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The Timeform Knowledge: Basic Probability


The latest edition of The Timeform Knowledge gives an overview of basic probability theory.

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.

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. The outcome observed is just one of these.

As 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.

Thinking in terms of probabilities is more important to a punter than knowing probability theory in detail. But a basic grasp of probability theory will not hinder and may well help in certain contexts.

It is easiest to illustrate the basics of probability by first reducing the number of possible outcomes. 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. The number of individual outcomes of tossing a coin or throwing a dice is finite.

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.

In the language of probability, this would be expressed – on a scale from 0 (no chance) to 1 (certainty) – as 0.1666 recurring.

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.

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. That is, 1 minus 0.1666, or 0.8333 recurring. This is known as a “complementary event” in probability.

Events may be independent, rather than complementary, such as the probability of throwing two consecutive sixes, again assuming a fair dice and true independence. The calculation of this is 1/6 multiplied by 1/6 = 1/36 or 0.0277 recurring in terms of probabilities.

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.

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. That is, the probability is 0.1666 again.

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. 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. 

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.

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.

Given that a horse which won the Kentucky Derby would, barring injury, almost certainly contest the second leg, the Preakness Stakes, at a short price, and then, if it won that second leg, contest the third leg as a dual classic winner at a very short price, the probability clearly becomes much less.

Perhaps something like 1 (certainty) multiplied by 0.28 (approximately 5/2 in terms of odds) multiplied by 0.4 (6/4 in terms of odds), which is 0.112, or around 8/1 (though others would doubtless assign different probabilities).

You might expect the US Triple Crown to be won about once a decade. It has been won 12 times in the last 100 years and the “famine” between 1978 and 2015 (which included several near misses) can be seen as unrepresentative.

Moving from the throwing of dice (an “aleatory” activity for those who like to know these things) to the uncertainty and subjectivity of horse racing has taken us into the far more interesting world of subjective and conditional probabilities.

In the above example, the probability of a horse winning the Preakness given that it had won the Kentucky Derby might be 0.28, and the probability of a horse winning the Belmont given that it had won the Kentucky Derby might be similar. But the probability of a horse winning the Belmont given that it had won the Kentucky Derby AND the Preakness will nearly always be greater.

The last-named scenario includes additional information, with probabilities clearly being influenced by the hypothetical chain of events. That is why bookmakers quote separate odds about conditional or contingent events, such as a horse winning both the 2000 Guineas and The Derby.

Probability Theory – not to mention common sense – shows that they are right to do so.


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PERTH 15:25

Wednesday 24 April
Brian Hughes silk Brian Hughes
Gavin Patrick Cromwell, Ireland hot trainer
Sean Bowen silk Sean Bowen
Gordon Elliott, Ireland
3. INSTIT (FR) 160
P. Townend silk P. Townend
W. P. Mullins, Ireland
Go to full race



1st Alicia Perkins silk 5. Q TWENTY BOY (IRE) 25/126
2nd Lewis Edmunds silk ½ 9. HIGHER LAW (IRE) 11/26.5
3rd Elisha Whittington silk nk 11. REBEL REDEMPTION 40/141
J: Alicia Perkins (7)  
T: Mark Usher  
12 ran. NRs: 1 


1st Joanna Mason silk 7. MUMCAT 7/24.5
2nd William Cox silk ns 8. MIDNIGHT FLAME (IRE) 22/123
3rd Rossa Ryan silk ns 6. PORFIN (IRE) 3/14f
J: Joanna Mason  
All 13 ran.


1st Rossa Ryan silk 4. COVERT LEGEND 10/34.33
2nd Rob Hornby silk ¾ 8. PLUMETTE 5/16
3rd Luke Morris silk 1 2. COOLREE (IRE) 11/43.75f
J: Rossa Ryan  
9 ran. NRs: 1  9 


1st Oisin James Orr silk 1. EVALUATION 4/15
2nd Luke Morris silk nk 5. MISS CYNTHIA 9/43.25f
All 6 ran.


1st Declan McDonogh silk 13. JOHANNA WHITTY (IRE) 11/26.5
2nd C. T. Keane silk ¾ 10. NEPTUNES STAIRCASE (IRE) 13/82.62
3rd C. Stone-Walsh silk ½ 7. CUT THE ROPE (FR) 18/119
12 ran. NRs: 12 


1st William Carson silk 1. INTERESTNPENALTIES (IRE) 13/27.5
2nd Rossa Ryan silk 1 2. AMROON 2/13f
3rd Aidan Keeley silk 2 6. TENYATTA (IRE) 9/43.25
T: Tony Carroll  
9 ran. NRs: 8 


1st Ben Martin Coen silk 5. CHEEKY WINK (IRE) 7/18
2nd G. F. Carroll silk ½ 4. TOTAL LOOK (FR) 10/111
3rd D. B. McMonagle silk 2 3. SOUL OF SPAIN (IRE) 1/41.25f
All 9 ran.


1st Kevin Stott silk 3. BEVERAGINO (IRE) 11/102.1f
2nd John Fahy silk 6. SMOULDERING 7/18
J: Kevin Stott  
T: Michael Bell  
All 6 ran.


1st William James Lee silk 13. ANNEXATION (FR) 13/27.5
2nd Wesley Joyce silk 1. DUKE OF LEGGAGH (IRE) 10/34.33f
3rd C. D. Hayes silk ½ 5. A SHIN UNDINE (IRE) 33/134
4th Ben Martin Coen silk 3 4. SIXPACK 6/17
17 ran. NRs: 18  19  20 
Go to Horse Racing Results