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.

1, 8, 1, 2, 5

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 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).

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

1.8125.

Crossrefs

Cf. A021061, A368008, A368009, A368476.

Sequence in context: A105473 A010518 A303321 * A372426 A356022 A077464

Adjacent sequences: A368143 A368144 A368145 * A368147 A368148 A368149

Keyword

nonn,cons,easy,fini,full

Author

Marco Ripà, Dec 13 2023

Status

approved