Perm Advice

[Space Cowboy]

Does anyone Know a site, or can explain, how many goliaths I can get from 30 or 40 selections etc?

[dashingcustomer]

The Goliath is an 8 selection bet consisting of 247 individual bets comprising:-
28 doubles
56 trebles
70 fourfolds
56 fivefolds
28 sixfolds
8 sevenfolds
1 eight fold accumulator

Now, if you made 9 selections and wanted to cover them via Goliaths, then there would be 9 Goliaths requiring 247×9 = 2223 bets.
However, you asked about selecting 30 horses, which would require 5,852,925 Goliaths which is 1445,672,475 bets.
Making 40 selections does not bear thinking about!
An alternative way of looking at the problem if you wanted, say 32 horses, is to choose 8 specific races and select 4 horses in each race. You could then cover all 32 selections using 65,536 Goliaths, but this is still a formidable 16,187,392 bets.
Has that put you off the idea?

[Space Cowboy]

Thank you very much.

As you anticipated I am put off.

[aaronizneez]

Stay well away from the Kevin Keegan bubble variety

[dashingcustomer]

OK, you wanted a challenge. I have told you how many Goliaths, and how many bets therefore, there would be if 30 horses were fully covered.
Is there anyone can meet my challenge of working out:-
(i) how many Goliaths there would be with 40 selections;
(ii) How many individual bets that would be?
The first answer is an 8 figure number and the second is an 11 figure number.
Good luck with that!!!

[llanrumneyboy]

DC
Perhaps
76904685

And
18995457195

Regards

[Space Cowboy]

how do you work it out?

[dashingcustomer]

Congratulations to lanrumneyboy who got it right first time!
If there are 40 selections then the number of Goliaths is:-
(40x39x38x37x36x35x34x33)/(8x7x6x5x4x3x2x1) = 76,904,685
and the number of bets is 247 x number of Golitahs = 18,995,457,195
I hope this helps and thanks for setting the original challenge.

[Drone]

Any chance of a work-through on your maths Dashingcustomer as I get lost at “30 horses, which would require 5,852,925 Goliaths”

A ‘simple’ way to calculate a 30-horse multiple without perming Goliaths is as follows. Whether it results in more or fewer bets than your method I don’t know!

The formula for full-cover multiples including singles is (2^n)-1 where n is the number of selections

Lucky 15 (2^4)-1 = 16-1 = 15

For multiples excluding singles the formula is (2^n)-(n+1)

Yankee (2^4)-(4+1) = 16-5 =11
Goliath (2^8)-(8+1) = 256-9 =247

So for a 30-horse multiple it would be
(2^30)-(30+1) = 1073741824-31 = 1,073,741,793 which is just over 1 Billion bets

or 40, which is
(2^40)-(40+1) = 1099511627776-41 = 1,099,511,627,735 which is just over 1 Trillion bets

So if Donald Trump walked into a bookmakers and asked for a 1 Cent 40-multiple even he’d struggle to pay as it would set him back around 10 Billion Dollars

This is really just a variation on the apochryphal ‘Wheat and Chessboard Tale’ emphasising how rapid and how counter-intuitive exponential growth is

The story is first known to have been recorded in 1256 by Ibn Khallikan.[1] Another version has the inventor of chess (in some tellings Sessa, an ancient Indian Minister) request his ruler give him wheat according to the wheat and chessboard problem. The ruler laughs it off as a meager prize for a brilliant invention, only to have court treasurers report the unexpectedly huge number of wheat grains would outstrip the ruler’s resources. Versions differ as to whether the inventor becomes a high-ranking advisor or is executed

https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem

[Drone]

dashingcustomer wrote:

Congratulations to lanrumneyboy who got it right first time!
If there are 40 selections then the number of Goliaths is:-
(40x39x38x37x36x35x34x33)/(8x7x6x5x4x3x2x1) = 76,904,685
and the number of bets is 247 x number of Golitahs = 18,995,457,195
I hope this helps and thanks for setting the original challenge.

Ah, factorials

Are you using Binomial Coefficients? n!/(n-k)!k! ?

I find the maths behind permutations fascinating but despite years of endeavour still struggle to get my cobwebby brain round it all

[dashingcustomer]

Your mathematics and welcomed detailed research is impeccable. In some ways, to do a full cover with n (any) number of horses is easier than the original problem set by Space Cowboy.
Maybe tomorrow I will set you (Drone) a betting problem to do with premutations.
In the meantime, congratulations, and thanks to Space Cowboy for the original.

[Nathan Hughes]

I’d have to throw a non runner or two into the equation

Charles Darwin to conquer the World

[dashingcustomer]

You are correct; it’s all to do with Binomials.
Which leads me on to your challenge, which also requires a bit of maths.
If you are lucky enough to get all 8 winners in a Goliath, what is your total return, to a £1 stake, if the winners were:-
Evens, 6/4, 2/1, 3/1, 4/1, 5/1, 6/1 and 7/1
Don’t go and miss your racing spending endless hours working out the 247 individual returns.
Good luck

[Drone]

An online calculator tells me it’s £635,001.50 but resorting to the all-knowing ‘net has been the death of quizzes so that’s no good

The sole eight-fold is easy enough (I hope!) – add 1 to all the odds and multiply i.e. 2×2.5x3x4x5x6x7x8 = £100,800

The formula for working out the number of combinations of doubles, trebles etc is the aforementioned Binomial Coefficient n!/k!(n-k)! where n equals number of selections, in this case 8, and k equals the subset requiring combination calculation

e.g. for the subset of Doubles it’s 8!/2!(8-2)! = 8!/2!6! = 40320/2×720 = 40320/1440 = 28 Doubles
for the subset of Trebles it’s 8!/3!(8-3)! = 8!/3!5! = 40320/6×120 = 40320/720 = 56 Trebles

But how you calculate the total winiings at the odds specified on those 28 or 56 I’ve no idea, though suspect it’s by a manipulation of the binomials

Over to you, or whoever

edit: for those unaware of the terminology !=Factorial. 8 Factorial = 8x7x6x5x4x3x2x1

[dashingcustomer]

You actually know a lot more mathematics than you give yourself credit for. Well done for getting the correct answer, whatever the means.

Let’s start with a simple case.
Select two runners and back them in singles and a double.
They both win at 2/1 and 3/1.
Therefore your total return to a £1 stake is (4×5) – 1 = £19

Now let’s up the pace by selecting 3 horses and covering them in singles, doubles and a treble.
This time their odds are 3/1, 4/1 and 5/1
Therefore your total return to a £1 stake is (5x6x7) -1 = £209
Had you not had the singles then the total would have been (5x6x7) – (1 + 4+ 5 + 6) =£194

The final lesson before the real thing.
You have a £1 yankee and get winners at 2/1, 3/1, 4/1 and 9/1
Your total return to a £1 stake is (4 x 5 x 6 x 11) – (1 + 3 + 4 + 5 + 10) = £1297

Now the Goliath.
You get 8 winners at Evens, 6/4, 2/1, 3/1, 4/1, 5/1, 6/1 and 7/1
Therefore your total return is ( 3 x 3.5 x 4 x 5 x 6 x 7 x 8 x 9 ) – ( 1 + 2 + 2.5 + 3 + 4 + 5 + 6 + 7 + 8 )
= £635,001.50 eh voila

[Space Cowboy]

Flippin amazing

I am trying to teach my son easy maths solutions to complicated problems based on these excellent examples.

Thank you

[dashingcustomer]

There are some quizzes the internet cannot help with. See Quiz 10 on the link below:-
http://www.greyhoundderby.com/Quiz%2010.html
Best of luck with that.

[Author]

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