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First of all congratulations on now being able to calculate the returns on your best ‘all winners’ Goliath.
Yes, you have underestimated the difficulty of the task by a gigantic factor.
Let me give you just one example.
You have selected 43 horses and asked to cover them in Goliaths. I think you are now able to work out what that costs. It is:-
(43x42x41x40x39x38x37x36x247)/(8x7x6x5x4x3x2)
In billions of those Goliaths you have selected 8 losers. But that does not necessarily make you a loser!?
The point is that in some of those bets you will have a Goliath in which you have selected 6 losers and your 20/1 and 22/1 winners. In fact I have calculated below exactly how many of your bets include this winning double.
(32x31x30x29x28x27)/(6x5x4x3x2x1) = 906,192
Now, each of these successul doubles returns 21×23 = £483
So your total return from these doubles alone is £437,690,736
You have to make a similar calculation for all the other times you just get a double, of which there are 54 more individual occasions.
Then there are the trebles, the fourtimers, fivetimers, sixtimers and seven timers. Finally, we reach the times when you get successful Goliaths.
If you did not have a headache before you started reading this, enjoy the one you have now!I analysed 5 more matches of Chapter 9 of ‘Racecourses Here Today and Gone Tomorrow’ last night in which each of today’s racecourses is matched against a nearby former course, Match 46 is Listowel v Rathkeale, Match 47 is Ludlow v Shrewsbury, Match 48 is Market Rasen v Lincoln, Match 49 is Musselburgh v Selkirk, Match 50 is Naas v Trim.
http://www.injuredjockeys.co.uk/fundraising-news.asp?$=323&o=
More tomorrow when I get that far.No, it is still fine even with weird prices. So 4/6 is 0.66666666 and the figures you would use would still be 2.6666666 and 1.6666666 (if deducting the singles). These numbers look daunting, but an excel spreadsheet will be provide you with an answer to the nearest penny.
I haven’t ventured into the discussion on this one because, although you are correct in calculating that you have 165 full Goliaths, you also have many more in which you have 7 correct, thousands in which you have 6 correct, and so on and so forth, with billions in which you have just a double for instance.
So, in your lifetime, you will not be able to work out exactly how much your return is and whether you actually make profit or not.Congratulations; that’s a brilliant way of summing it up. Yes, bookmakers would have used this method before their online calculators did it for them.
You now fully understand the mathematics and have extended it to suit your own example.
If I were your teacher I would give that 10/10 and a house point.Apologies for sending you to a link which did not work for you. I forgot to say that the quiz is in Powerpoint, so might not suit everyone’s computer.
As you read your Christmas racing books, do get in touch if you feel that any of them will still be being read in 100 years time so that I can include them on the list.
1. A Long Time Gone by Chris Pitt
2. The Derby Stakes/The Oaks by Michael Church
3. Seabiscuit; Three men and a racehorse by Laura Hillenbrand
4. Men and Horses I have known by George Lambton
5. Eclipse; The horse that changed horse racing forever by Nicholas Clee
6. McIllvanney on horse racing
7. Arkle by Ivor Herbert
8. Brigadier Gerard by John Hislop
9. A Jockeys Life by Dick Francis
10. Racecourses Here Today and Gone Tomorrow by John Slusar
11. Queen of the turf by Quintin Gilbey
12. Mr Darley’s Arabian by Chris McGrath
13. Neck or Nothing: The extraordinary life of Bob Siever by John Welcome
14. Horsesweat and Tears by Simon Barnes
15. Frankel, edited by Andy Pennington
16. Dawn Run by Anne Holland
17. Go Down to the Beaten by Chris Pitt
18. Masters of Manton by Paul Mathieu
19. Mince Pie for Starters by John Oaksey
20. Winner: My Racing Life by A P McCoyJust a week after Remembrance Sunday it was heart-wrenching to read of the Alexandra Park racegoer who, a century ago, bought his members badge expecting to enjoy a years racing and instead was killed in battle. His parents reaction was to inscribe his owners badge.
http://www.greyhoundderby.com/Alexandra%20Park%20Racecourse.htmlManaged to read 5 more matches of Chapter 9 of ‘Racecourses Here Today and Gone Tomorrow’ last night in which each of today’s racecourses is matched against a nearby former course, Match 41 is Laytown v Skerries Strand, Match 42 is Leicester v Loughborough, Match 43 is Leopardstown v Bray, Match 44 is Limerick v Ennis and Match 45 is Lingfield v Tunbridge Wells.
http://www.injuredjockeys.co.uk/fundraising-news.asp?$=323&o=
More tomorrow when I get that far.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.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 = £19Now 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) =£194The 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) = £1297Now 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 voilaYou 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 luckYour 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.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.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!!!I have researched 5 more matches of Chapter 9 of ‘Racecourses Here Today and Gone Tomorrow’ last night in which each of today’s racecourses is matched against a nearby former course, Match 36 is Huntingdon v Cambridge (no that’s an interesting match!), Match 37 is Kelso v Berwick, Match 38 is Kempton v Hurst Park, Match 39 is Kilbeggan v Athlone, Match 40 is Killarney v Tralee.
http://www.injuredjockeys.co.uk/fundraising-news.asp?$=323&o=
More tomorrow when I get that far.As could have been predicted, both Lambourn and Ilsley once had racecourses (see links below), but does anyone from the Lambourn area know the exact whereabouts of the former Lambourn course?
http://www.greyhoundderby.com/Lambourn%20Racecourse.html
Interest has been rekindled with the Injured Jockeys Fund advertising 4 books on the subject of Lost Racecourses, see the link below:-
http://www.injuredjockeys.co.uk/fundraising-news.asp?$=323&o=
Do people know of others?
