Tennis is an (abstract) strategic

pencil and paper game Paper-and-pencil games or paper-and-pen games (or some variation on those terms) are games that can be played solely with paper and pencils (or other writing implements), usually without erasing. They may be played to pass the time, as icebre ...

for two players. The

game A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator s ...

field consists of 4 fields and a centre line. These are called (-2,-1,0,1,2), with negative numbers belonging to player 1, positive to player 2. At start, the ball is at the centre line (0). Both players start with the same initial number (e.g. 50 points). In each draw, both players choose a number, and the ball is moved towards the player with the smallest number. The number chosen reduces the points for the next draws. The aim of the game is to move the ball beyond the second field of the opponent. The game is described in ''Das große Buch der Block- und Bleistiftspiele''.M. Mala. Das große Buch der Block- und Bleistiftspiele. Irisiana. 1998 (in German)

Mathematical description

For a simple description, we include the numbers -3 and 3 to denote the ball being beyond the second field. This results in a playfield as (-3,-2,-1,0,1,2,3). The draw of player i at time t will be denoted as

S_

, the ball is at time t in

B_

. At start is

B_0=0

and for both players is

S_=50

. Each player chooses a whole number

0\le Z_\le S_

, with

Z_=0

only if

S_=0

. The number reduces the points of this player (

S_=S_-Z_

). The ball is moved as follows: * If

Z_>Z_

, then the ball is moved towards player 2. ** If the ball was on a field of player 1, it will be moved over the centre line (

B_t=1

). ** Otherwise, the ball will be moved one field towards player 2 (

B_=B_+1

). * Symmetrically, the ball will be moved towards player 1 if

Z_.
* If Z_=Z_, the ball remains where it is.

For the result of the game, the following rules apply:
* The game ends if the ball is moved beyond the field of any player, of if both players do not have any points left.
* In both cases, the game is lost for that player on whose side the ball is.
* If the game is played repeatedly, it can be defined to give two win points if the ball is moved beyond the field, otherwise only one point.

Example games

In the first example, player one wins, but the ball is still on the playfield when both players do not have any points left. Tennis-Game1

In the second example, player 1 wins again, by hitting the ball beyond the other playfield using the last points he has left. Tennis-Game2

References

{{Reflist Abstract strategy games Mathematical games Paper-and-pencil games