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Probability and Odds discussions Category - Blog

    • 21
    • st
    • December

Special note from Bob Rothman

If you’re reading these series articles,  I imagine you’re interested in a Professional approach to calculating the true winning probabilities of horses, either by deriving your own bookmakers tissue or simply trying to estimate the true odds in a race.

Constructing your own betting tissue is a highly skilled job but we will be creating a step-by-step report on the procedure of  how to do this shortly as well as discussing the subject here.  You may also wish to consider subscribing to the Lunchtime Traders’ Service, which provides betting information based on my team’s own tissue.  Check out the results and see if it’s what you’re looking for.

Enjoy the articles. Most are written by a good friend and Racing Correspondent.  He actually produced a tissue for bookmakers for 20 years and now enjoys commentating on a wide range of gambling related topics for this website.  His insights can be extremely valuable.



Calculating True Odds

IT WOULD APPEAR yesterday’s article proved controversial. Well what a surprise!

I can denigrate the prime minister, slag off bookmakers, criticise the fixture list and those responsible for its draft, bemoan the state of prize-money, but mere mention of betting patterns provokes skeletons rattling their vociferous paths out of cupboards in my direction.

To recap, I outlined a fictitious event that involved six participants in a game of Russian roulette. There was one six-shot revolver containing a solitary live bullet. The chamber was spun only once and each player was required in advance to nominate the order of play that appealed most. To add a touch of spice, one million pounds was payable to each successful and therefore surviving participant.  Is survival a question of luck or the ability to calculate the true odds?

The important component in this was the preferred order of play. The mathematicians predictably claimed it made absolutely no difference, as the odds in the favour of each player were 5/1 irrespective of the order they chose. That seemed to be the majority view. But are they the true odds?

What is interesting in this conundrum is the introduction of the Theory of Probability, which crosses swords with mathematics. Those sticking to the mathematical claim that the sequence is irrelevant are not incorrect. But they have overlooked one vital aspect.

The absolute odds against being the unlucky member of the sextet who ends up minus a head are 5/1. That’s easy to calculate and requires no advanced mathematics degree.  You have one chance in 6 of surviving hence the odds are 5/1.  However, once the game is in progress, those odds change because we are in a position to observe what has happened. The first to try his luck is playing the true odds. Irrefutably those odds are 5/1 in his favour. Survival means the odds are 4/1 in the favour of the next to fire and then, providing he dodges the fatal bullet, the odds  become 3/1 in the favour of the next to pick up the revolver. Now the remaining players are in trouble. After three successful players, only three remain and the odds of the next being a survivor are narrowing, being only 2/1 in favour. If he puts down the revolver with his head intact, two players remain facing odds of even money.  Their probability of  survival is now only 50%.This pair, who gambled incorrectly on never reaching such a cliff-hanging situation, now stare death in the face.

The true mathematician will cling to his belief that it has been a 5/1 chance all along, but of course so far down the line that is no longer the case. The only certain way to ensure you face odds of 5/1 in your favour is to fire first. Then, without question, the odds are absolute. There is no guarantee after that so, if you have deferred your choice to later in the sequence, there is always going to be a shift in your chance of survival.

Probability suggests that if a proposition contains a one-in six chance, then it is mostly likely to manifest itself in the middle of the proposed sequence of events, not at the beginning or the end. Here, the true entrepreneur, the gambler who is always seeking an angle or edge in his favour, will invariably succeed over the man who relies on statistics. To be truly successful at gambling you must be prepared to swim against the mainstream of opinion. Following the herd means you will be paid accordingly – in other words you will share your dividend with the rest of the players. You must strive to seek out overlooked factors and therefore reap the rewards of originality.

Betting is a pool. The more tickets that have the same name on them, the less the winning dividend will be should that named selection win. The object is to seize on the flaw in the obvious argument, accepted by all except those with the foresight to see through it. Edges and angles are what differentiate the successful gambler from the loser. Such advantages are not always prevalent or obvious. But when they can be sniffed out, that is when the nose of the gambler who makes it pay starts to twitch.

Let us return to the mythical question of the order to play the Russian roulette game highlighted. You can try this for yourselves using six cards face down, five blank and one with a bullet drawn on its surface. Alternatively, you can take five ordinary playing cards and the ace of spades. Place them at random in a line and attempt to avoid the bullet or the ace. Please don’t buy a Smith and Wesson and a box of bullets to prove a point!

I have made my submission: Play first or last. Both require nerve but then so does the whole scenario. Personally, I would not risk my life against a 1/5 chance for an incentive of a million pounds.

And this raises another point which I am sure we can return to at a later date. That is the question of value. If you have concluded a bet is not a good one, the price should not alter your decision. Be it a million pounds, or ten million, I consider a 20% chance of losing my life to be an unacceptable risk whatever the reward.

The same should apply to any wager you strike. Always evaluate the winning chance of the selection first, its price second. If you feel the chance of a horse winning is unlikely, then 10/1 or 25/1, or, in these days of Betfair, an inflated price of 42/1, should make no difference to your betting plan.

Remember, a lime green Prada suit you see in the sales at a knockdown price that you will never wear is a waste of money at a pound!

Such seriousness in today’s piece perhaps warrants a joke. It is not normally my style to relate jokes but this did strike me as amusing and I would prefer to leave you with a smile rather than a bullet.

A professor in social studies is lecturing a class of students. The subject shifts to sex. To illustrate some vague point, the professor asks three students at random how many times a year they indulge. About fifty says the first. Thirty says the second. The last, an elderly man with a broad smile on his face, confesses that he has sex just once a year.

