6 Pick Bet Grouping

[tleeuwenburg at gmail.com]

bullockbefriending bard wrote:
> (I apologise in advance for posting something slightly OT, but plead in
> mitigation that I'm trying to re-write an old, suboptimal VB6 (erk)
> brute-force attack in a shiny, elegant, pythonic manner. I would really
> appreciate some ideas about an appropriate algorithmic approach to this
> + pointers to any relevant implementations in Python. Along the way,
> I'm also trying to get Python into my organisation through the back
> door - so a further plea for tolerance in posting this here! :))
>
> A single 6 Pick bet looks like this:
> RACE1    RACE2    RACE3    RACE4    RACE5   RACE6
> runner1 / runner 2 / runner 3 / runner4 / runner5 / runner6  - $amount
>
> e.g. we might have:
>
> 5 / 3 / 11 / 7 / 1 / 9  - $50  (5 to come 1st or 2nd in Race1, 3 to
> come first or 2nd in Race 2, etc.)
> 7 / 3 / 11 / 7 / 1 / 9  - $50
> 5 / 3 / 11 / 14 / 1 / 9  - $50
> 7 / 3 / 11 / 14 / 1 / 9  - $50
>
> The totalizator system allows us to merge or group these four bets as
> follows:
>
> 5 + 7 / 3 / 11 / 7 + 14 / 1 / 9 - $50  ($200 total)
>
> This method of expressing multiple bets in one line is advantageous
> because we may have many thousands of combinations we wish to bet and
> only a limited amount of time in which to bet them.
>
> There are up to 14 horses in each race, so 7,529,536 possible 6 Pick
> bets. In practice, one might wish to bet (say)15,000 combinations out
> of these 7.5 million. However, it would be very nice to be able to
> *optimally* merge (as shown above) these 15,000 combinations so that
> they might fit on (say)  2,000 betting tickets instead of trying to
> write out 15,000 single tickets.
>
> To keep things simple, let's assume that all single bets are for the
> same amount. (In practice, however, this is not so.)
>
> Now, it's certainly possible to go about this via brute force
> iteration, but I would really appreciate it if anyone with a CS
> background could point me toward a smarter plan of attack. I have
> perused Skiena's Algorithm Handbook and various websites and can't seem
> to find an analogous problem. I'm hoping this is just my ignorance and
> that my brief exposition rings a bell for someone here.

I don't understand exactly. Why not merge all your bets into a single
line? What constraints exist on how many bets you can put onto one
ticket?

Do you meant you have some bag full of incoming bets, which you are
re-lodging after some merging process? Does this mean you will have one
ticket for each amount?

Cheers,
-T