# Why ‘related contingency’ in horseracing bets is a rip-off

Stan James’ front man Rory Jiwani raised some long dormant hackles in me yesterday when he tweeted SJ’s offer of Cinders And Ashes to win The Fighting Fifth and Champion Hurdle at the ‘special price’ of 12/1. At the time of his tweet C&A could be backed for the Champion at 10/1 – his SP in the Fighting Fifth was 10/11. What Mr Jiwani was effectively saying was ‘I’m assuming he has already won today and will therefore offer a shade over 11/2 for the Champion Hurdle’.

C&A lost and drifted to 16/1 for Cheltenham encompassing nicely the folly of taking related contingency prices on horse racing bets. I rarely meet an experienced punter who questions these RC bets – it has always been the way and to many it seems logical, ‘If my horse wins the first leg of my bet, I’d expect him to shorten for the second one’. What they never consider is what the odds would be if their horse lost the first leg. The fact that it doesn’t matter then because the bet is down anyway does not make the odds correct.

Take, in hindsight, what the ‘correct’ odds for C&A appear to have been – 31.45 to 1 (10/11 & 16s). But you cannot argue that this is accurate either, because that assumes that leg 1 of the bet is lost. The correct odds, in my opinion should be the simple multiplied odds that apply to any normal double – in this case, 20/1.

RC bets are valid in some sports, football for example. Chelsea to win 2-0 and Chelsea to win the match should obviously not be accepted because if the first part happens the second part is certain. ‘Man Utd to win today and win the League’ would also see a perfectly fair application of RC odds – 3 points enhance their chances of winning the league, no question.

In horse racing the bookmaker wants the best of both worlds. At the time the bet is struck the punter has no advantage over the bookmaker, he knows no more than the bookie does. The bookie assesses the horse’s chances based on the info available and prices the horse accordingly for both events. In quoting you a ‘special’ RC price what he is saying is,”Even though we are both in possession of the same information, I want to reserve the right to insure myself in case I got it wrong – and I am not going to pay that insurance premium, you are”.

Now, if there were a rider that allowed your insurance premium to be returned in the event of your horse losing leg 1, RC bets would be much fairer.

If you’re in any doubt about the value of RC bets, ask yourself this; supposing you wanted a double yesterday on Countrywide Flame to win the Fighting Fifth and Cinders And Ashes to win the Champion, do you think you’d have been the beneficiary of RC in that the bookie would have laid you 16s C&A for the Champion, before the Fighting Fifth?

Joe

Posted on December 2, 2012, in General and tagged Bookmaking, Dick Francis. Bookmark the permalink. 28 Comments.

Two notes: 1. I don’t make the odds. 2. The bet was based on our price for Cinders for the CH which was 8/1.

As with any bet it’s up to the punter to work out whether it’s worth a punt or not. To some, Cinders winning yesterday was a penalty kick which then might make it ‘value’.

I remember when we had Danedream at something like 60/1 to win the King George and the Arc which looked big before and massive after the King George.

We regularly offer these bets and as with anything, sometimes they are going to be better value than at others. But then you could say that for any bet.

Regards,

Rory

Just found that Danedream double was actually 50/1.

Much of it comes down to that unquantifiable concept ‘value’. We had Kingsbarns at 16/1 to win both RP Trophy and the Derby. After the race the best price you could have got for the Derby was something like 9/2! Nice to be sitting on 16/1 for the Derby whether that fits in with your idea of value or not.

Rory, Thanks for making the comments to give balance to things. I ought to stress I mentioned Rory and Stan James only because the example was timely – I have nothing against either party. All bookmakers behave in the same fashion when it comes to related contingency.

Joe

I’m no fan of Stan James Joe but you may be approaching your rip off conclusion from the wrong angle. This, I believe, is because the phrase ‘related contingency’ is misused in this instance.

In your example, Cinders and Ashes was quoted at 10/1 for the Champion Hurdle prior to the Fighting Fifth. This is the price the bookmaker believes represents the true chance of Cinders And Ashes winning the Champion Hurdle given the information available before the Fighting Fifth. What the bookmaker is NOT saying is that 10/1 is the multiple of the cumulative prices of Cinders and Ashes winning his races this season up to and including the Champion Hurdle, which is where you are coming from with your multiple odds scenario.

