certainty that the probability of getting ten heads in a row is exactly 1/2 * 1/2 * 1/2 * 1/2, etc (keep multiplying ten times) which comes to one chance in 1,024. But if we throw five heads in a row, the probability of the next five tosses coming up heads isn't one in 1,024 of course, it is one chance in 32.

This is because the slate is cleaned, so to speak, after each toss. Chance has no memory. (Even if it did, how would we know that somewhere else in the world it hadn't just come up five tails in a row?)

Casinos generously pander to the ignorance of punters by providing little pads and pencils to keep track of utterly meaningless sequences of Roulette numbers that have occurred. The money spent on ridiculous items such as this could be better given back to punters by providing slightly better odds or cheaper bar prices.

Random number sequences

Are the chances of 1,2,3,4,5,6 coming up in a Lotto draw any less than a so called 'random' sequence? Of course not! The chances of getting 1,2,3,4,5,6 out of a possible 40 balls is very small indeed, but it's exactly the same probability as any other six numbers.

The fact that some humans consider numbers one through six, or a birth date, or whatever, as some special numerical sequence, is completely lost on the balls themselves as they roll out of their cage. Any combination of numbers in a random selection such as Lotto is equally as likely to occur as any other. Given that chance has no memory it is also clear that an analysis of the frequency with which past numbers have fallen, cannot help to predict future numbers.


Lotto is a bad game to play purely in terms of percentage returns, you are paying for a pleasant dream really, but there are ways of maximising any prospective returns based on the point raised above. (See Lotto section)


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