‘Once?’ questions the professor: ‘If you only have sex once a year, why the stupid grin on your face?’

‘It’s tonight,’ reveals the man.

Think like an  Odds Compiler

LAST WEEK we addressed horses in general. This week I thought we would look at odds and races. With the fixture-list reaching saturation point, it is becoming increasingly difficult to keep pace with all the racing. My advice is not to try. If you insist on keeping up it is my contention you will end up either burnt out or a jack-of-all-trades and master of none. You will be unable to spend the necessary time on races you can solve and you will be dizzy with a mish-mash of half-ideas, which have not been thought through to a satisfactory conclusion.

Target your meetings, then your races and use your time wisely. There used to be an advertisement on television, one of the few to make sense; its slogan was, ‘Don’t Work Harder – Work Smarter.’ That is excellent advice. Take it and apply it to racing!

Decide where your strengths lie. If you are a Flat man, then do not try to turn yourself into some sort of National Hunt aficionado. There is enough all-weather racing during the winter and you may always have the odd opinion over the jumps that you can utilise. If your expertise rests in the jumping code, that means no winter holidays for you and you will have to concentrate your efforts on the nine or ten-month period that suits best. I know some (a handful admittedly) that actually bet solely in hunter chases. Personally, I would rather try my luck in a casino, but those that major in such a discipline make it pay. The problem is they are dealing with a very small window of opportunity, but the bottom-line in this business is that if you can make a profit, then your approach cannot be argued with.

Whatever your strength, it is important you understand certain principles that apply to all forms of gambling. Before I move on to the specialised area of dissected races, it is worth spending some time on basic gambling rules.

There are two forms of odds: Absolute Odds and Indefinite Odds. I will make the distinction. Absolute Odds reflect the exact chances of any eventuality. The most obvious example is the spin of the coin. There are only two possibilities – heads or tails. Therefore, the odds are evens you do or do not name the spin correctly. There is a 50% chance of being right and the same about being wrong. Similarly, if you take ten boxes, randomly place white balls in nine of them and one black in the remaining box, the odds against you correctly identifying the box containing the black ball is 9/1. There are ten possibilities. By picking one, nine are against you and only one is in your favour.  This is incontrovertible. I have cited Absolute Odds in both cases. So would you be tempted if I were to offer you odds of 12/1 against correctly nominating the black ball?

Now I have changed the scenario. You are still unlikely to pick the black ball with the odds stacked so heavily against you but I am offering you a greater price than the proposition warrants. There is no strict answer to this poser. A mathematician would encourage you to take the bet. A gambler, despite the epithet, would probably conclude that, unless these odds are to be extended beyond one pick, the black ball is likely to remain elusive so the price should not influence a decision. This presents an interesting crossover between thought-processes of the mathematician (who merely pontificates) and the man who has to put his judgement into practice.

We are now in the realms of value. At this point, some of you may wish to refer back to an earlier article concerning a mythical game of Russian roulette that covers the weakness a pure, and blinkered mathematical approach in my view, contains. Value is the trap the bookmaker and punter use to ensnare each other. The bookmaker, confident you are unlikely to call correctly, is often prepared to offer over the odds on a proposition. In Godfather parlance, he will make you an offer you cannot refuse. Always beware of such generosity. Some punters are vulnerable to these offers, meaning they become duped into backing on an event or horse they would otherwise by-pass. Value is a complex issue. I will return to it.

So we have established what Absolute Odds are. They reflect an indisputable set of propositions. The problem is that by offering Absolute Odds on a regular basis, the layer cannot make a profit. A roulette wheel only makes the house a profit because it contains one, or two Zeros. One Zero and 36 numbers on a wheel offering odds of 35/1 against any particular number coming up, means a 2.5 percent profit to the house. Two Zeros gives it a five percent advantage. When you consider how many times a wheel is spun in any given session, that is enough to tilt the overall odds away from the player. So on a roulette wheel, the Zeros represent the margin of profit to the house. On one-armed bandits – the worst possible form of gambling there can be – the profit is even greater. In fact, it can be as great as the operator wishes. In some cases, these infernal machines keep 60% of turnover. Anyone playing such an item wants to have a brain scan. The object for serious punters is to obtain 5/4 about heads on a regular basis. Being offered it once is still a gamble.

Indefinite Odds are just that. They are someone’s interpretation of the possibilities that exist. Therefore, in any sporting event you are pitching yourself against the odds setter. It therefore follows that the odds offered on a horserace are not necessarily correct. Put bluntly they are largely a guess. This is especially true when the odds compilers are in the midst of a busy day. Maybe it is Friday afternoon and they have to produce odds for six races run on Saturday. The races are hard handicaps, full of runners. Despite various fail-safe techniques employed by bookmakers, they are vulnerable. They are working against the clock and unless they have a large contingent of compilers, they run the risk of overlooking a vital component or of events, such as a going change, conspiring against them.

As a punter, if you allow yourself to be under the same amount of pressure you are also likely to make mistakes. This is where you should be able to raise your nose to the wind and see if you can smell a hint of blood. You can afford to spend much more time on chosen races than the over-worked and stressed odds compilers. Use it wisely to see if you can unearth a mistake or two. But do not just back a horse because it is too big. Only back it if you fancy it. Remember the white ball/black ball example. If you are unlikely to be right, the price is incidental as it is more than likely you will strike a losing bet. By the same token, do not be tempted to strike a bet because you consider it is bombproof – the each-way double that cannot fail to produce a yield. You reason they may not win but they will both place. If that is your starting point then it is a poor bet to strike. Much better to strike an each-way bet as insurance when you think both horses will win. That way the place part of the bet will save you losing in the event of you having one winner and a short-head loser.