To develop this further, say Donald McCain had publicly announced Cinders And Ashes would only run in the Fighting Fifth, the Christmas Hurdle and the Champion Hurdle this season. The bookmaker is not offering a price of 10/1 to win all three but he is offering a price of 10/1 to win the Champion Hurdle IRRESPECTIVE of what happens before March 2013 given what we know at the time the price is made available. Of course, the price of 10/1 will fluctuate based on how Cinders And Ashes and others perform in the interim. In your multiplied odds scenario, if currently 1/1 for the Fighting Fifth (for simplicity), 4/1 for the Christmas Hurdle and 10/1 for the Champion Hurdle the price offered to the customer should be 109/1 to win all three but this is a totally different bet to the 10/1 being offered to win the Champion Hurdle given the information to hand before he has run this season.

Cinders And Ashes got beat and drifted to 16/1. He could have won and still drifted because after the race both bookmaker and punter had more information available (e.g. if he was unimpressive) or could have shortened significantly (if he’d won hard held and the form looked to have value).

The ‘related contingency’ doesn’t exist as you point out. It is for the punter to decide if he believes 12/1 is VALUE to win both races by determining a). how impressive Cinders and Ashes is likely to be in winning and b). whether the best option is to take 10/1 outright now or an extra 2 points to win both races. Again you are right to state that the value was indeed poor because Cinders And Ashes would have needed to be 11/2 or less after the race for any value to have been obtained but it doesn’t make it a rip off because the bookmaker is not claiming there is a relationship between the outright price of 10/1 or the 12/1 to win both races, each being different bets.

Hi Steve,

This subject, as ever, aroused lengthy debate and a few tirades from some suggesting I don’t understand the concept. I understand it fully, what others don’t seem to understand is exactly what my point is.

My argument is that, win or lose, the RC odds are wrong. If RC applies, it must be applied to all probabilities so if win/win is a related contingency, lose/win must also be.

If all probabilities are not taken into account when the bet is struck, then the price cannot be accurate (fair).

The key RC probability omitted here is lose/win. Bookmakers only quote for win/win (of course, because that is what the punter has asked for, many say) but just because that is what has been requested, it does not remove the probability of lose/win.

Now perhaps full multiplied odds is not the correct price, but nor is the one always offered by bookmakers; the answer probably lies somewhere between the two.

Joe

I absolutely understand your point Joe and don’t disagree with it. However, the trading department must frame the odds so they obtain the very best value for their company and the punter must, in turn, determine if the price is value to him (given what he believes he knows that the bookmaker does not). 12/1 to win both races might be an amazing price to some punters (if the outright price for the Champion Hurdle for Cinders And Ashes was indeed only 8/1 with Stan James) while to others it is/was a very poor price.

The bookmakers make so many mistakes nowadays, Stan James being a prime example, that by definition they must keep the odds as tight as possible hoping to attract mug interest. There is nothing wrong with this approach from the bookmaker as he tries to put ‘value cash’ into his own tills but as your original point indicates any punter worth his salt will know that 12/1 Cinders And Ashes to ‘do the double’ offered nothing in terms of value. That said, we now know the result and anyone accepting the offer of 12/1 pre race would be pretty smug, rightly or wrongly, if Cinders And Ashes had prevailed in the Fighting Fifth and was now quoted at 6/1. The fact he didn’t win simply means those who took the 12/1 have been made to pay for not understanding the concept of value and/or odds and probabilities….

Great point as ever Joe.

Steve, bookmakers ‘invent’ these bets for the bookmaker, not the punter. Anything over and above a single bet has been developed down to years to rid punters of their cash.

As a general rule of thumb, only one bet will result in a bookmakers closing a punter’s account and that it a win single.

Rack up a good record of win singles without ever having other bets and the layer will run for cover, pure and simple.

Hi Joe

Glad you have conceded that it isn’t a straight multiplication.

However you are still wishing the bookmaker to consider the lose/win scenario, which is irrelevant as you are not betting on that event.

I think I get what your issue is though, and I think it’s thus;

The bookmaker ALWAYS assumes that the chances of winning the second leg are increased by winning the first, which is not necessarily the case. If C&A had scrambled home by a neck, all out, from Bothy, for example, his CH price may well have increased.

