Assorted Brain Teasers by Kundan Pangtey - HTML preview

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TEASER - 19

SERVING FIRST

Andy (A) and Sandy (S) are facing each other in a tennis match where Andy (A) is serving first in first set;

i     What  will  be  the  score  if  Andy  retains  his  service  and breaks 1st  service of Sandy (S) in the 1st  set ?

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ii    What  will  be  the  score if  Sandy  retains  his  service  and breaks 1st  service of Andy in the 1st  set ?

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THE EXPLANATION:

Andy (A) is serving first in 1st  set.

(a)    Andy  (A)  retains  his  service  ( )  and  breaks  (X)    the  1st service of Sandy (S) and wins first set,

Table - a

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(b)   Sandy  (S)  retains  his  service  ( )  and  breaks  (X)  the  1st service of Andy (A) and wins first set,

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When A breaks 1st  service of S (Table - a), the maximum gap created between A and S is of the order of 3 games where as when S breaks 1st  service of A (Table-b) the maximum gap is of the order 2   games only. Here A and S do exactly same thing but A achieves a gap of 3 games to 2 of S without doing any thing extra.

It can have a psychological impact on the performance of S. When  A  breaks  1st   service  of  S,  he  wins  set  at  6  -  3  and plays a total of 9 games (Table-a) where as when S breaks 1st  service of A, he wins set at   4 - 6 and plays a total of 10 games, one game more than A (Table-b).  By breaking  only once in the whole set A gets away by playing only 9 games (serves  five  time  to  four  of  S),  where  as  for  exactly  same number of break S is required to play 10 games for none of his fault, why this discrimination ?

(c)    Now, what happens if score line is:

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Table - c

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Table – d

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The total number of games played (in both cases) (Table - a & b) are seven (1 to 7) with 4 odd numbers (1st, 3rd & 5th) and 3  even  numbers (2nd,  4th  &  6th).  By virtue  of  serving  first,  A shall get an opportunity to serve odd numbers (4 times) and S shall have opportunity to serve even numbers. So A gets 4 serves and S gets 3 serves. Therefore, for same score line (6 - 1) A is required to break serve of S only two times (Table-c) where as S toils to break A three times (Table-d).

Why this inequality ?

In  all  above  cases,  it  is  very  obvious  that  A  is  enjoying  a certain  amount  of  advantage  over  S  only  because  he  is serving first. In today’s hyper sports and intense competitive era even a hair line gap advantage may have impact on the final result, especially if winner and loser are of same caliber.

What is the solution:  Equality ?:

Each player must be given equal number of services in each set  and  in  each  match,  so  that  equal  opportunity  level  is achieved.

Each set / match can be played in two stages.

•     1st  stage to be of 4 serves in total (2 each continuously).

Whosoever win maximum points with a gap of 4 wins the set else set goes to 2nd  stage.

•     2nd  stage would consist of maximum of six Steps (S-1 to S-6). Each player will be given one service alternatively at each   step.   One   who   wins   maximum   points   with   a difference of four (4) at any step wins the set.

•     In  case  of  a  tie  at  the  end  of  6th   step,  either  the  set  is terminated, irrespective of points difference and points in each  set  are  added  at  the  end  of  match  and  winner  is decided    on    the    basis    of    maximum    points    won cumulatively in a match.

•     Alternatively set can continue till a difference of 4 points is  achieved.  Set  itself  can  be  converted  into  a  match beyond a certain point.

1)   1st  STAGE: Total:  4 services (2 each with no gap).

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2)   2nd  STAGE:  2nd  stage consists of maximum 12 services

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In  each  set  there  will  be  seven  (7)  opportunity  (one  in  1st stage & six in 2nd  stage) to win the set early. If each set ends in  1st   stage  itself,  match  will  be  over  very  quickly.  It  would indicate  that  the  looser  is  not  of  equal  caliber  and  match deserves to end fast.

Alternatively, games or points won in each set can be added together at the end of match and who so ever wins maximum points,  in  whole  match  (cumulative)  with  a  difference  of  4 shall win the match.

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