One Point Two Points

MORRA
A Game of Strategy

From The Teahouse of Experience YOU

The Rules of PlayRULES


MORRA
SHOW:  One  Two CALL:      
ONE   TWO
CALL:  One    Two
ONE   TWO
SHOW:      
ONE   TWO

SCORES
YOU: 

MORRA


SUMMARY OF    PLAYS
YOUR
PLAYS
SHOW
1 2
CALL 1
2
MORRA'S
PLAYS
SHOW
1 2
CALL 1
2

THE RULES OF PLAY
In its ancient form Morra is a hand game played for points by two people,1
both players show either one or two fingers, and simultaneously call,
out loud, the number of fingers that the other player will show.
A correct call wins the number of points showing as fingers (2, 3, or 4,)
if both players call correctly there is no winner.

In this version you play against a JavaScript - click your choices
for SHOW and CALL and then click the PLAY button.
Morra will make its choices (without peeking at yours) then compute winnings,
and update the points and results counters.

The JavaScript in this page uses a numerically optimal strategy
to play Morra - can you beat it?

Click RESET to clear the scores and play summary.


Notes
Morra is classed as a zero-sum two person game2 by virtue
of what is called the payoff matrix:
If by [1,1] we designate that a player shows one finger and calls
that the other player will show one finger we can construct
the following matrix of points that can be won by a player:

 Other
 Player
Player
  [1,1] [2,1] [1,2] [2,2]
[1,1] 0 +3 -2 0
[2,1] -3 0 0 +4
[1,2] +2 0 0 -3
[2,2] 0 -4 +3 0
  Zero-sum player payoff matrix

If both players play randomly then they will tend to win the
same number of points during a game, but if one player uses
a strategy the outcome can be weighted.

A strategic decision, made in the face of uncertainty
on the basis of past experience, is one which is intended to lead
to a desireable outcome.*

In the game Morra the player's past
experience is limited to knowledge of previous plays,
which reveals Morra's strategy. The uncertainty in the game
Morra is limited to 4 possible moves on each player's part,
the decision each time is to choose one of those plays, so randomly,
you'd expect to see each play about 25% of the time. In the long run,
Morra's strategy should win most points playing against random choices.

You might not lose a lot playing randomly but if you learn Morra's strategy you can win.

* your accumulation of electronic points in this game.


References
  1. J.C.C. McKinsey.
    Introduction to the Theory of Games.
    The Rand Corporation. New York: McGraw-Hill Book Company; 1952. p. 7.
  2. John von Neuman and Oskar Morgenstern.
    Theory of Games and Economic Behavior.
    Princeton: Princeton University Press; 1953. pp. 87 & ff.

The Teahouse of Experience Morra is copyright© 1976, 1999, 2000, 2001, 2002 by John B. Griffiths and is
based upon Human Factors Engineering research conducted
at the Graduate School of Library and Information Sciences,
University of Pittsburgh, 1976, and a presentation for the
Graphics and Display Research Department,
Sandia National Laboratory, Albuquerque, New Mexcico, 1979.