%I #24 Jan 08 2024 11:36:15

%S 1,8,1,2,5

%N Decimal expansion of 174/96 = 29/16, being the highest possible win/loss points ratio in a completed 5-set tennis match, with 10-point final tie-break, which the player loses.

%C Tie-break games are played to 7 points in all sets except the last of the match, which is a 10-point tie-break.

%C The structure of sets and games in tennis means a player can win more points but lose the match.

%C The highest win/loss ratio for 5 sets occurs with game scores 6-0 6-0 6-7 6-7 6-7, where player A wins games by points score 4-0, and loses by 2-4 in ordinary games and 5-7 5-7 8-10 in the three tie-break games.

%C Player A wins 174 points and player B wins 96 points, but player A loses the match.

%C This ratio is a little lower than when the final tie-break is played to 7 points (see A368008).

%F Equals (2*6*4 + 2*(6*4 + 6*2 + 5) + (6*4 + 6*2 + 8))/(2*(6*4 + 7) + (6*4 + 10)).

%e 1.8125.

%Y Cf. A021061, A368008, A368009, A368476.

%K nonn,cons,easy,fini,full

%O 1,2

%A _Marco Ripà_, Dec 13 2023