Do not allow the odds makers to dictate your betting patterns. They may influence them and there are undoubtedly times when a horse is too short for you to wish to back, even though you consider it will win. Well, we all have to live with that. But if you spend your time waiting for the perfect bet, you will spend a long time on the sidelines. There have to be occasions when, although the odds may not be ideal, you are so sure the horse in question will win that you bet. Let the odds on offer be the last thing you consider. If you take them as your first point of reference, the bookmaker is dictating your betting patterns. That is a situation that suits the bookmaking fraternity. You are on the receiving end of an offer of the bookmaker’s choosing. You are being made an offer you think you cannot refuse.  But you can refuse it and you should unless it was in you mind to back the horse in the first place. There is one person that should decide when you bet. That person is you!

If you wish to identify value in betting there are a couple of ways you can do this. Firstly, remember that we are not dealing with an absolute proposition but one that contains a variety of factors. That means there is no blueprint price but you can get close to such a thing. When evaluating a race, discard as many of the runners as you can. Don’t worry if you discard a horse, often as a result of perfectly sound reasoning only for it to win. That can always happen, 33/1 winners appear in the formbook, particularly early and late in the season. It does not mean your judgement is faulty. There is a random factor to be considered and it will kick in from time to time. That is the drawback with the Indefinite Proposition.

Competent odds compilers know how to break down a race. They start from the outside and work in. They price up the outsiders first, putting them as big as they dare. That way the percentage they are left with dictates the prices of the participants that really count. An odds-compiler that takes a stab at the price at the favourite and then builds the rest of the runners round that guess is likely to price races incorrectly on a regular basis. Assume the same method when you assess any race. Take out the horses you think won’t win, see how many you are left with, juggle with a few prices and that, roughly, will indicate what the winning chances of the leading protagonists are. But, and this is important, remember you are not dealing with the stony absolute of the flick of a coin or the balls in their boxes. The unforeseen can occur. Such issues as jockey error, horses breaking down, getting a poor run, being hampered, losing lengths at the start, can and do influence results. That has to be built in; horseracing is not decided by a computer. In case it has escaped your notice, horses are comprised of flesh and blood.

Note from Bob

If you’re interested in reading more about compiling odds and the thought processes an odds compiler goes through Spy will be discussing this subject in greater detail so check back here for updates.  If you have any specific questions you ‘d like answered about the odds compilers job drop us an email or call the ofiice

For many years Spy was actually paid by bookmakers for his skill in compiling the odds for races. While I don’t agree with all his comments about odds and value I certainly respect his opinion and can vouch for the fact he has an amazing ability to spot horses likely to win races and whose true odds are less than the odds available with bookmakers making them profitable betting opportunities.

He is now a gamekeeper turned poacher and we welcome his comments here on a variety of racing subjects and especially one of his pet subjects, that of the true odds of a horse.


FROM TIME TO TIME, these articles provoke comment. The last piece attempted to make a distinction between Absolute Odds and Indefinite Odds. Not everyone seemed to appreciate the difference, so I thought I would elaborate in the hope of clarifying what was meant.

No one seemed to have a problem with Absolute Odds, which are self-explanatory. They are the odds that denote an absolute and incontrovertible event – the flip of a two-sided coin representing an even-money proposition being the most obvious example. However, I also gave an example of nine boxes containing white balls and one box hiding a black ball. The odds against identifying the black ball are 9/1. But to widen the argument I asked whether, if offered 12/1 about picking out the black ball, you should consider this a bet worth striking. As we have established, the offer means you will be paid over the odds if you call correctly. That said, what many of you seem to have overlooked was the conditions attached to this proposed wager.

Always read the small print or conditions! In this instance, the odds were available for one bet only. Therefore, if you felt lucky, you could chance your arm in the knowledge that if you pulled off the unlikely you would be overpaid. What the professional punter would ask before availing himself of this offer is: would this be a bet I would wish to strike irrespective of the odds? A bet that offers you only one chance in ten is not attractive. You are clearly unlikely to win. There is nothing you can do with a bet of this type to tilt the odds in your favour. It is an Absolute Bet, meaning no amount of homework, no amount of insider knowledge (unless you know the person who placed the balls in the boxes) is available to you. You are merely taking a stab at a 9/1 chance. Now, if someone would offer you odds of 12/1 for, let us say, three individual attempts, you would have a very real chance of winning and my answer would be different.

This game can be played two ways so let us examine each. If a losing box is removed each time it has been nominated, then the odds shift. After the removal of one box, the odds are 8/1, then if you call wrong again, they become 7/1. Your chance of naming the right box in this example, given three attempts, is, surprisingly, 15/8, so clearly, with the promise of the odds of 12/1 on offer for each attempt, it is a bet you should strike. Some of you might consider that the odds are three in ten, or 10/3. That is understandable but incorrect. Under these circumstances, the odds are on a sliding scale, marginally tipping the odds in your favour as you go. What was 9/1 becomes 8/1 and then 7/1. Put simply, with the withdrawal of boxes no longer relevant, the odds and percentages they represent alter.

