Appendix
Competitive Strategies adequate for a Minsky Register machine

This section was converted directly from the original WordPerect 6.0 file, with no tweaking whatsover.


In the specifications that follow, please note that

                010101...01 
                             
                 100 plays

indicates 100 Prisoner's Dilemma competitions, in the first of 
which the player defects, in the second of which he cooperates, 
and so on.  The notation above thus specifies a block of 100 
plays.  The notation below, in contrast:

               01010101010 
                            
                100 times

indicates that a block of 11 set moves is to be repeated 100 
times.  It thus specifies a sequence of 1100 plays.

strategy b: Start with 0000.  Then:
     If opponent started 0000, play 11111111111100000, repeat.
         (gives bb = 2.412)
     If opponent started 0001, play 010101...01 followed by 011,
                                                 
                                     100 plays
        repeat. (gives br = 2.534)
     If opponent started 0010, play 111111111100, repeat. (gives bp = 3.000)

     If opponent started 0011, play 1000000000 followed by               
                                        
                                      10 times
        000000, repeat. (gives by = 2.472)
     If opponent started 0100, play 01010101...01, followed by 
                                                 
                                     500 plays
        11111000001 (gives bf = 2.495)
     If opponent started 0101, play 010101...01 followed by 011,
                                                 
                                     100 plays
        repeat. (gives bg = 2.534)
     If opponent started 0110, play 1000000000 followed by 
                                              
                                     20 times
        0000000000000, repeat.  (gives bw = 2.502)
     If opponent started 0111, play 111111111100, repeat. (gives bo = 3.000)
     If opponent started 1000, play 1000000000 followed by               
                                        
                                     10 times
        000000, repeat. (gives bx = 2.472)
     If opponent started 1001, play 010101...01 followed by 011,
                                                 
                                     100 plays
        repeat. (gives bz = 2.534)
     If opponent started 1010, play 1000000000 followed by               
                                        
                                     10 times
        000000, repeat. (gives bl = 2.472)
     If opponent started 1011, play 111111111100, repeat. (gives bs = 3.000)

strategy r: Start with 0001.  Then:
     If opponent started 0000, play 101010...10 followed by 111,
                                                 
                                     100 plays
        repeat. (gives rb = 2.485)
     If opponent started 0001, play 11111111111100000, repeat. (gives rr = 2.412)
     If opponent started 0010, play 010101...01 followed by 
                                                 
                                     180 plays
        111...111 and 111, repeat. (gives rp = 2.542)
                 
        20 plays
     If opponent started 0011, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives ry = 2.472)


     If opponent started 0100, play 11111111111111000000, 
                                                         
                                           31 times
        followed by 11111..11, repeat. (gives rf = 2.341)
                             
                    20 plays
     If opponent started 0101, play repeated 0.  (gives rg = 1)
     If opponent started 0110, play 1000000000 followed by
                                              
                                     20 times
       00000000001, repeat.  (gives rw = 2.526)
     If opponent started 0111, play 010101...01 followed by 
                                                 
                                     180 plays
        111...111 and 111, repeat. (gives ro = 2.542)
                 
        20 plays
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives rx = 2.472)
     If opponent started 1001, play 11111111111100000, repeat. (gives rz = 2.412)
     If opponent started 1010, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives rl = 2.472)
     If opponent started 1011, play 010101...01 followed by 
                                                 
                                     180 plays
        111...111 and 111, repeat. (gives rs = 2.542)
                 
        20 plays

strategy p: Start with 0010.  Then:
     If opponent started 0000, play 111111111101, repeat. (gives pb = 2.583)
     If opponent started 0001, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives pr = 2.567)
                 
        20 plays
     If opponent started 0010, play 11111111111100000, repeat. (gives pp = 2.412) 
     If opponent started 0011, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives py = 2.472)
     If opponent started 0100, play 111111...111, followed by 
                                                  
                                    19,854 plays
        000...000, followed by 0, repeat.  (gives pf = 2.485)
                    
        5146 plays
     If opponent started 0101, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives pg = 2.567)
                 
