I've got a 3x3 Nash game cube I'm trying to interpret. The decimals below represent the number of times a player 'wins' against the other player.
A B C
A 0.722,0.278 0.722, 0.278 0.800, 0.200
B 0.750, 0.250 0.780, 0.220 0.875, 0.125
C 0.286, 0.714 0.200, 0.800 1.000, 0.000
When I run this through the method for solving 3x3 Nash squares, this is the equation I use:
A->B: (p+q+(1-p-q) = p1 + q1 + (1-p1-q1))
B->C: (p1+q1+(1-p1-q1) = p2 + q2 + (1-p2-q2))
and I substitute p from one into the other to find q.
The result I get for the horizontal player, from the above square however, don't make sense:
Horizontal Player
A = 0.07460291360037259
B = 0.18149088118987192
C = 0.7439062052097555
This would indicate that the horizontal player should play 75% of the time. Yet, strategy B clearly produces better results for the horizontal player consistently. Am I interpreting this correctly? It is possible I made a programming error, but the Vertical Player makes sense:
Vertical Player
A = 0.14930944382232172
B = 1.1347517730496453
C = -0.28406121687196695
It's gobbledy gook. But just visually analyzing the square indicates that B is the best strategy.
Any feedback you can provide is much appreciated.