Betting to Win – the solution
The first thing to notice is that if the odds are 15 to 1 then a bet of, say £10, will give a profit of £150 if you win, i.e. you get your stake back, so it is better to think about “outlay £10, income £160”. We can draw up a table showing what will happen in the case of each horse winning:
| Horse | odds | outlay | return if win |
| KNOW HOW | 15 - 1 | k | 16k |
| EQUATION | 11 - 1 | e | 12e |
| FIBONACCI | 8 - 1 | b | 9b |
| FERMAT | 7 - 1 | f | 8f |
| PASCAL | 3 - 1 | p | 4p |
| NEWTON | 2 - 1 | n | 3n |
Total outlay, T = k + e + b + f + p + n
Now Mr H makes a profit of £120 whichever horse wins, so we have six equations:
120 = 16k – T = 12e – T = 9b – T = 8f – T = 4p – T = 3n – T.
Dividing each of these equations we get a new set:
|
| = k – |
| ; |
| = e – |
| ; |
| = b – |
| ; | |||||||||||||||||||
|
| = f – |
| ; |
| = p – |
| ; |
| = n – |
|
If we add these equations together we get:
| 120 |
|
|  |
| = T – T |
|
| |
The fractions in the brackets add up to
|
| Thus |
|
|
|
| = |
| × | T. |
| So T = |
| = 3336. |
With this value for T we can calculate the values of k, e, b etc.
This gives the amounts as:
| KNOW HOW: | £216, | EQUATION: | £288, | FIBONACCI: | £384, |
| FERMAT: | £432, | PASCAL: | £864, | NEWTON: | £1152. |
| The key to all this is that bracket |
|
| . | This is the |
Unfortunately, the bookies know this!
Barry Humphreys
