A368476 - OEIS

A368476

Decimal expansion of 109/65, being the highest possible win/loss points ratio in a completed 3-set tennis match, with 10-point final tie-break, which the player loses.

1, 6, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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

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 8-10 in the two tie-break games.

Player A wins 109 points and player B wins 65 points, but player A loses the match.

This ratio is a little lower than when the final tie-break is played to 7 points (see A368009).

LINKS

Table of n, a(n) for n=1..87.

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

FORMULA

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

EXAMPLE

1.6769230... (periodic part 769230).

MATHEMATICA

First[RealDigits[109/65, 10, 100]] (* or *)

PadRight[{1, 6}, 100, {3, 0, 7, 6, 9, 2}] (* Paolo Xausa, Jan 30 2024 *)