However, if constantly switching around the boxes after each game, technically the odds remain at 9/1 for each pick. If the odds are an absolute 9/1, given enough chances, the player is likely to call correctly eventually. The mathematician will tell you that the odds are 9/1 add infinitum but that is wrong. Once a game is instigated, no set of odds remain constant. Probability dictates that you must reach a point when, having called wrongly for more than a set number, the odds tip in your favour meaning you will finally get it right. Remember no skill is required here. As the proposition gathers steam, we are talking about what is likely as opposed to what is unlikely. Probability has to be factored in and that is separate from Absolute Odds. Most people have trouble accepting this as a concept. Logic is fine when you are trying to solve a puzzle that involves shapes placed in a framework or the next number in a sequence but odds, although a puzzle of sorts, have set boundaries. If a proposition is established as being a 9/1 chance, then once you have had nine unsuccessful tries, odds tip in your favour, meaning you are probably set to randomly unearth the black ball or whatever is in hiding.

The key with the first example is that the offer of 12/1 was only available ONCE. In this instance, that is the difference between a bet that offers a chance of profit and one that does not. In offering the player 12/1, the layer is merely taking a chance or a gamble. But his gamble is far less than the one the player is required to make, so it is a bad bet to take.

As I stated in the original article, if you take advantage of inflated odds just because they are offered, you are allowing the layer to dictate your betting patterns.

For those of you that do not understand how I have arrived at the odds of 15/8, I will explain the composition of odds as transposed to a percentage in my next article on this subject.

Let me offer one more example. There is a universal game known as Find The Lady. Depending on where you are in the world, it presents itself under all sorts of different guises but essentially the principle is the same. In Las Vegas, it is Call The Spot.

As we are in England let us stick to our version. There are three cards – two numbered and one Queen. She represents the lady and the object is to pick her out of the three face-down cards as they are cleverly manipulated by the handler. At first, he takes the three cards, shows them to the crowd face-up, then reverses them and shuffles them around slowly before spreading them in a line. It is temptingly easy to identify the Queen as members of his gang display by slapping £20 notes on the cards and picking up the dealer’s money. So far so good: the Absolute Odds knowing nothing are 2/1 but the dealer looks like he is slow and inept and this is surely easy money. Yeah! Like hell it is!

As soon as you put your money down, the dealer suddenly acquires a newly found skill and is able to mix the cards with such rapidity that you have no idea where the Queen is. You might think you do, but of course, when your money is down, you discover you do not.

Knowing this, let us say the dealer shows you the cards as before, shuffles them and then states he will offer you the same odds less a bit, say 6/4, but with a twist. He is going to make the whole process easier. Once you have put your money down he will reveal one card, effectively leaving only two possibilities. If this game is above board then he is offering 6/4 about an even-money shot.

Tempted? Do not be. This is a conditional bet and the layer is setting the conditions. Examine what is going on. He knows where the Queen is. He always knows where the Queen is. By asking you to nominate her whereabouts after his sleight of hand and then removing a duff card, he is giving you nothing. However, when you look down at the two remaining cards in the knowledge that you are likely to be paid out at 6/4 for calling one against one, those odds seem attractive. The catch is that you made the bet when there were three possibilities and all the dealer has done is to remove a loser that he knew all along was a loser. It was 2/1 against you beating him when you struck the bet and, because of his insider knowledge, it is still 2/1 now even though only two cards remain.

For those of you who doubt this, I urge you to try it at home. Take the cards or three of anything, shuffle or rearrange them so that you know what is where and try it with a friend. Metaphorically speaking, you will take him to the cleaners by offering  6/4 about what appears to be a 2/1 chance. Of course, this only works as long as you know which card to reveal once he has made his bet. On the times the player is right, you are paying under the odds. When he is wrong, which will be twice in three even on a straight guess, more if you are misleading him into believing he knows the whereabouts of the Queen, he is being similarly fleeced.

Just to close this particular scam, punters catch on quickly that the dealer knows what he is doing. As a result, for the dealer this game has a limited life span so after a few marks have put themselves forward and lost their money, it is a case of, ‘Here comes the Law,’ the table is upended and the gang is gone only to set up somewhere else.

Next up, the variations of Indefinite Odds…



How the bookmakers look at odds and probability…

IN MY LAST ARTICLE on the subject of odds and probability, I mentioned the difference in odds that are absolute as against those that are indefinite. It is useful for punters to make the distinction because most odds offered are of the indefinite variety and require a fair degree of scrutiny.

                 A book can be made against any eventuality, but some eventualities are more likely than others. These days most bookmakers will bet on anything. However, some propositions are plain ridiculous, making their odds incalculable. How, for example, would you go about offering odds against a spaceship landing in Hyde Park? With no form to go on, other than it has never happened before; therefore it is highly unlikely ever to happen, what odds would one put on such a random possibility occurring? A million?

What if the bettor was Stephen Hawking? Could it be he had an edge of sorts? Might he at least know that an unidentified craft was on a collision course with our planet, and he has struck a similar bet that it would land in Central Park, Gorky Park or Tiananmen Square? On the face of it though, bookmakers offer odds on snow at Christmas, the proven sighting of UFOs, citizens reaching the age of a hundred, for publicity. They are silly bets to lay even so, because offering, let’s say 1,000/1 for any eventuality is bad business. No one wants a pound so badly he will, or should, risk a thousand to get it. In the case of the UFO, 1000/1 is almost certainly underpriced but that is not the point. The punter only has to risk a tenner to net £10,000. Long after the stake has been absorbed by day-to-day living, he is unlikely to lament its loss and there is a probably a greater chance of collecting than of winning the infernal lottery.