So, I think your argument should not be that bookmakers do consider

…Should consider the lose/win scenario, but your argument should be that they should consider the win scenario which doesn’t increase the chance of winning the second leg.

The fact is, it’s very difficult to price a related double, but the bookmaker always errs on the side of caution and quotes a price based on the horse winning the first leg well… And ignores the possibility that the horse could win, yet not enhance his chances of winning the second leg…

“The key RC probability omitted here is lose/win. Bookmakers only quote for win/win (of course, because that is what the punter has asked for, many say) but just because that is what has been requested, it does not remove the probability of lose/win.”

As I said before, this is the bit that’s wrong. This is like having a straight win bet, but asking the bookmaker to enhance the price on the basis that he hasn’t considered the chances of the horse losing! Just forget the lose/win scenario, it’s completely irrelevant.

What I think you do want to bookmaker to consider is the win scenario (but in a way that decreases chance of winning the CH).

Go back to the formula for calculating probability of two events occurring;

P(A&B) = P(A) x P(BgA) … g = given

or

(Chances of winning both races) = (Chance of winning race 1) x (chance of winning race 2 given you’ve won race 1)

Now P(A) we knew, 10/11, or 1.91

The tricky bit is knowing what P(BgA) is before the race, that is C&A price for the CH after winning the FF.

You were correct in saying that Stan James assumed P(BgA) was about 11/2. Well that’s one scenario, but there are of course many others. If we try to break down P(BgA) into 10 different scenarios and have a go at pricing P(BgA) in each;

5/1 Cinders wins by 20l on the bridle

11/2 Cinders wins by 10l on the bridle

6/1 Cinders wins by 7l on the bridle from CW

7/1 Cinders wins by 7l pushed out

15/2 Cinders wins by 4l pushed out

8/1 Cinders wins by 2l pushed out

9/1 Cinders wins by 1l pushed out

10/1 Cinders jumps ok wins by less than a length, but satisfactory

12/1 Cinders jumps badly and wins by a length

14/1 Cinders jumps terribly and wins by a head, all out from Bothy

Now those odds are of course disputable, but I’m just trying to show how varied P(BgA) can be. Stan James have chosen to use a price right at the positive end of that spectrum to frame their related double. Perhaps if we took an average of those 10 scenarios then the double would look fairer;

Average of the 10 odds above is just over 8/1, actually more like 17/2 (9.4)

SO, in this example, you could argue that the fair price of P(BgA) is 9.4, not 11/2 (6.5) as Stan James chose to take.

If we put that 9.4 back into the orginial equation;

P(A&B) = P(A) x P(BgA)

P(A&B) = 1.91 x 9.4

P(A&B) = 17.95 = 17/1

So, in this example, I would suggest that 12/1 is pretty poor value, and only value if you think C&A was going to win extremely well. Perhaps a fairer price, one which takes into account ALL of the various win scenarios, and not just the wins well scenario (but still ignores the lose/win scenario, Joe!!), would have been 17/1…

Alex,

I think that’s a very fair compromise you propose on the ‘style of success’ aspect of the bet, but (frustrating as it might be) it does not change my view on the lose/win.

I accept that, on the face of it, the argument seems completely bonkers because the punter, whether he is laid 12/1 or 100/1 about C&A on Saturday, no longer cares what the odds were once the horse has lost. But, the fact that the key player in the scenario has no further interest, does not mean that the principles of fair betting should have been abandoned.

It’s not an ethical question either; for example, if you desperately need to borrow £20, a moneylender might be your only option but he will charge you 4,000% interest – way above what anyone would call ‘fair’ or portraying an accurate reflection of the risk of that cash not being repaid.

The bookmakers simply quote these prices because, historically, it has never been questioned. When I called it a rip-off I meant in the broad accepted sense, not as an intentional tactic by bookmakers. Had I thought it intentional, I’d have used the word ‘con’. I’m actually a staunch supporter of bookmakers and the much-maligned industry as quite a few other posts on this blog demonstrate (I worked in the betting industry for most of my life).

Anyway, let us return to the issue and to the line of questioning I was pursuing yesterday. I’d ask you once again to set aside the probability formulas (not probabilities themselves) because those you cited were based on the prospect of leg 1 being successful. Let us look simply at how the price should be constructed.