        20 plays
     If opponent started 0110, play 1000000000 followed by
                                              
                                     20 times
       00000000001, repeat.  (gives pw = 2.526)
     If opponent started 0111, play 11111111111100000, repeat.          
(gives po = 2.412)
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives px = 2.472)
     If opponent started 1001, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives pz = 2.567)
                 
        20 plays
     If opponent started 1010, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives pl = 2.472)
     If opponent started 1011, play 11111111111100000, repeat. (gives ps = 2.412)

strategy y: Start with 0011.  Then:
     If opponent started 0000, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives yb = .868)
     If opponent started 0001, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives yr = .868)
     If opponent started 0010, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives yp = .868)
     If opponent started 0011, play 111...111 followed by 
                                               
                                    1612 plays
        000...000, repeat.  (gives yy = 2.612)
                   
        388 plays
          (For yy = 2.667, as outlined earlier:
     If opponent started 011, play 111111111100, repeat.)
     If opponent started 0100, play 111...111 followed by
                                               
                                    187 plays
        000...000 followed by 1010...10, repeat.                          
                                 
        213 plays             402 plays
        (gives yf = 1.216)    
     If opponent started 0101, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives yg = .868)
     If opponent started 0110, play 1000000000 followed by
                                                
                                     20 times
       000000, repeat.  (gives yw = 2.615)
               
       3 times
     If opponent started 0111, play 1111...111 followed by 
                                                
                                    1292 plays
       000...000, repeat 1871 times, followed by 
                  
       708 plays
       1010...1010, repeat 629 times, repeat whole.                    
             
       2000 plays
       (gives yo = 1.841)
     If opponent started 1000, play 1000000000 followed by
                                                
                                     20 times
       000000, repeat.  (gives yx =  2.615)
               
       3 times
     If opponent started 1001, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives yz = .868)
     If opponent started 1010, play 1000000000 followed by
                                                
                                     20 times
       000000, repeat.  (gives yl = 2.615)
               
       3 times
     If opponent started 1011, play 1111000000 followed by               
                                       
                                     10 times
        111100, repeat. (gives ys = .868)

strategy f: Start with 0100.  Then:


     If opponent started 0000, play 01010101...01, followed by 
                                                 
                                     500 plays
        11111000000 (gives fb = 2.485)
     If opponent started 0001, play 11111111111111000000, 
                                                         
                                           31 times
        followed by 1010...10, repeat. (gives fr = 2.419)
                             
                    20 plays
     If opponent started 0010, play 111111...111, followed by 
                                                  
                                    19,854 plays
        010101..01, followed by 0, repeat.  (gives fp = 2.99992)
                    
        5146 plays
     If opponent started 0011, play 111...111 followed by
                                               
                                    187 plays
        000...000 followed by 0000...00, repeat.                        
                                 
        213 plays             402 plays
        (gives fy = 2.469)    
     If opponent started 0100, play 11111111111100000, repeat. (gives ff = 2.412)
     If opponent started 0101, play 111...111 followed by 
                                               
                                    188 plays
        000000000000, repeat 2373 times, followed by
        0000...00, repeat 127 times, repeat whole.  
                   
        200 plays
        (gives fg = 2.886)
     If opponent started 0110, play 1000000000 followed by
                                                
                                     12 times
       000111, repeat.  (gives fw = 2.476)
     If opponent started 0111, play 111...1111 followed by 
                                                
                                    1184 plays
       000...000, repeat 55 times, followed by 000...000,
                                                          
       816 plays                               200 plays
       repeat whole.  (gives fo = 2.819)
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives fx = 2.472)
     If opponent started 1001, play 101010000010 followed by 
                                                  
                                     90 times
        111111111111, repeat.  (gives fz = .692)
     If opponent started 1010, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives fl = 2.472)
     If opponent started 1011, play 111111...111, followed by 
                                                  
                                    19,854 plays
        010101..01, followed by 0, repeat.  (gives fs = 2.99992)
                    
        5146 plays

strategy g: Start with 0101.  Then:
     If opponent started 0000, play 101010...10 followed by 111,
                                                 
                                     100 plays
        repeat. (gives gb = 2.485)
     If opponent started 0001, play repeated 0.  (gives gr = 1)
     If opponent started 0010, play 010101...01 followed by 
                                                 
                                     180 plays
        111...111 and 111, repeat. (gives gp = 2.542)
                 
        20 plays
     If opponent started 0011, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives gy = 2.472)
     If opponent started 0100, play 111...111 followed by 
                                               
                                    188 plays
        000000000000, repeat 2373 times, followed by
        0101...01, repeat 127 times, repeat whole.  
                   