Indefinite odds vary from being odds that are hard to assess to downright impossible. Lightning striking certain areas, UFOs, the spotting of a flag on Mars, are all genuinely indefinite propositions. Under normal circumstances, the possibilities of such events occurring are so remote and random that no one is in a better position to ascertain the likelihood of these sorts of eventualities than anyone else. Bookmakers will of course flimp the punter with their odds but, to be fair, that is understandable for reasons explained: namely, there is nothing in it for the layer and plenty to be gained by the punter should only one of these unlikely occurrences actually occur in a literal blue moon.

But some implausible propositions are not as outlandish as they seem. Always, always beware of the man who says: ‘How much do you want to bet that I can’t…’ Whatever it is he is claiming to do, from walking upside down on his fingertips to producing a rabbit from his underpants, you can be pretty sure he can do it. Either that or he is a nutcase. From all the improbable feats in the universe, he has chosen to nominate these two. Most propositions have a clause attached. That is to say, in this case he has not specified how or where he will achieve the proposed feat. As far as the rabbit proposition is concerned, he did not specify the animal was to be hoisted from underpants he was wearing. That was assumed. If he were to open a case and pull a rabbit from a giant pair of undergarments in which it had been secreted, technically he has won the bet. The devil is in the detail. I have no idea how he would walk on his fingertips but would not bet against it if he proposed such a thing

A famous bookmaker once told me he was always reluctant to bet on anything that spoke. I guess that meant football was off his board but I take his point. Betting history is littered with incidents where insider knowledge has held sway. Snooker matches involving brothers, football matches where a lop-sided betting pattern on correct frames or scores suddenly emerges. The ridiculous proposition stating which colour dress the Queen is to wear at Royal Ascot is another notable example. It is inconceivable that someone somewhere does not know in advance what dress she is going to wear. Bookmakers have had their feathers ruffled here on more than one occasion. Frankly, it serves them right. This occurrence involves too many outsiders for it to be anything but an open secret in certain circles. Similarly, with television programmes like X Factor and Strictly Come Dancing, those on the inside know the voting patterns leading up to the closing stages of the competitions and are in a better position to make an educated guess than Aunt Hilda. These examples involve a degree of dishonesty or insider dealing. However, there are occasions when bookmakers know less than the punter. This makes them of legitimate interest.

Bookmakers have this all-consuming desire to bet on everything, even if they do not always know that much about the subject. Take golf, tennis, rugby and certainly other events like the Oscars. They are vulnerable to those that major in these sports and pastimes. In 1997, bookmakers offered odds on the number of Oscars the film Titanic would scoop. They got it spectacularly wrong because they underestimated the categories the film was likely to win: Best Special Effects, Costume, Sound, Visual Effects, Screenplay, Editing, being prime examples. I suspect they had not considered such categories. They may be minor awards in comparison to the biggies: Best Film, Director, Best and Supporting Actor/Actress and Producer, but they count and the misinformed bookmakers concentrated on the obvious, making six or seven their favourite, whereas the film took eleven Academy Awards and I some of their money.

When I worked as an odds-compiler, I only ever put my name to horseracing or events I knew anything about. That in itself was hard enough as there was many an occasion when I was forced to put prices to a race I had no feel for. But that was the job and, as a job it is one where you need to be right more often that you are wrong. In any event, bookmakers have a fail-safe device in that virtually all the prices you see are compiled by an industry man, which he sends to all the firms. He makes a tidy living out of this but has a top class team backing him up and their mistakes are minimal. As individuals, they as capable of getting it wrong as anyone else but, united, with mistakes picked up by other members of the team, they are on the money most of the time as it takes an across the board error for a horse to be wrongly assessed. So the task of beating them is not straightforward. However, there are occasions when they call it wrongly. This is why I advocate serious punters should maintain a system unique to themselves for evaluating the performances of racehorses.

Odds-compilers are well paid and have two masters to serve. Essentially, they wish to play it safe. They want to second-guess how punters will assess a race. Often, spurred on by hyperbole from Timeform or Raceform, they will under price a certain favourite on the assumption the betting public will (which they often do) fall over themselves to take 6/4 about what looks like a blot in a handicap. In-house odds-compilers are paid to produce their own prices but the emphasis is on them to sail pretty close to the ship charted by the industry men. This means, even if they feel a horse is too short, or too big, they will want to be seen by their employers as being in tandem with the industry men, whose record is proven.

This is why, when you open the paper or check the internet, the firms seem to have little variance in their prices. Independently compiled prices would create a vast difference from firm to firm, with many bookmakers often producing contrasting favourites. The reasoning behind this form of similitude is that bookmakers, even in the early days when such a term as arbitrage was unheard of, wished to avoid a situation where collectively they were betting over-broke. I could never follow this.

Privately I argued, as a firm, so long as your prices were right, that was what mattered; but no; bookmaking is little short of a cartel when it comes to pre-show prices. There are a few points difference here and there, when compilers talk their employers into extending the price of one horse and shortening the price of another, but we are only talking a minor variance. An in-house odds-compiler can price a horse up at 10/1, but if the industry price is 4/1, the ten is pie in the sky. The firm may extend the 4 to 9/2, 5/1 or even 11/2 if they have utmost faith in their man and he convinces them his price is a considered one and not a mistake. That is as far a they will go. All the firms tend to do is tinker with the prices they receive from the central source. The industry man and his band of helpers comprise the equivalent of the Glass’s Guide in the motor trade, where only dealers know the retail price of a second-hand car at any given time.

As a serious punter, little of this should concern you. For, in pricing up horses we are dealing with an indefinite proposition. The prices merely reflect an opinion. They do not represent the absolute generated by a heads-or-tails scenario. So-called professional opinion often gathers pace as others run with it on the assumption it is correct. Opinion in itself is a fragile commodity. Even when the most successful of players is expressing a view, it can be wrong. That presents an opportunity for those who believe in themselves to take on the consensus of opinion.

