Huge Permutation Problem

[LukeClosely]

[COLOR=rgba(0, 0, 0, 0.701961)]Hello. Please could I have some advice to help solve a problem which has an extraordinary amount of permutations. I feel like I have got lost in the numbers somewhat and could be missing a relatively simple way to solve the problem.[/COLOR][COLOR=rgba(0, 0, 0, 0.701961)]
I have a simple sheet that records 100 bets and each bets potential winnings in ROW 2 to ROW 101.
Each bet involves 4 teams, one from each of 4 leagues (entitled League 1, League 2, League 3, League 4).
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[COLOR=rgba(0, 0, 0, 0.701961)]COL A = team from League 1[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]COL C = team from League 2[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]COL E = team from League 3[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]COL G = team from League 4[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]COL H = potential winnings for that individual bet.[/COLOR]
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[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]For a bet to be successful ALL 4 TEAMS MUST WIN. If any of the 4 teams does not win the return from that bet is £0.[/COLOR]
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[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]There will only be 3 winning teams from League 1,[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]3 winning teams from League 2,[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]3 winning teams from League 3,[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]4 winning teams from League 4.[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]This makes 13 winning teams in total.[/COLOR]
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[COLOR=rgba(0, 0, 0, 0.701961)]However 12 different teams have been selected from League 1 (giving 12 unique values out of 100 entries),[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]16 selected from League 2,[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]15 selected from League 3,[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]17 selected from League 4.[/COLOR]
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[COLOR=rgba(0, 0, 0, 0.701961)]My question is what combination of 13 teams would give me the maximum return?[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]Remember only 3 teams will win from Leagues 1,2+3 and 4 teams from League 4.

I am happy to answer any questions as without a photo I may not have explained clearly enough.

Thank You[/COLOR]

 

[StephenCrump]

The 5 teams with the largest values for each league (6 in league 4) can then be used.

The workbook I posted used 5,5,5 and 6 teams just as a simple example, which also allowed me to list the relatively few possible combinations (COMBIN(5,3)^3*COMBIN(6,4)=15,000) so that you could easily validate the VBA algorithm).

The code in Sub TestBets is dynamic, and in theory will accommodate as many bets and as many teams as you like to choose from. In practice, you can certainly go beyond 5 and 6, but not much further without generating too many possible combinations to test.

On my machine, checking 100 bets using 8 teams chosen from each league takes nearly two minutes. If you tried to test many more teams, the leagues would finish before the program!

 

[shg]

If you tried to test many more teams, the leagues would finish before the program!

 

[LukeClosely]

There is some discussion taking place at

Huge Permutation Problem - Page 2

The original post was put on a couple of forums because I didn't think I had a high chance of getting a reply and I had no idea that people may use several of these forums