Small Fields And Exotic Convex Bets (Part 2)

In horse-racing, as already outlined in Small Fields And Exotic Convex Bets (Part 1), we can look for better prices in the exotic markets when we are faced with small fields of runners.

On this occasion, we will focus on trifecta bets in eight and nine-runner fields.

As before, using an Excel spreadsheet, we can set up a table as follows to generate trifecta tickets subject to the following conditions:

• Runner saddle numbers as both row and column labels,
• Populate the table with 1s and 0s subject to the following constraints:
  • Row totals must equal three.
  • Column totals must equal three.
• Use Solver to generate a possible solution. Otherwise, use trial and error.
• Read off the column labels of the rows containing 1s to generate a minimum set of tickets.
• There are multiple valid combinations of tickets.
• No matter what is the winning combination of the race, the generated set will contain one ticket with at least two of the winning numbers (not necessarily in correct order).

This is an example of generating a trifecta solution for an eight-runner field.

and this is an example of generating a trifecta solution for a nine-runner field.

Ideally, to generate a valid set of tickets that meet our constraints, we should use solver (3-5 mins).

The following tables show the probabilities of getting one or more tickets with at least two of the winning numbers (not necessarily in correct order) For example, we have a 23% chance of getting one such ticket in a nine-runner field.

CombCount	Count	Probability
0	0	0%
1	19	23%
2	44	52%
3	20	24%
4	1	1%

One possible approach is, having selected a positive expected value trifecta combination, that we generate a random, solver set to cover the remainder of the field.

Enjoy!

Small Fields And Exotic Convex Bets (Part 1)

Small Fields And Exotic Convex Bets

In horse-racing, Convex betting is predicated on frequent small losses and infrequent big wins. But in order to take advantage of this strategy, we require markets with fields of 11+ runners to generate live outsider prices.

Unfortunately, in the last couple of years, British racing has begun to noticeably decline in terms of competitive fields in both Flat and Jump codes with the consequential drop in price ranges! We, sports traders, cannot fix the current problems facing British racing so we must either adapt or die!

One possible solution for us is to look for better prices in the exotic (e.g. Betfair's 'Forecast' and 'Reverse FC') markets.

To that end, using an Excel spreadsheet, we can set up a table as follows to generate either 'Forecast' or 'Reverse FC' tickets subject to the following conditions:

• Runner saddle numbers as both row and column labels,
• Populate the table with 1s and 0s subject to the following constraints:
  • Row totals must equal two.
  • Column totals must equal two.
• Use Solver to generate a possible solution. Otherwise, use trial and error.
• Read off the row labels of the columns containing 1s to generate a subset of all possible tickets.
• There are multiple valid combinations of tickets.
• No matter what is the winning combination of the race, the generated set will contain two tickets with at least one of the winning numbers.

This is an example of generating a 'Reverse FC' solution for an eight-runner field.

and this is an example of generating a 'Forecast' solution for a five-runner field.

Enjoy!

Benfords Law Favorites and Exotic Bets

In various horse-racing jurisdictions (e.g. Australia, UK, Ireland, France), there is a very strong correlation between the winning rates of favorites and Benford's Law. In other words, favorites win approximately 30% of races, second favorites approximately 18% and third favorites approximately 12%. One could conceivably use this information to generate some tickets for Daily Double, Pick 3, 4, 5, or 6 exotic pools by using a random number generator and a "Benford distribution" of win rates. Though unscientific in validation, this method proved invaluable to me over the Breeders Cup weekend (given many upsets to expected outcomes)!