But when taking such a stance, be warned; if you disagree markedly with the prices on offer, you are pitching yourself against some clever people. That does not mean they are right and you are wrong. On the contrary, because odds-compilers understand there is safety in numbers, they are keen to come to the same conclusion. So the King Without Any Clothes On principle can creep in. But be aware, those with an edge, those possessing knowledge you do not have – such as the wellbeing of a leading participant – do have the drop on those without such information. In his case, bookmakers are the front line. Often, their reluctance to lay bets, combined with their eagerness to shorten a horse, betrays their knowledge. When they think they are right and you are wrong, they will soak up money on so-called fancied runners. They may alter the price but, the fact they do so on a sliding rather than a panicked scale, gives a clear indication as to how concerned they may be. When they know they have got it wrong, it is a case of whang, – now you see the price – now you don’t. When they are full up but prepared to continue laying bets, it is more a case of, Go ahead punk; make my day!

If we are on a level playing field, then only an expert knows, or has a darned good idea, when a proposition such as a horserace is likely to be correctly analysed.

As I said last time, there is also the time factor to consider. Odds- compilers are racing against the clock, having to produce prices by mid-afternoon for inclusion in an advert for the next day. Non-runners, ground changes, jockey changes, can often occur after they have gone to press, as can a vital piece of form, particularly now we have so much racing at night, that can alter the complexion of a race. As an individual, you are in a position to pounce on such mistakes when and if they occur. If a week is a long time in politics, twelve hours (often the time between pricing a race and its taking place) can be an eternity.

To a degree, I have become lost in my own rhetoric in this piece. It had been my intention to demonstrate how prices are constructed and what each fraction represents. I shall set myself that task for the next article, which I trust will make this issue somewhat clearer for those who may be struggling with the concept of odds in general and their impact on life as a whole. Everything has a price (except perhaps that flag flying on Mars) so the ability to weigh up the pros and cons in any given situation allow those that can perfect it something of an advantage.



I ENDED the last piece with the suggestion that everything has its price. In Godfather parlance, everybody has his or her price; although I am not convinced that is true. There must be some things that individuals would refuse whatever the reward.

Mathematics knows such moral divide. Prices are merely a basic form of arithmetic and can be simply broken down. They are fractions. 6/4 suggests that the punter has four chances in six, or two in three. 2/1 reflects his chance as being exactly that: one chance in two. 5/2 implies he has one two chances in five and 3/1 that he has one in three. And so it goes…Place £20 at 5/2 and you are betting what we call money-to-money. But of course, you don’t have to adjust the stake to suit the fraction.

The examples I have used are simple to follow. What if the fractions are more complicated? Let us say 13/8, or the ugly 85/40, or, as I contend it should be – 17/8. They present no problem to the man that deals with these figures every day of his life.

We are in a different age now, but at one time, when you struck a bet with a racecourse bookmaker, he would call out what you would win commensurate to your stake. Ask for £10 at 10/1 and he would shout: ‘£100 to 10; ticket number 776,’ before handing you one of those old-fashioned cards containing Jolly Jack’s photo.

Now we are in the age of the computer those days are gone. The ticket was your receipt and what he was indicating was that you had staked £10 and were liable to win £100. Like the man who can calculate the ever-decreasing amount left on a dartboard and what the player requires to win, the bookmaker gave an impression of being some kind of wizard with sums by converting each bet thrown his way. It was an example of an acquired knack I referred to in an earlier article. Here is a man that can convert odds to percentages in his head. Ask both him and the dart man to wrestle with a logarithm table and it will be a different story.

Odds and percentages represent the toolbox of a bookmaker’s business. Professional punters need to be equally conversant with their meaning.

So let us break them down, starting with the easy examples first. We all know that Evens represents just that – literally a fifty-fifty situation. We can prove that by converting the fraction. Evens is written as 1/1. To convert a fraction to a percentage, you add two noughts to the denominator [bottom part of the fraction], add the two figures together, that is the denominator and the numerator [top part of the fraction] and divide the sum into the denominator. Sound complicated? It does but it isn’t. A small demonstration will prove how easy it is. 1/1 becomes 1/100. Add the original 1 and 1 together, which gives you two, divide two into 100, you get 50.

Ready for another? Take 6/4, which we know represents a 40% chance. Add two noughts to 4 and you arrive at 400. Six plus four is ten; divide 10 into 400 – answer 40.

Last one, a tricky fraction, 13/8. The 8 becomes 800, divide it by 21 [13 plus 8] and we get a percentage of 38.

Follow exactly the same principal when calculating odds-on chances. Thus 8/13 becomes 1300 divided by 21. In this case, the odds tilt in favour of the player, meaning his winning chance is theoretically 62 percent. And here is a little tip. You may have noticed that the odds against 13/8 are 38 and the odds-on 62. Add the two together and you get 100 percent. That applies to all odds against and odds-on chances that match. 6/4 against is 40%, 4/6 is 60 percent. 5/4 against is 45 percent, 4/5 is 55 percent. So it follows that when you back a 7/4 chance it is 4/7 to lose and when you back a 4/7 shot it is 7/4 to lose. That is the mathematical theory, but that assumes the prices on offer represent a fair reflection of the selection’s chance.

