A368009 Decimal expansion of 53/31, being the highest possible points won/lost ratio in a completed 3-set tennis match which the player loses.

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, 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, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5

Offset: 1

Author

Marco Ripà, Dec 07 2023

Keywords

• nonn
• cons
• easy

Comments

Tie-break games are played to 7 points in all sets.

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 in the two tie-break games.

Player A wins 106 points and player B wins 62 points, but player A loses the match.

Examples

			1.709677419354838... (periodic part 709677419354838).
		

Links

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

Crossrefs

Cf. A021428, A368008, A368146, A368476.

Programs

Mathematica

First[RealDigits[53/31, 10, 100]] (* Paolo Xausa, Jan 29 2024 *)

Formula

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