REQUISITE VARIETY 11/4 



D must play first, by selecting a number, and thus a particular row, 

 R, knowing this number, then selects a Greek letter, and thus a 

 particular column. The italic letter specified by the intersection 

 of the row and column is the outcome. If it is an a, R wins; if not, 

 R loses. 



Examination of the table soon shows that with this particular 

 table R can win always. Whatever value D selects first, R can always 

 select a Greek letter that will give the desired outcome. Thus if D 

 selects 1, R selects )S; if i) selects 2, R selects a; and so on. In fact, 

 if R acts according to the transformation 



,12 3 



^ « y 



then he can always force the outcome to be a. 



R's position, with this particular table, is peculiarly favourable, 

 for not only can R always force a as the outcome, but he can as 

 readily force, if desired, Z) or c as the outcome. R has, in fact, 

 complete control of the outcome. 



Ex. 1 : What transformation should R use to force c as outcome ? 



Ex. 2: If both i?'s and Z)'s values are integers, and the outcome E is also an 

 integer, given by 



E = R-2D, 



find an expression to give R in terms of D when the desired outcome is 37. 

 Ex. 3: A car's back wheels are skidding. D is the variable "Side to which the 



tail is moving", with two values, Right and Left. R is the driver's action 



"Direction in which he turns the steering wheel", with two values, Right and 



Left. Form the 2 x 2 table and fill in the outcomes. 

 £,v. 4: If i?'s play is determined by Z)'s in accordance with the transformation 



I 1 2 3 



^ y P a 



and many games are observed, what will be the variety in the many outcomes ? 

 Ex. 5: Has R complete control of the outcome if the table is triunique? 



11/4. The Table used above is, of course, peculiarly favourable 

 to R. Other Tables are, however, possible. Thus, suppose D and 

 R, playing on the same rules, are now given Table 11/4/1 in which 

 D now has a choice of five, and R a choice of four moves. 



If a is the target, R can always win. In fact, if D selects 3, R 

 has several ays of winning. As every row has at least one a, R 

 can always force the appearance of a as the outcome. On the other 

 hand, if the target is b he cannot always win. For if D selects 3, 

 there is no move by R that will give b as the outcome. And if the 

 target is c, R is quite helpless, for D wins always. 



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