A021061 -id:A021061 - cp's OEIS frontend

A368008 Decimal expansion of 171/93, being the highest possible points won/lost ratio in a completed 5-set tennis match which the player loses.

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

Offset: 1

Marco Ripà, Dec 07 2023

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 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 in the three tie-break games.
Player A wins 171 points and player B wins 93 points, but player A loses the match.

			1.838709677419354... (periodic part 838709677419354).

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

Cf. A021061, A368009, A368146, A368476.

First[RealDigits[171/93, 10, 100]] (* Paolo Xausa, Jan 30 2024 *)

Equals (2*6*4 + 3*(6*4 + 6*2 + 5))/(3*(6*4 + 7)).

A368146 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.

Original entry on oeis.org

1, 8, 1, 2, 5

Offset: 1

Marco Ripà, Dec 13 2023

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 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.
Player A wins 174 points and player B wins 96 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 A368008).

			1.8125.

Cf. A021061, A368008, A368009, A368476.

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

A021574 Decimal expansion of 1/570.

Original entry on oeis.org

0, 0, 1, 7, 5, 4, 3, 8, 5, 9, 6, 4, 9, 1, 2, 2, 8, 0, 7, 0, 1, 7, 5, 4, 3, 8, 5, 9, 6, 4, 9, 1, 2, 2, 8, 0, 7, 0, 1, 7, 5, 4, 3, 8, 5, 9, 6, 4, 9, 1, 2, 2, 8, 0, 7, 0, 1, 7, 5, 4, 3, 8, 5, 9, 6, 4, 9, 1, 2, 2, 8, 0, 7, 0, 1, 7, 5, 4, 3, 8, 5, 9, 6, 4, 9, 1, 2, 2, 8, 0, 7, 0, 1, 7, 5, 4, 3, 8, 5

Offset: 0

N. J. A. Sloane

A021061 shifted right. - R. J. Mathar, Apr 19 2025

			0.001754385964912280701754385964912280701754385964912...

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

First[RealDigits[1/570, 10, 100, -1]] (* Paolo Xausa, Aug 22 2025 *)

cp's OEIS Frontend

A368008 Decimal expansion of 171/93, being the highest possible points won/lost ratio in a completed 5-set tennis match which the player loses.

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A368146 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.

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A021574 Decimal expansion of 1/570.

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