I'm betting on sports from time to time, mainly football (soccer) and I usually bet very small amounts of money on the "correct score". I usually make a combination of 3 games so I get the odds up. Of course since it's extremely hard to get 3 scores correct in the one and same combination I loose almost every time but it's fine since it's such a small amount of money. I bet like 0.10€ per combination.
But I have always wondered one thing and since my math skills are extremely limited I need help with this.
So here's the question:
How many different full time score-combinations can it possibly be out of a 3 game-combination in football? If you follow some of these rules...
In this calculation you will not count any away team wins. Meaning the only scores possible are home team wins and ties.
There can only be a maximum of 1 tie score per combination.
The only scores that should be a part of this calculation are: 0-0, 1-0, 1-1, 2-0, 2-1, 2-2, 3-0, 3-1, 3-2, 4-0, 4-1.
Even with these rules I obviously understand that it will be a lot of different combinations, probably over 200 but I'd still like to know if anyone would like to help.
We have 3 games. Of course it's the same 3 games that we bet on in all these correct score - combinations.
(G1 = Game 1, G2 = Game 2, G3 = Game 3).
Combo 1. G1: 1-0 G2: 1-0 G3: 1-0
Combo 2. G1: 1-0 G2: 1-0 G3: 0-0
Combo 3. G1: 1-0 G2: 0-0 G3: 1-0
Combo 4. G1: 0-0 G2: 1-0 G3: 1-0
Combo 5. G1: 1-0 G2: 1-0 G3: 1-1
Combo 6. G1: 1-0 G2: 1-1 G3: 1-0
Combo 7. G1: 1-1 G2: 1-0 G3: 1-0
Combo 8. G1: 2-0 G2: 2-0 G3: 2-0
Combo 9. G1: 2-0 G2: 2-0 G3: 1-0
Combo10. G1: 2-0 G2: 1-0 G3: 1-0
Combo11. G1: 2-0 G2: 1-0 G3: 2-0
Combo12. G1: 1-0 G2: 1-0 G3: 2-0
Combo13. G1: 1-0 G2: 2-0 G3: 2-0
Combo14. G1: 2-0 G2: 2-0 G3: 0-0
Combo15. G1: 2-0 G2: 0-0 G3: 2-0
Combo16. G1: 0-0 G2: 2-0 G3: 2-0
Combo17. G1: 2-0 G2: 0-0 G3: 1-0
Combo18. G1: 2-0 G2: 1-0 G3: 0-0
Combo19. G1: 0-0 G2: 1-0 G3: 2-0
And so on...
As you can see I don't really have a good counting system for solving this and it gets pretty messy and not very easy to follow. But I hope some of you guys understand the question and what I'm looking for.
I want to know ALL different scores possible, in any order, for a 3-game combination following the rules and only using the scores mentioned in the rules.
I don't want to give away what I'm supposed to do with this calculation if someone can provide it but I promise, it's not what you probably think.
I would be very satisfied if someone just could give the exact number of possible score-combinations for 3 games, it's not necessary to demonstrate ALL the possible scores. Wouldn't mind if someone did that too though hehe... :)
Thanks for reading all of this and I hope I can get an answer on this! Take care