(a) In any bet, in an effort to reach an accurate/fair price, should all the probabilities be taken into account?

Yes

(b) Does a probability exist that leg 1 can be lost?

Yes

(c) Does the bookie take that probability into account when compiling the RC price?

No

Refer back to (a) and you see that price cannot be accurate/fair.

Contingency:A future event or circumstance that is possible but cannot be predicted with certainty.Now, in the case of this double, what is the future event in question here? It has to be Leg 1, does it not? Because once the result of Leg 1 is known, no contingency applies to leg 2 because we have a fresh set of information.

So what is it about the performance of your horse in leg 1 that cannot be ‘predicted with certainty’?

Beyond all else (setting aside for now your point, Alex, about style) it cannot be ‘predicted with certainty’ the horse will win. And yet, that is the only contingency considered when pricing up.

The reality is that the bookie wants to have his cake and eat it. If there is a related contingency that the horse might win, and shorten for leg 2, there must also be a related contingency that the horse might lose, and lengthen. Contingency 2 is ignored. The fact that it does not matter to the outcome of the bet, for either party, is a secondary point for the purposes of this argument (and that has always been the toughest aspect to convey). In summary, the crux of my position is that a major probability, which is vital for accuracy and fairness in the compiling of any set of odds, has been disregarded.

Joe

OK Joe, let’s apply your preposterous argument to a simple win bet;

“(a) In any bet, in an effort to reach an accurate/fair price, should all the probabilities be taken into account?

Yes

(b) Does a probability exist that the simple win bet can be lost?

Yes

(c) Does the bookie take that probability into account when compiling the price?

No

Refer back to (a) and you see that price cannot be accurate/fair.”

You are completely and utterly wrong, and I’m staggered you can’t see it.

If you want a bookie, when pricing up a win/win bet, to consider the lose/win probability, then by the same token you should want a bookie when pricing up a straight win bet, to consider the lose probability.

Simplifying this argument shows how ridiculous it is.

I can’t believe you can’t see that the piece that is missing is the WIN/WIN scenario, but which results in the price lengthening for the 2nd event. The LOSE/WIN scenario does not form ANY part of the Probability formula for calculating the odds of two events occurring.

You never answered my question yesterday; Do you think the following formula is correct or not? It either is, or it isn’t.

P(A and B) = P(A) x P(B given A)

If you think it’s correct, can you not see that the argument P(B given not A) doesn’t feature in the formula and is therefore irrelevant?

If you think it’s incorrect, then you are wrong. This formula is correct for ALL events A and B.

All you need to do to make the following paragraph correct is change one word (in caps)

“The reality is that the bookie wants to have his cake and eat it. If there is a related contingency that the horse might win, and shorten for leg 2, there must also be a related contingency that the horse might WIN, and lengthen. Contingency 2 is ignored.”

So yes, the bookie does want his cake and eat it, because he only ever considers that the horse might shorten, he rarely takes into account that the horse might WIN, but lengthen…

As I’ve already proved, P(B given not A), ie the price if the horse loses, forms no part of the probability equation for calculating P(A and B) and is therefore irrelevant to the price quoted.

Alex,

Try, for a while, to forget about formulas – your fixation on them is, I think what is causing you to pursue a single line of thought here.

Also, please let me put my side of this without pejoratives like ‘preposterous’, a subjective word which I could also use in this response but will not do so because, however much I disagree with what you say. I respect your position on it and won’t condemn it.I am not trying to ‘beat’ you here, it’s not a competitive debate for me; I’m just hoping that the different opinions can be explored for general enlightenment.

Now, to your assertion that the bookmaker does not and should not factor in the probability of a horse losing when pricing up a single win bet:

If he quotes you evens he has factored the lose probability at 50%

at 4/7 the ‘lose’ probability is 36.4%

at 2/5 the lose probability is 28.6%

Etc,. Etc.

Do you accept this?

Joe

No, of course not.

The probability of event A occurring is P(A)

The probability of event A not occurring is 1-P(A)

If a punter says, what price will you offer me for event A occurring, the bookmaker quotes P(A). He doesn’t quote anything to do with 1-P(A).