        200 plays
        (gives gf = 2.759)
     If opponent started 0101, play 11111111111100000,
       repeat. (gives gg = 2.412)
     If opponent started 0110, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives gw = 2.472)
     If opponent started 0111, * (any strategy will do.  Gives go)
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives gx = 2.472)
     If opponent started 1001, play 111...1111 followed by 
                                                
                                    6996 plays


        000...0000, repeat 521 times, followed by 
                                                   
        13004 plays                               
        101010...10, repeat 729 times, repeat whole.                      
                                            
        20000 plays                               
        (gives gz = .9999)
     If opponent started 1010, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives gl = 2.472)
     If opponent started 1011, play 010101...01 followed by 
                                                 
                                     180 plays
        111...111 and 111, repeat. (gives gs = 2.542)
                 
        20 plays

strategy w: start with 0110.  Then:
     If opponent started 0000, play 1111000000 followed by 
                                              
                                     20 times
        1111101111100, repeat.  (gives wb = .859)
     If opponent started 0001, play 1111000000 followed by
                                              
                                     20 times
       11111111111, repeat.  (gives wr = .867)
     If opponent started 0010, play 1111000000 followed by
                                              
                                     20 times
       11111111111, repeat.  (gives wp = .867)
     If opponent started 0011, play 1111000000 followed by
                                                
                                     20 times
       111111, repeat.  (gives wy = .849)
               
       3 times
     If opponent started 0100, play 1111000000 followed by
                                                
                                     12 times
       111111, repeat.  (gives wf = .9285)
     If opponent started 0101, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives wg = .868)
     If opponent started 0110, play 111...1111 followed by 
                                                
                                    1667 plays
        000...000, repeat. (Gives ww = 2.667)
                   
        333 plays

     If opponent started 0111, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives wo = .868)
     If opponent started 1000, * (any strategy.  Gives wx)
     If opponent started 1001, * (any strategy.  Gives wz)
     If opponent started 1010, * (any strategy.  Gives wl)
     If opponent started 1011,  play 1111000000 followed by
                                               
                                      20 times
        11111111111, repeat.  (gives ws = .867)

strategy o: Start with 0111.  Then:
     If opponent started 0000, play 111111111101, repeat. (gives ob = 2.583)
     If opponent started 0001, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives or = 2.567)
                 
        20 plays
     If opponent started 0010, play 11111111111100000, repeat.          
(gives op = 2.412)
     If opponent started 0011, play 1111...111 followed by 
                                                
                                    1292 plays
       000...000, repeat 1871 times, followed by 
                  
       708 plays
       0000...0000, repeat 629 times, repeat whole.                                       
       2000 plays
       (gives oy = 2.470)
     If opponent started 0100, play 111...1111 followed by 
                                                
                                    1184 plays
       000...000, repeat 55 times, followed by 111...111,
                                                          
       816 plays                               200 plays
       repeat whole.  (gives of = 2.180)
     If opponent started 0101, * (any strategy will do.  
       Gives og)
     If opponent started 0110, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives ow = 2.472)
     If opponent started 0111, play 11111111111100000, repeat. (gives oo = 2.412)
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives ox = 2.472)
     If opponent started 1001, * (any strategy.  Gives oz)
     If opponent started 1010, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives ol = 2.472)
     If opponent started 1011, play 11111111111100000, repeat. (gives os = 2.412)

strategy x: Start with 1000.  Then:
     If opponent started 0000, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xb = .868)
     If opponent started 0001, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xr = .868)
     If opponent started 0010, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xp = .868)
     If opponent started 0011, play 1111000000 followed by
                                                
                                     20 times
       111111, repeat.  (gives xy = .849)
               
