I am sure even the most disciplined of punters will have had a more ‘exotic’ bet at least once in their life, be it an exacta, tricast, placepot, double/treble, or some type of accumulator bet involving four or more selections, writes Dave Renham.

The lure of a bigger payout has a big appeal to many punters; I certainly include myself in that category in the past. I have been very lucky to have what I consider to be one monster betting payout in my life which was thanks to a tricast / CSF combo back in 2004. At the time this one bet paid the equivalent of around ten months’ worth of my take home pay from my teaching job. I wouldn’t mind that happening again now, I have to say!

The problem of course with any exotic bet is that the margin in favour of the bookmaker is usually bigger than it is if solely betting win singles. The more selections you have in an accumulator the bigger the bookmaker’s edge generally is. I am not going to dive deeply into the maths here but to give you a basic understanding of what is going on let me look at a hypothetical fourfold win only accumulator that has been placed with a bookmaker. I am going to assume that the four selections come from races with ten runners in each race and the decimal odds obtained for each horse are:

4.0, 6.0, 3.0, 7.0

In this scenario, the unlikely event of all four winning would net a profit of £503 for a £1 stake (£504 total return, including stake).

The problem is that the true odds of each of the four horses should be bigger. This is due to the inbuilt bookmaker overround/edge. On average the bookmaker’s edge in a 10-runner race will be around 20% (using a rough guide of 2% per horse). Hence when you add up the percentage chance of all the runners this will equal around 120%, not 100% which would, of course, give punters a fair playing field due to the odds be true/correct.

To find odds for these four horses much closer to their true odds we can look on the Betfair Exchange as their betting book for each horse race is always closer to 100%. This means the odds are as near to the true odds as we can get. Of course, we cannot place a fourfold on the Exchange, but I can at least borrow their ‘true’ prices to see what the winning return on this wager should pay, rather than the payout we saw earlier. Here are prices for our four horses that will be nearer to their true odds – the type of odds you would find on the Betfair machine:

4.6, 7.2, 3.25, 8.6

As can be seen each corresponding price is bigger, not by that much, but enough to make a huge difference overall. In this case, the winning profit on the fourfold would stand at a much healthier £924.70 for your £1 stake – over £420 more than would have been returned using the odds available from the bookmaker.

To make money on betting we need to get a value price. For example, if we can get odds of 2.2 on the toss of a fair coin, which should be priced at 2.0 we have value. Hence one could argue that multiple bets or accumulators can offer the punter value as long as all the selections are value prices. One immediate downside of course is that even if we are effectively getting value on each horse, we still need all of them to win!

Staying with the tossing the coin example, we can apply this to horse racing. Let’s assume that we have found four horses priced 2.2 that we believe have true odds of 2.0. If we combine them in a fourfold accumulator, the chances of all four winning equals 1 in 16. This is based on probability theory where we multiply the individual chance of each event together with each other – in this example each horse has a 50% or 1 in 2 chance of winning their respective race so we calculate thus ½ x ½ x ½ x ½ = 1/16.

Hence, we would be expected to win this fourfold bet one time in every 16 attempts. Of course it is not going to pan out perfectly like that in real life – we will not have 15 losing bets followed by a win, then another 15 losers followed by a win and so on. However, over the long term we will win with this type of bet on average around once in every 16 races (if we are correct about our true odds estimate).

But what is the edge on this bet?

Let us imagine we place £1 on each fourfold using the probability theory scenario of one win in 16. Over the 16 bets we would lose £15 on the 15 losing bets but win £22.43 on the one winning bet plus our stake back. This gives us a profit of £7.43 from £16 staked which equates to a Return on Investment (ROI%) of 46.4%.

As I have mentioned this calculation has been based on probability theory being played out perfectly in real life over 16 fourfold bets involving 64 horses priced at 2.0 with true odds of 2.2.

Let’s now compare the winning fourfold return with 64 individual win singles on these same horses using £1 stakes. With a 50% chance of winning this means we win 32 times and lose 32 times. The 32 losses lose us £32. Each win nets us a profit of £1.20 so 32 x £1.20 equals £38.40 giving us an overall profit of £6.40.

Now the eagle-eyed mathematicians will have noted that in the second example the total outlay of the bets comes to £64 and in the fourfold example it came to £16. We were correct, so comparing simply the two profit figures here is not a fair test. We need to calculate the ROI% as before by dividing the profit of £6.40 by the total stake of £64. This gives us an ROI of 10% - a good deal lower than the fourfold return. Therefore, by doing that comparison, we can see that fourfolds where we have value on each horse, potentially gives us extra value in the long term when compared to win singles.

However, this is all well and good, but a massive downside to the multi approach is finding four horses that offer value on the same day. For some of us it hard enough to find one each day, let alone four. In theory, four value selections combined in fourfolds offer us the chance to really enhance our long-term returns, but in practice it is going to be nigh on impossible to achieve it.

Even if we did find four value selections what are the chances these value selections will all be available with the same bookmaker? Not only that, but the example I gave looked at four very short-priced runners giving us returns on average once in 16 races.

If we instead consider say four horses that all had a bookmaker price of 4.0 (3/1) where their true odds were all say 4.3 (3.3/1), based on probability theory this bet is going to be landed just once in every 256 bets (because ¼ x ¼ x ¼ x ¼ = 1/256).

So, if we assume we are able to find four 4.0 priced horses with true odds of 4.3 on the same day with the same bookie, let’s say once every week, and we place them in a win fourfold accumulator, on average we will have one successful bet every 4.92 years! Perhaps this is starting to help explain why bookmakers push their multiple and accumulator bets so much!