Yes, obviously one is a product of the other, and they are inextricably linked, because all probabilities must add up to one. ie the Probability of the event not occurring, plus the probability of the event occurring, is 1;

(P(A)) + (1-P(A)) = 1

Back to my question, do you, or do you not believe that the following equation is correct in ALL cases for calculating the chances of events A and B both occurring?

P(A and B) = P(A) x P(B given A).

YES or NO, please.

Don’t patronise me by saying, don’t get fixated about formulae. The formula above is indisputably correct, how you you be so arrogant as to say it isn’t?

If you accept it’s correct, can you not see that P(B given not A) does not feature in it?

It looks like we are reaching the stage we did yesterday where this is causing you immense frustration. I shall now bow out.

By the way, it was not my intention by any stretch of the imagination to patronise you and I’m pretty sure anyone who knows me would not describe me as arrogant

Joe

So you won’t answer the question as to whether the formula is correct or not?

Do I take that as a no?

You’d rather ‘bow out’ than answer a simple yes or no question? Why is that?

Ultimately, this debate is not about “different opinions being explored for general enlightenment”, or some kind of compromise being reached. The simple truth is you are wrong – all I’ve tried to do, endlessly, and evidently in vain, is show you why, but you are either unable or unwilling to accept what the maths proves.

The formula is what it is, there is no middle ground, no compromise, it’s a simple mathematical truth. The formula shows that the element of probability which you want bookmakers to take into account, is totally irrelevant to the calculation of A & B. If you can’t accept that, that is your loss, and just devalues your understanding of probability.

The crux of your whole argument IS correct – that bookmakers related doubles are often stingy, but unfortunately the reason for this is not the reason you keep citing.

You seem to be under the impression that maths is something you can take or leave, and that one shouldn’t get too fixated on it. Well maths underpins the whole of betting and combined probabilities and in my opinion, ignoring it is arrogant. I’m sure you’re not an arrogant person in general, as you say.

I enjoy reading your blogs, but on this particular subject you appear to have a blind spot, and I’ve run out of ways to help you understand why.

Sorry if it’s got heated – yes it has been incredibly frustrating, there is nothing more frustrating than knowing something is correct, but being unable to convince someone of it, but there you go!

Thanks

Alex

Joe’s point is valid, if selecting any other double the odds of winning compensates accurately for either the first of second leg losing. However, in these pre-emptively manipulated ‘related contingencies’ prices the win price does not compensate for the loss in the first or second leg.

Before both races the bookmaker has given a price relating to their estimation of the probability of winning each race. Since the bet is placed before either result is known and the results not genuinely related then both prices should stand.

I can understand the bookmakers perspective not wanting to offer the cumulative price, the information provided by the first leg can influence the price of the second leg if the bookmaker believes this to be the case the antepost price should be reduced accordingly so that the double is an appropriate price.

Of course the rules are made up to suit the situation, hence my bet on Septimus winning the Dante and the Derby getting a quote in one of the bookmaker’s rule book for a while.

My point is when bookmakers make up the rules to suit a situation where does it end? One of the best bets I have ever made was Le Havre to win the 2009 Prix Djebel doubled with Sea the Stars for the 2000 Guineas. Le Havre was 4/1 second favourite to the Naaquoos who was odds on to win that day and one of the favourites for the guineas. One result did marginally influence the price of the other but were the races related?

To the letter of some bookmakers’ laws my bet should have had the odds on the second leg altered following the first result, of course this didn’t happen but how can we ever know exactly what bookmakers consider related.

Aha, another person who laughs in the face of basic probability rules!

Richyy – would you care to answer the question below which Joe chose to decline to answer?

Is the following formula correct for calculating the probability of events A & B occurring?

P(A and B) = P(A) x P(B given A).

Simple question…

As an Odds compiler, my golden rule of pricing up any scenario is why offer 28/1 about a horse if you can lay the animal at 25’s.

You can offer whichever formula you like but offering prices comes down to pure arithmetic (not Maths).

The original comment was made to make the unaware aware of the nasty ways bookmakers have if ridding punters of their money pure and simple.

Anything beyond that is surplus to requirements in my book!

I always knew that making ‘Westminster’ open to the public via live television would complicate lives up and down the land.

All we have witnessed since that first broadcast is ‘waffle’ trying to hide the truth and I have the same notion about the comments made here.