This is where mathematics and chance collide. This is why I have been at pains to separate the absolute odds from the indefinite. Prices levelled against horses are indefinite, they are someone’s idea of the chance that horse has. As a punter, it is your job to decide how accurate that price is. There are no rights and wrongs here. You have to make that decision before a race and not after the result is known. There is nothing wrong with taking correct odds for a horse if you really think it will win. If you make a horse a 7/4 shot and that is the price on offer, there is a major margin for error to consider on both sides of the fence. What is more important than the price of a horse is whether you truthfully believe it will win. If you are unsure, the price should not come into the equation unless it is so massive that it becomes irresistible. But a knowledge of how to translate prices to percentages gives you a realistic opportunity to evaluate the chance you are about to take. Once you know the formula you can transform any price to a percentage, meaning you are now in a better position to establish whether you are betting to value or not.

Some punters do their own issues, or make their own prices. I used to do this for a living and have no wish to return to it now. But it is one way of identifying value, be it good or bad. Once again, it is a lot of work and only as effective as the person inputting the information. Sometimes, I feel these things can be diversions that tend to steer us away from the core of the issue, which, in this case, is to identify winners. On the other hand, I may just be getting lazy. Making a living at racing is a young man’s business and being truthful, I feel only the names have changed when going through some cards. Possibly that is because I am going through a barren spell, and under those circumstances confidence and enthusiasm do tend to slip. All gamblers know the sinking feeling associated with this, as do jockeys who cannot seem to ride a winner. They lose that edge, that wave of confidence and for a short time, seriously doubt their ability. This is especially true of jockeys; whereas, as a punter you can take the day, the week, the month off and forget the whole damn business – providing that is, your finances can stand it.

There is a hidden advantage in compiling a tissue and that is it makes you look at every horse and evaluate its chance. Therefore, surreptitiously, you become more and more conversant with the product you are handling – the formbook – and you are able to recall form lines in an instant. That is a desirable situation to reach and means you are on top of the business rather than it getting on top of you.

To give yourself the best chance of sorting a race out, you have to break it down. If you cannot do that, the race is of little use from a betting point of view. Start at the bottom of the handicap, or with horses you perceive as having little or no chance. Price them accordingly so that you are working outside in, rather than the other way round. Put the outsiders as big a price as you can. That way, when you come to the head of the market, you are left with the percentage that covers those with realistic chances. This enables you to price them more correctly than if used as your starting point.

Races of primary import are those that appear to contain some fragment of flawed logic. A favourite that is too short, too much emphasis placed on a piece of form you know to be suspect, an overpriced outsider that has been crying out for a step up in trip. The only way you will identify such inconsistencies is to watch plenty of races and to make notes. Compile a list of horses you are waiting to back if conditions appear right; do not rely on your memory as it will let you down.

We started this piece with an explanation of percentages, perhaps it is fitting to conclude it in a similar vein. Depending on your style of betting, you can only expect to bust the percentages by between two to five points. So, these figures are pretty much absolute. If you adopt the scatter-gun approach – that is to say to back and lay in most races on any given day – expect your winning percentage to be low. You will be betting at long odds-on when you consider your stake. So a profit of between six or seven percent on your turnover is probably as much as can be expected. The advantage with this type of wagering is that you are diluting your losses with a juggernaut-type approach to betting. By removing the need for pinpoint accuracy, you are spreading your liability thinner than the punter that backs on a more selective basis. As always, stake is important here. Even the best of players will have bad days. They go with the territory. You have to expect this, withstand them and not let the dark days, the long hours wasted, the feeling that you have lost your touch, get the better of you.

If you are the discriminating type who only bets when things appear to be cherry ripe, you have to aim for a higher strike rate – between thirty of forty percent – and be patient when a well-thought out bet goes astray. Depending on your degree of exactitude, you may only unearth between six and twenty bets a year. That matters not, so long as you achieve the required target of winners. And now that you understand percentages, you can see that if the best you can hope to achieve is a thirty-five percent strike rate, that does mean the average price of your winners must exceed 15/8. That is a break-even figure. To make money, 15/8 has to become 3/1 if you are to show a profit of 40% of your turnover. Back twenty horses a year, placing £500 on each, and you will make in the region of £4,000 per annum, providing you achieve the target. If you have another income and time on your hands, this is fine. Assuming you do not, one of three things must happen. You must increase your percentage profit, your stakes, or the price of your winners. The first option is unlikely. The last two are possible, with the easier being an increase in stakes so long as you possess the necessary finances. This enlarges your risk of losses but increases the chance of success. In the example quoted, you have staked £10,000 over a year to win £4,000. Following the same strike rate, to make £20,000, you will need a tank of £50,000 in order to stake £2,500 per selection. Increasing the average price of your winners may mean cutting your bets down even further but, believe me, 6, 7 and 8/1 winners are out there and often they only have one horse to beat. But, the less horses you back, the higher your strike rate needs to be.

So we have travelled full circle. The options are, back a lot win a little but make a steady income. Back a little, stake big and be extremely selective. Go the arbitrage route, which means an awful of work for a potentially small amount.  Alternatively, see if your local council requires drivers for their  road gritters.



THE CONCEPT OF VALUE is all-consuming for many. Allow me to make a statement before continuing. I am not exempt from many of the pitfalls I detail in these pieces. There is nothing worse than some know-it-all espousing theory and then demonstrating that he is incapable of following his own advice. We all struggle in this business and are vulnerable to the same mistakes, but at least if you are aware of the elephant trap laid, you tread a path with your eyes wide open.

So, let us get a few essentials out of the way before we continue. Firstly, over time, we all bet at odds-on. It is no different from investing in stocks and shares. Unless you hit the jackpot (in the case of betting on horses, win the wretched Scoop Six or whatever it is called) or in your stocks and shares dealings, sell Woolworth just before the whole company becomes worth an estimated one pence, you are playing to win a fraction of your overall stake.

