Probability theory is an important area of mathematics, with many applications to real life. It is absolutely central to learning how to play lotteries "intelligently". It is not necessary to learn the maths provided you can accept the simple facts presented here.
Probability will not dance to your tune no matter how much you wish it would. Probability 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 person 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 kiss your lottery ticket before it is handed over the counter.
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 people still allow irrational thoughts that something 'must be due to happen' to affect their thoughts. The smart lottery player, 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 occuring 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 1 chance in 1,024. But if we then get five heads in a row, the probability of the next five tosses coming up heads isn't 1 in 1,024, it is 1 in 32.
This is because the slate is cleaned, so to speak, after each toss of the coin. 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?)
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 49 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 birthdate, or whatever, as some special mathematical 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.
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.
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