%I #47 Jan 29 2024 04:05:10
%S 1,7,0,9,6,7,7,4,1,9,3,5,4,8,3,8,7,0,9,6,7,7,4,1,9,3,5,4,8,3,8,7,0,9,
%T 6,7,7,4,1,9,3,5,4,8,3,8,7,0,9,6,7,7,4,1,9,3,5,4,8,3,8,7,0,9,6,7,7,4,
%U 1,9,3,5,4,8,3,8,7,0,9,6,7,7,4,1,9,3,5
%N Decimal expansion of 53/31, being the highest possible points won/lost ratio in a completed 3-set tennis match which the player loses.
%C Tie-break games are played to 7 points in all sets.
%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 3 sets occurs with game scores 6-0 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 in the two tie-break games.
%C Player A wins 106 points and player B wins 62 points, but player A loses the match.
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F Equals (6*4 + 2*(6*4 + 6*2 + 5))/(2*(6*4 + 7)).
%e 1.709677419354838... (periodic part 709677419354838).
%t First[RealDigits[53/31, 10, 100]] (* _Paolo Xausa_, Jan 29 2024 *)
%Y Cf. A021428, A368008, A368146, A368476.
%K nonn,cons,easy
%O 1,2
%A _Marco RipĂ _, Dec 07 2023