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There is one type of multiple that some people believe can offer us some value though and that is an each-way double. An each-way double is when we place a bet on two horses to win and/or place. If both horses win, the win part is worked out in the same way as a win double. If both horses place, or one horse wins and the other one places, we will win the place part of our each-way double. And, naturally, if one or both horses fail to at least place the bet is a losing one.

Let’s look at example with prices. We’ll assume both horses are priced at 5.0 (4/1) and the place odds are ¼ of the win odds. Here are the possible outcomes based on a £1 each-way double (£2 staked):

Advocates of this bet will say that one advantage of an each-way double compared with a straight win double is that we can get a return even if both horses fail to win, as long as they get placed. They will also say, quite rightly, that compared to the fourfold accumulators looked at earlier we only need two horses to perform well, not four. Hence the bookmaker edge / margin is less pronounced.

Personally, I do play each-way doubles from time to time. When running my tipping service back in the early 2000s I put up the odd each-way double as actual main bets/selections, and I nailed an each-way double that returned a profit of £128 for an outlay of £2. So, with the right selections in the right race, I view this bet as having potential to make money long term. However, as with anything in betting, we need lots of patience to find the right opportunities.

The ideal type of race we are looking for is when we have a race with a very short-priced favourite, with the second favourite clear in the betting of the remainder. Such a race could look like this – let us assume it is a non-handicap:

We could find that a maiden or a novice chase/hurdle race could be priced up in this way. In this example the second favourite is ideal as one of our each-way double selections, because there will be value in the place part of the bet. The chance of the place based on the bookmaker price is even money (2.0) thanks to the place paying 1/5 of the odds, but in reality, the true chance of placing is much shorter, probably somewhere around the 1.80 mark.

The maths behind proving this is complicated, so I won’t bore you with that, but after the next race I look at I hope you are able to trust me on it. Therefore, allow me to now give a real-life example from a race in October 2024 with a similar market dynamic, because you will be able to see the place value more easily:

The ‘shape’ of the market for this race is not quite as good as my hypothetical example purely because the second favourite is only four points clear of the third favourite in the betting. However, the top two in the betting have the same prices (30/100 and 5/1) as in the imaginary race, and if we look at the Betfair place odds we see the following:

Now I noted earlier that Betfair odds on the win market are as close to true odds as we can find. It is a similar story for the place market, especially for the top two in the betting. Hence in the Sedgefield race we can see that the ‘true’ place price for Path Of Stars was 1.72. Remember the place part of this bet, if successful, would pay 2.0 at the bookies. This gives us the edge as far as the place part of the bet is concerned because the true chance of Path Of Stars placing in percentage terms was 58.1%, a full 8.1% higher than the bookmaker percentage chance of placing which was 50%.

Hopefully that makes sense, and you can see that there can be a place edge to be found given the right race shape / market make-up.

Unfortunately, before one gets too over excited, there is an issue with a possible each-way double even if you are able to find two similar place edges on the same day with the same bookie, which is that we have not considered the bookmaker win odds versus their true odds.

Ideally, we need to find horses that not only have this place edge, but whose exchange price is as close to the bookmaker price as possible. As we know, this does not happen often, but in this real-life example Path Of Stars was only marginally above his bookmaker price of 6.0 on Betfair as the BSP was 6.16. To give you some maths here, the chance of a true 6.0 priced runner winning is 16.7%, a true 6.16 priced runner has a 16.2% chance of winning.

For the record Path Of Stars did not finish in the first two, but that is not the point. The point is that in terms of the place part of the bet, the probability/maths was in our favour and he was very much a value play.

Five-runner races offer the best value from a place perspective when two horses count for places, hence why I chose that field size to try and illustrate my point. Likewise, eight-runner races offer the best value from a place perspective in terms of three placed horses where the bookmakers pay one fifth of the odds. These races also lend themselves to getting that place edge we have seen already. Below is an eight-runner race from 10th October 2024 which was actually a handicap. The race was at Exeter:

Again, we have a short-priced favourite, and the second favourite War Lord is again priced at 5/1. With 1/5 the odds a place, the second favourite once more has a 2.0 chance of placing according to the bookmaker odds. However, when we look at the Betfair Placed Odds we see that War Lord’s ‘true’ odds are 1.76 not 2.0.

This type of race offers the same place edge as before. Unfortunately, in this example War Lord’s win price on Betfair was significantly higher at 8.55. On the upside he finished third and did land the place.

At this juncture I should mention that using five- and eight-runner races for these bets has some inherent danger. One non-runner in either would scupper plans instantly as the place terms will be altered essentially turning the bet on its head. The value place bet would suddenly become a very bad value bet. Hence, it may be better to think about six-runner or nine-runner races as an option just in case, even though these are slightly poorer value in place terms. This is assuming of course you can still gain the same type of edge within the place part of the bet.

That’s all for this article. However, my plan is to go into more detail about each-way doubles in a follow up piece. I have spent several hours creating a spreadsheet that can simulate thousands of races where theoretical each-way doubles with specific prices can be placed, and the long-term returns can be calculated based on ‘true’ win and placed percentages.

Why an article solely looking at each-way doubles? Well, as I said, bookmakers hate these types of bet: they know that there can be a place ‘flaw’ in the type of races I have discussed. Bookmakers have been known to close accounts for people they consider to be successful “each-way double thieves”. [If you value your accounts, you’ll have more success placing these bets on the high street!]

Right, I’m off to play with my spreadsheet and I looking forward to sharing some findings with you next time.

-      DR