## What is Probability Slicing ? Please explain !

One of my good clients, (Pauline H. :-)) contacted me the other day and said “please explain” why Probability Slicing is such a good way to make exotic bets such as Quaddies. So I thought I’d do a posting on it with an example which will hopefully explain the concept .

**All up betting vs. Quaddie**

Firstly just a bit of background about how Quaddie dividends are calculated. Let’s take a 5 runner field where the TAB Tote win divvies of the 5 runners are 2.0, 4.0, 6.0, 8.0 and 10.0. If you do the maths then this represents a margin of 14% which is roughly what the TAB take out of the Win pool.

And for the sake of the example let’s say that all 4 races in the Quaddie have 5 runners with the same odds.

That means that the All-Up dividend if the 4 favourites win will be $16.00. However if you do the maths and take into account that the TAB takes out 20% of the Quaddie pool before declaring the dividend, then the equivalent Quaddie dividend is $21.75 which is an inherent advantage of +36%. Similarly if all 4 outsiders won then the All-Up dividend would be $10,000 compared to the Quaddie dividend of $13,590 which again is an advantage of +36%.

If you are wanting to outlay $100 in a flexi bet and take the top 3 in each of the 4 legs then that would mean there are 81 combinations being covered in one flexi bet and this means that you would have 123.46% of the winning dividend . If the 4 favourites salute then you get back a princely amount of $26.85 resulting in a loss of $73.15. However if the 4 runners with odds of 6.00 get up then the return would be a huge $2,174.54 for a profit of $2,074 ! But clearly this is not a very satisfactory way to bet.

**Dutchbook staking**

Instead of taking one flexi bet why not take every combination in proportion to its expected dividend. This would result in 81 individual bets having to be placed. But the smallest unit of investment is $0.50 and if you take the longest paying combination for $0.50 (the 4 runners with odds of 6.00) then you will return would be $880.69. But to get this same return if the 4 favourites win you would have to have $40.50 on this combination. And then your total outlay to get the same return back for every one of the 81 combinations would be $464.50 instead of your targeted $100. There must be a better way … and the better way is **Probability Slicing. **

** ****Probability Slicing**

What TAB Probet does is to combine runners whose win odds are close together but also considering the total outlay that you require. Sometimes it’s impossible to combine runners in such a way that will exactly achieve your outlay. But it will do the best it can. So instead of having to outlay $464.50 to cover the 81 combinations individually (with bet sizes of between $0.50 and $40.50) TAB Probet uses its **probability slicing **algorithm to :

- give you your required outlay (as close as possible)
- give you the roughly the same return on every combination

So for the same 81 combinations TAB Probet will group like paying combinations together and instead of having to outlay 81 individual bets, TAB Probet generates a series of flexi bets in an attempt to give you the most uniform return for your outlay. In the above example TAB Probet would generate individual bets ranging between $9.00 and $0.50 for a total outlay of $101.

**Taking runners with similar odds**

Let’s suppose that instead of 5 runners per race there are actually 12 runners per race with their odds as follows :

What I’ve done now is to split up the win percentage equally between all runners in the same colour band. For example instead of there being one runner with a win dividend of 10.0 there are now 4 runners with a win dividend of 40.0. You’ll notice the sum of the win dividends still add up to 114% even though there are 12 runners.

Now suppose that in one of the legs you actually took the 4 runners that were at 40.0. TAB Probet will recognise this and effectively combine your 4 runners at 40.0 as if there was just one runner at 10.0. Or if you have 3 runners at 21.0 it’s as if there was just one runner at 7.0. Or if you have 2 runners at 10.0 it’s as if there was just one runner at 5.0. And so on. In this way TAB Probet minimises the total number of bets that have to be placed but at the same time gives you the benefits of Dutchbook exotic betting.

Sometimes you just know that the dividend will not pay very well unless it falls within a particular range. TAB Probet also has the concept of being able to filter out combinations that are expected to pay either less than a minimum specified amount or greater than a maximum specified amount. In that way it will give you the best bang for your buck.

There is also a number of other nice features of TAB Probet to allow you to optimise your betting returns. So if you’re interested go to www.tabprobet.com.au where you can download a free version (TAB Probet Lite ) with many of the features talked about above.

**In summary – Advantages of betting Quaddies using TAB Probet **

- inherent advantage of taking Quaddies vs All-Ups
- extra value when TABs provide Jackpots
- combine runners whose win odds are close together
- top and tail combinations – using dividend filtering

## Is a Quaddie better value than an All-Up ?

*What do you think is a better bet ? A Quaddie or an All-Up ? When you take a Quaddie you have to place all bets before the 1 ^{st} leg. For an All-Up you can decide which win bets to make right up until the start time of each successive leg. You can also shop around for the best odds available on each bet in each leg. But does that make an All-Up bet better value than a Quaddie ? I thought I would carry out a little experiment to highlight the differences.*

I did a comparison using live data on Saturday 16^{th} November 2013 … Comparing TAB Probet’s Quaddie product verse betting the same runners using TAB Probet’s Dutchbook win bet capability.