Yes, bookmakers can offer whatever prices they choose, that’s their prerogative, and it’s up to the punter to decide whether they offer value or not. No disagreement there!

However, both Joe’s & Richyy’s assertion is that when pricing a double, the prices should simply be multiplied together. Well the formula proves that view is incorrect. Ignore it if you like, but it’s a simple fact.

Actually, Joe appears to have conceded that a straight multiple is incorrect, but he would still like the formula to contain an argument P(A given not B), which unfortunately it doesn’t.

Anyone who thinks that because bookmakers estimate Champion Court’s chances of winning (A) the King George at 25/1 and (B) the Gold Cup at 50/1 should be obliged to offer a straight double of 1325/1 P(A & B) needs to have a good think about what’s going on.

The bookmaker is not obliged to do that because the events are related. The bookmaker is therefore basically allowed to offer whatever he wants on the double. A savvy punter should be using the formula to work out whether what the bookmaker is offering is value or not.

The punter should do this by considering “what price would CC be for the Gold Cup, on average, if he wins the King George.” This price is represented by P(B given A) and makes up the second part of the formula for calculating P(A & B).

If you prefer, you can moan about what ‘feels’ fair, or just pluck a price out of thin air for yourself, or just moan about bookmakers. Or you could do the maths, work out what YOU think the fair price is, and then bet, or not, on that basis.

Hi Alex, while it is quite a compelling suggestion that the odds of the second outcome should be made on the basis of what might happen in the first event. I don’t think this equation is correct. The prices for these independent events are derived before any result so a straight multiplication should be applied. Only if one event has a genuine influence on the other (scorecast in football for example) should this formula be applied.

My point is the rules could be under constant flux if we make the suppression that two unrelated events are related by virtue of the information provided. If a jockey has won 3 in a row, there maybe an adjustment on the odds of them winning in the forth race, but there wouldn’t be an adjustment in the price made in a multiple for winning these four races together.

Clearly this is a slightly different scenario to bookmakers offering a ‘special price’ for the double, but in essence I think a fairer position would be to adjust the price of the second event to account for the double. eg if C&A was evens for the Fighting Fifth and had been 12/1 for the Champion Hurdle, the Champion Hurdle price should be reduced to account for the likelihood that it would win the Fighting Fifth. I guess that would be about 8/1 and that should remain the price until after the race. The double should be accepted and it would be up to the punter to decide whether the double or either single is good value.

This may end with very little difference in what is being offered by then bookmaker but at least the rules about doubles and multiples would remain consistent and not open to the vagaries of deciding how ‘related’ events that are actually unrelated are.

“I don’t think this equation is correct.”

Stopped reading at that point – the equation is correct for all events A & B, irrespective of whether they are independent or dependent. It’s not a matter of debate.

Richyy

In the interests of fairness, I did read the rest of the post!

I’m a bit confused why you think the formula doesn’t apply, but then later in the post come up with your own valuation of P(B given A) of 8/1? Which is basically what I estimated P(B given A) to be some time ago – I came up with 9.4 in an earlier post, a shade over 8/1.

You seem to then imply you’d be happy with the double of 8/1 x 10/11? Therefore you have applied the formula to come up with a price of the double, ignoring the straight double of 12/1 x 10/11…

So are we on the same lines, or not?

Anyway, I really don’t think we’re all going to reach a consensus. I can’t explain it any better than I’ve already tried, and don’t think I can add much more!

Hi Alex,

No problem I understand if you prefer not to continue, maybe we are as close to a resolution as we will ever get.

The difference may seem subtle if it ends in the same price but I think it is an important one for the integrity of how prices are arrived at. It should be possible to get double price of two unrelated events by a straight multiplication of both prices. If this means the price of the second event has to be changed to accommodate this then that is what should happen. So for Stan James to quote a double price of 12/1 their price of C&A for the Champion should have been 6/1.

This would mean some relatively stingy antepost prices and more fluctuations in the price but at least the system for deriving prices for multiples would be consistent and wouldn’t involve the introduction of another variable.

I don’t see this happening because the bookmakers are in competition and some will want to offer a larger price for the second event to attract business and will refuse the double.

Several bookmakers have closed my account with them because of these price discrepancies unless their traders are able to consider all of the implications of events they call ‘related’ there will always be an opportunity for punters to take advantage and disputes are likely.