That a horse – any horse – would win the first leg, The Kentucky Derby, was a certainty (for these purposes), so the true probability of a horse winning the Triple Crown was the probability that a horse which HAD WON the Kentucky Derby then won the Preakness Stakes and the Belmont Stakes. The probability of this happening in any given year was not the multiplied probability (perhaps derived from race-day odds) of a given horse in the three separate legs, let alone the implied probability that one specific horse from the tens of thousands bred each year would pull off the feat. American Pharoah, in 2015, was the first horse to manage this feat since Affirmed in 1978: a magnificent effort by the horse himself but nowhere near as improbable an event as stated in some quarters. This can be illustrated in horse racing terms by reference to the US Triple Crown, which is the achievement of winning the Kentucky Derby, Preakness Stakes and Belmont Stakes with the same horse. That is, the probability is 0.1666 again. It is a certainty that a number – any number, not a specified number – is thrown with the first dice, so it simply becomes that (probability = 1) multiplied by 1/6 (probability = 0.1666) that two unspecified numbers are thrown consecutively. One aspect of probability which often trips up the novice (and even sometimes the expert) is that the probability of throwing two consecutive identical numbers is NOT the same as 0.0277. The calculation of this is 1/6 multiplied by 1/6 = 1/36 or 0.0277 recurring in terms of probabilities. This is known as a “complementary event” in probability.Įvents may be independent, rather than complementary, such as the probability of throwing two consecutive sixes, again assuming a fair dice and true independence. It follows that the probability of any number OTHER THAN six showing is this second probability (1, or certainty) minus the probability of throwing a six. The probability of an even number (2, 4 or 6) occurring would be 3/6, or 0.5, while the probability of ANY number showing, given that we throw a fair dice, is 1 (certainty) in this context. In the language of probability, this would be expressed – on a scale from 0 (no chance) to 1 (certainty) – as 0.1666 recurring.
If you want to throw a six with a dice (assuming a fair dice and fair environment) then the probability of this occurring is defined as the number of favourable outcomes divided by all possible outcomes, or 1/6. The number of individual outcomes of tossing a coin or throwing a dice is finite. The number of possible outcomes of a horse race is almost infinite if you include everything that might happen in that race and not just the order at the finish. It is easiest to illustrate the basics of probability by first reducing the number of possible outcomes. But a basic grasp of probability theory will not hinder and may well help in certain contexts. Thinking in terms of probabilities is more important to a punter than knowing probability theory in detail.
The outcome observed is just one of these.Īs every event (such as a race or a performance) will have a subtly different context, it is only by striking bets a large number of times that we may approximate the effectiveness of an overall betting approach.
There is only one outcome to an event, but, in theory, if you repeated that event many times you would get a multitude of outcomes.
It should be clear from some of what has gone before in The Timeform Knowledge that the good bettor should think in terms of probabilities rather than in terms of certainties. The latest edition of The Timeform Knowledge gives an overview of basic probability theory. By Simon Rowlands - published 20th September 2015
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