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Tennis probability problem:
How many different possible paths within a set are there til the end of a set?
For example:
Game: 1 2 3 4 5 6 7
Player A: W W W W W W
Player B: L L L L L L
So, there are 2 possible pathways for 6-0. But how many are there total possibilities?
Cheers guys
How many different possible paths within a set are there til the end of a set?
For example:
Game: 1 2 3 4 5 6 7
Player A: W W W W W W
Player B: L L L L L L
So, there are 2 possible pathways for 6-0. But how many are there total possibilities?
Cheers guys
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I make it 2(6C6 + 7C6 + 8C6 + 9C6 + 10C6 + 11C6 + 12C6)
= 2(1 + 7 + 28 + 84 + 210 + 924)
= 2508
= 2(1 + 7 + 28 + 84 + 210 + 924)
= 2508
sorry meant 2(6C6 + 7C6 + 8C6 + 9C6 + 10C6 + 12C6)
I don't agree TCS.
Your figures give all the number of 'folds of 6' from 6,7,8,9,10,11 & 12 games respectively for each player. Therefore, I don't think that you've fully accounted for tennis' scoring structure.
For example your figure for a player winning a set 6-1 is 7 (7!/(6!*1!)). Unfortunately that figure would include the 'fold' where a player went 6-0 up and the opposing player then won 1 game.
e.g. There are only 6 ways each player could win a set in 7 games (6-1); LWWWWWW, WLWWWWW, WWLWWWW, WWWLWWW, WWWWLWW, & WWWWWLW.
Your figure of 7 would also seem to include WWWWWWL, which is not possible under the tennis scoring system.
Your figures give all the number of 'folds of 6' from 6,7,8,9,10,11 & 12 games respectively for each player. Therefore, I don't think that you've fully accounted for tennis' scoring structure.
For example your figure for a player winning a set 6-1 is 7 (7!/(6!*1!)). Unfortunately that figure would include the 'fold' where a player went 6-0 up and the opposing player then won 1 game.
e.g. There are only 6 ways each player could win a set in 7 games (6-1); LWWWWWW, WLWWWWW, WWLWWWW, WWWLWWW, WWWWLWW, & WWWWWLW.
Your figure of 7 would also seem to include WWWWWWL, which is not possible under the tennis scoring system.
Pretty much what I was thinking
only outcomes are;
6-0 = 6 matches
6-1 = 7 matches with the final match being a "W"
6-2 = 8 matches with the final match being a "W"
6-3 = 9 matches with the final match being a "W"
6-4 = 10 matches with the final match being a "W"
7-5 = 12 matches with the final match being a "W"
7-6 = 13 matches with the final match being a "W"
It should be easy to work out the number of paths for each of these outcomes then add them and double the result.
only outcomes are;
6-0 = 6 matches
6-1 = 7 matches with the final match being a "W"
6-2 = 8 matches with the final match being a "W"
6-3 = 9 matches with the final match being a "W"
6-4 = 10 matches with the final match being a "W"
7-5 = 12 matches with the final match being a "W"
7-6 = 13 matches with the final match being a "W"
It should be easy to work out the number of paths for each of these outcomes then add them and double the result.
yep agree with you both, needs a little more thought than I first thought!
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