A368008 -id:A368008 - cp's OEIS frontend

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

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 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.

			1.709677419354838... (periodic part 709677419354838).

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. A021428, A368008, A368146, A368476.

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

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

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.

Original entry on oeis.org

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

Offset: 1

Marco Ripà, Dec 26 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 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).

			1.6769230... (periodic part 769230).

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

Cf. A368008, A368009, A368146.

Apart from leading digits the same as A021017.

First[RealDigits[109/65, 10, 100]] (* or *)
PadRight[{1, 6}, 100, {3, 0, 7, 6, 9, 2}] (* Paolo Xausa, Jan 30 2024 *)

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

cp's OEIS Frontend

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.

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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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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.

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