I have selected the Caulfield Quaddie races which today are races 6 through 9. I have outlaid $100 on the Quaddie (actually only $99.50 ) and have taken 4 selections in each leg.

I have used TAB Probet’s very smart “probability slicing” algorithm to dutchbook the 256 combinations and there were some 108 bets generated as shown in the attached :

As it so happens I managed to get the winner in each leg. When the the favourite #10 Floria saluted in the last , the results of the Quaddie vs Dutchbook comparison were as follows :

**Dutchbook**

so we would have got back $284.70 for our total outlay of $100.

**Quaddie**

The winner was #10 Floria but I have also included the approximates for the other 3 runners we would have taken. We could have taken it on either NSW or VIC so I’ve shown below both returns. Notice how “consistent” the approximate returns were on VIC TAB and how “lucrative” the approximate returns were on NSW TAB. And the actual return on NSW TAB ($556.43) was almost DOUBLE the return compared with the Dutchbook win based on fixed odds ($284.70).

I call this the TAB Probet ADVANTAGE !!

**Conclusion**

** **The Quaddie will be a **better value bet** compared with a Dutchbook All-Up about 95 % of the time. Why ? Because in every leg of an all-up there is a bookie margin of around 15%. If you do the maths then that equates to a total take out of 48% of the all-up “pool” . Compare this with a Quaddie where there is only one take out of 20%. So on the average you are 28% better off taking a Quaddie versus All Up betting.

## Melbourne Cup 2013 – The Play Of The Day

**Well it’s that time of year again when THE race that stops the nation is being run at 3 PM on Tuesday 6 of November 2013.**

In my opinion based on disclose form it’s one of the most open fields in years with the invasion of so many international horses. Some have excellent credentials but the question is can they adapt to Australian conditions in time. With the cost of bringing a horse to Australia estimated to be between $200,000 and $400,000, one would think the owners would not take the decision lightly. **But still they come !**

This year there are only 5 locally bred runners (Super Cool, Fawkner, Hawkspur, Dear Demi and Ethiopia) in the field of 24. Historically they haven’t performed very well but in recent years this has started to change. Trainers are becoming more aware of cup preparation and the need to get it right to have any chance. Bart Cummings has always maintained that it was the miles in the legs that won him the Cups, but if Frequent Flyer miles has anything to do with it then the Aussie contingent have no chance.

*But the Cup is not just about breeding or fashion or time off work. It’s a chance to win a motza for a small outlay. And that’s what my website and blog is all about. The Melbourne Cup is a unique betting opportunity. With due respect, with the amount of mug money invested, you would have to be a mug not to make some money 🙂*

**How can a “newbie” punter make money on the Cup ?**

Well you could join up with one of the corporate bookmakers and get a nice upfront joining bonus of around $500 but be warned there are all sorts of t&c’s with a common one being the need to turn over your winnings 3 times before they will pay you out. And if you happen to win for a few weeks then it’s *“Hasta la vista, baby”*

**So what is my suggest Play Of The Day ?**

**Step 1** – work out how much you can afford to lose. Let’s say it’s $100

**Step 2** – work out every runner in the cup that you have some sort of affiliation with and that you think can win or run a place. You can use your birthday , your mother’s birthday, your father’s birthday , your children’s birthday, the dartboard, car number plates. But then trim your selections to your top 10.

**Step 3** – download TAB Probet Lite from www.tabprobet.com.au. This is a free product being supplied by TAB Corp. It features my very smart (if I say so myself :-)) “probability slicing” algorithm which allows you to take many many combinations and bet them in proportion to their odds.

**Step 4** – Bet on the **Melbourne Cup Trifecta** by combining all of your selections using the Dutchbook flexi bet method. Tick all of the selections that you want to take (Note: tick the “Box” box to take your selection for 1^{st} 2^{nd} 3^{rd}, or just tick the positions you want) and enter the total outlay you want, say $100.

**Step 5** – Press the **“Calculate”** button , wait a couple of seconds and then view your bets by clicking on the **“View”** button. If you are happy with the bet list generated then close this window and hit the **“Submit”** button to submit your bets. If you are not happy and want to change your bets then just modify your selections and hit the “**Calculate” **button again. Note that no bets will be submitted until you hit **“Submit”.**

**What are my Cup Selections ?**

As a said above I feel it’s as open as the Sydney Heads. But using my **Paradox of Odds algorithm** (go to www.puntforprofit.com.au for details) for price assessment I have come up with what I believe to be the best value runners.

My top pick is** #19 Simenon** from** #15 Mount Athos **and** #7 Foreteller.**

**So best of luck no matter what you do on the day. The MC is a great Aussie tradition. Let’s hope it keeps on keeping on !**