Discounting the improbable and the downright impossible, let us concentrate on the possible. If you bet on a regular basis and your returns are less than your turnover (which under normal circumstances they will be), then it follows that the more turnover you generate, the higher your overall dividend. This assumes you will be able to make a profit of anywhere between three and eight percent, which I might add is not a given. Therefore, at the higher figure, a turnover of £100,000 per annum means a paltry return of up to £8,000. Double your turnover, and in theory you double your profit to £16,000, which, depending on your circumstances, will keep the wolf from the door and little else. To put that figure into perspective, it is the equivalent of driving a van for one of those door-to-door delivery firms. Such a job does not require you risking up to £200,000 (you will not lose the lot unless you are a complete idiot, and even then the law of averages states you must enjoy a few returns along he line). But you are risking capital. If you are to put such a sum on the line, it does help if you have an idea what you are doing.

So let us take a closer look at the proposition. If you agree that your profit is only going to be a percentage of your betting tank, or turnover – £200,000 is not actually required as that is a turnover figure, as opposed to one invested up front – you are still potentially putting a sizeable sum at risk. Therefore, it is important to pick your bets carefully. Value is not backing a horse at a bigger price than you think its chance warrants unless you think it can win. I have covered this before – essentially a horse you think should be 10/1 that is available at 20/1 is of no use. By assuming it is a 10/1 chance, you have already admitted it is an unlikely winner.

Similarly, backing a horse at 4/1, which is a perfectly acceptable price, becomes less acceptable when you are backing the likes of Big Buck’s in a Hennessy, where anything can happen to sabotage the best thought out reasoning. With the weight-rise it already has! You may fancy Big Buck’s for your life, but is he value as opposed to taking 4/1 about a horse in a maiden at Lingfield that has only one to beat and you think should be favourite?

Plenty of punters fall into the trap of backing horses in high profile races just because they enjoy the kudos of being right. Satisfying though that is, pursuing such vanity allows the wolf to get a paw inside the door followed by a slavering mouth. For every Big Buck’s you get right, you will get six wrong, meaning you will lose overall. There is nothing wrong with trying to solve races like the Hennessy or the Paddy Power or the Derby; but 4/1 is 4/1 whether at Lingfield, Epsom or Cheltenham. This does not mean you have to target 10/1 chances in such races. What it does mean is that unless you can find one you genuinely fancy, as opposed to a horse you are prepared to back because of its attractive odds, it is probably a race to sit out. Should Big Buck’s win, cheer it home. Do not be unsporting and bad-tempered about the loss of a winning bet. Rejoice in your exact judgement and in the knowledge that over a time, backing such horses will lose you money.

Targeting punter-friendly races is as important as finding winners. But there are occasions when two or three results can swing a season completely round.

Two years ago, I came close to winning big amounts on two occasions in high-profile handicaps. Had the horses in question won, they would have made a big difference to my bank account, but both lost. In between their running, there was the usual put-and-take associated with gambling: winning a bit, losing a bit, paying the mortgage, topping up the wine cellar, managing to get the car serviced, spending days with my head down, others with a spring in my step. The two horses in question were chancy bets but I thought they had excellent prospects. Firstly, there was Dhuluar Dhar in the Bunbury Cup. I backed it to win with the books at 33/1, 40/1 and got a small amount on at odds around 80/1 with Betfair. It was beaten into fourth place, finishing half-a-length behind the winner. Great shout; but a losing bet!

The other was Shevchenko in the Tote International at Ascot, a horse that ended up as Pricewise on the day. I took odds varying between 14/1 and 10/1. He finished second and again, not being an each-way punter, I lost. Losses were absorbed by other transactions, but had either or both won; it would have made an incalculable difference to my betting year. I did not back either horse because of being drawn in by the price, but because I considered they were bets. That is the point I wish to illustrate here. The price one is prepared to take must depend on the complexity of the race. Your Bankables in the Hunt Cup, your Kauto Stars in the King George are horses to fancy, but not horses to bet. Not enough of them win; meaning in the end you lose! Horses do not represent football teams. You are not obliged to support them. They will not take exception if you do not and your bank balance will be healthier.

If you cannot find alternatives to the obvious in certain races, wait until you can. By backing big-priced horses you actually fancy, you are tipping the scales in your favour. As I said, you only need to pull off one or two chunky-priced winners in a season to put all that 7/4, 9/4 stuff (that we all back) into perspective. Finding such contenders is not easy; but there are an awful lot of races run in a season. You should be capable of unhooking ten or so horses that are double-priced fancies that you are prepared to open your shoulders over. I am not talking about having small covering bets here, or going for a week’s wages, what I am advocating is having the courage and the self-belief to go for a crack at a big pot.

Personally, although I know plenty of professionals that state the Tote Scoop is a great bet when the pot is big enough, I think that is balderdash and this is a much better alternative. If you have to risk £10,000 in various perms to receive a potential return of £100,000 for backing six winners in the hardest races of the day, and need to find the inevitable 20/1 0r 33/1 shot in the process, for overall odds of 10/1 you might as well stand in  Caesar’s Palace and pick a gaming table.

Anyone who has a contrary opinion and can elucidate a clear case suggesting I am wrong is more than welcome to get in touch. I will not take cover behind the fact that I am in a position to shelter behind the editorial advantage I have. Your case will be put in a proper and fair manner and should you be able to back it up, I will be the first to admit it.