       3 times
     If opponent started 0100, play 1111000000 followed by               
                                                                                  
            10 times
        111100, repeat. (gives xf = .868)
     If opponent started 0101, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xg = .868)
     If opponent started 0110, * (any strategy.  Gives xw)
     If opponent started 0111, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xo = .868)
     If opponent started 1000, play 111...1111 followed by 
                                                
                                    1667 plays
        000...000, repeat. (Gives xx = 2.667)
                   
        333 plays
     If opponent started 1001, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xz = .868)
     If opponent started 1010, * (any strategy.  Gives xl)

     If opponent started 1011, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives xs = .868)

strategy z: Start with 1001.  Then:
     If opponent started 0000, play 101010...10 followed by 111,
                                                 
                                     100 plays
        repeat. (gives zb = 2.485)
     If opponent started 0001, play 11111111111100000, repeat.          
(gives zr = 2.412)
     If opponent started 0010, play 010101...01 followed by 
                                                 
                                     180 plays
        111...111 and 111, repeat. (gives zp = 2.542)
                 
        20 plays
     If opponent started 0011, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives zy = 2.472)
     If opponent started 0100, play 000000000000 followed by 
                                                  
                                     90 times
        111111111111, repeat.  (gives zf = 2.340)
     If opponent started 0101, play 111...1111 followed by 
                                                
                                    6996 plays
        000...0000, repeat 521 times, followed by 
                                                   
        13004 plays                               
        000000...00, repeat 729 times, repeat whole.                      
                                            
        20000 plays                               
        (gives zg = 2.458)
     If opponent started 0110, * (any strategy.  Gives zw)
     If opponent started 0111, * (any strategy.  Gives zo)
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives zx = 2.472)
     If opponent started 1001, play 11111111111100000, repeat. (gives zz = 2.412)
     If opponent started 1010, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives zl = 2.472)
     If opponent started 1011, play 010101...01 followed by 
                                                 
                                     180 plays

        111...111 and 111, repeat. (gives zs = 2.542)
                 
        20 plays

strategy l: Start with 1010.  Then:
     If opponent started 0000, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lb = .868)
     If opponent started 0001, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lr = .868)
     If opponent started 0010, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lp = .868)
     If opponent started 0011, play 1111000000 followed by
                                                
                                     20 times
       111111, repeat.  (gives ly = .849)
               
       3 times
     If opponent started 0100, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lf = .868)
     If opponent started 0101, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lg = .868)
     If opponent started 0110, * (any strategy.  Gives lw)
     If opponent started 0111, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lo = .868)
     If opponent started 1000, * (any strategy.  Gives lx)
     If opponent started 1001, play 1111000000 followed by               
                                        
                                     10 times
        111100, repeat. (gives lz = .868)
     If opponent started 1010, play 111...1111 followed by 
                                                
                                    1667 plays
        000...000, repeat. (Gives ll = 2.667)
                   
        333 plays
     If opponent started 1011, play 1000, repeat.  (gives ls = 0.75)

strategy s: Start with 1011.  Then:
     If opponent started 0000, play 111111111101, repeat. (gives sb = 2.583)
     If opponent started 0001, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives sr = 2.567)
                 
        20 plays
     If opponent started 0010, play 11111111111100000, repeat. (gives sp = 2.412)
     If opponent started 0011, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives sy = 2.472)
     If opponent started 0100, play 111111...111, followed by 
                                                  
                                    19,854 plays
        000...000, followed by 0, repeat.  (gives sf = 2.485)
                    
        5146 plays
     If opponent started 0101, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives sg = 2.567)
                 
        20 plays
     If opponent started 0110, play 1000000000 followed by
                                              
                                     20 times
       00000000001, repeat.  (gives sw = 2.526)
     If opponent started 0111, play 11111111111100000, repeat. (gives so = 2.412)
     If opponent started 1000, play 1000000000 followed by                    
                                    
                                     10 times
        000000, repeat. (gives sx = 2.472)
     If opponent started 1001, play 101010...10 followed by 
                                                 
                                     180 plays
        111...111 and 011, repeat. (gives sz = 2.567)
                 
        20 plays
     If opponent started 1010, play 0000, repeat.  (gives sl = 2.000)
     If opponent started 1011, play 11111111111100000, repeat. (gives ss = 2.412)