1 player 
2 players 
3 players 
4 players 

Average game 
39.13 cards 
51.79 cards 
63.51 cards 
74.53 cards 
Mode game (most common ending
turn) 
26 turns 
16 turns 
16 turns 
15 turns 
Median Game (half are longer) 
32 turns = 32 cards 
23 turns = 46 cards 
19 turns = 57 cards 
17 turns = 68 cards 
Longish game (10% are longer) 
73 cards 
88 cards 
102 cards 
116 cards 
Long game (one in a thousand are
longer) 
189 cards 
204 cards 
213 cards 
232 cards 
1 player 
2 players 
3 players 
4 players 

Average game 
55.96 cards 
70.72 cards 
75.7 cards 
98.08 cards 
Mode game (most common ending
turn) 
28 turns = 28 cards 
26 turns = 52 cards 
18 turns = 36 cards 
17 turns = 68 cards 
Median Game (half are longer) 
44 cards 
60 cards 
75 cards 
88 cards 
Longish game (10% are longer) 
109 cards 
126 cards 
141 cards 
156 cards 
Long game (one in a thousand are
longer) 
294 cards 
312 cards 
327 cards 
344 cards 
Analytic 
Monte Carlo A 
Monte Carlo B 

Average game 
39.16 cards 
39.178 ± 0.003 
39.161 ± 0.003 
Mode game (most common ending
turn) 
26 cards 
25.79 ± 0.05 
25.90 ± 0.05 
Median Game (half are longer) 
31.57 cards 
31.659 ± 0.002  31.57 ± 0.002 
Longish game (10% are longer) 
72.40 cards 
72.29 ± 0.008  72.91 ± 0.008 
Long game (one in a thousand are
longer) 
188.8 cards 
186.86 ± 0.07  184.80 ± 0.07 
1 player 
2 players 
3 players 
4 players 

Average
game 
Analytic. 
39.16 cards 
51.79 cards 
63.51 cards 
74.53 cards 
Monte Carlo 
39.77 ± 0.004  50.64 ± 0.007  61.10 ± 0.10  70.91 ± 0.14  
Mode
game (most common ending
turn) 
Analytic 
26 turns 
16 turns 
16 turns 
15 turns 
Monte Carlo 
26.2 ± 0.2  31.2 ± 0.2  45.7 ± 0.3  57.8 ± 0.6  
Median
Game (half are longer) 
Analytic 
32 turns = 32 cards 
23 turns = 46 cards 
19 turns = 57 cards 
17 turns = 68 cards 
Monte Carlo 
33.84 ± 0.007  45.84 ± 0.009  55.95 ± 0.015  65.61 ± 0.014  
Longish
game (10% are longer) 
Analytic 
73 cards 
88 cards 
102 cards 
116 cards 
Monte Carlo 
71.11 ± 0.01  83.24 ± 0.025  95.93 ± 0.02  108.1 ± 0.03  
Long
game (one in a thousand are
longer) 
Analytic 
189 cards 
204 cards 
213 cards 
232 cards 
Monte Carlo 
162.1 ± 0.16  173.7 ± 0.16  186.8 ± 0.17  200.2 ± 0.16 