Info: numba.jit seems to be available.
For depth = 2 ...
Starting to explore every transitions up-to depth 2 for this root state:
State : M = 2, K = 3 and t = 0, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Using these policies:
- Player #0/2 uses Selfish_UCB_Ubar (which is )...
- Player #1/2 uses Selfish_UCB_Ubar (which is )...
Using these arms:
- Arm #0/3 has mean mu_1 ...
- Arm #1/3 has mean mu_2 ...
- Arm #2/3 has mean mu_3 ...
For depth = 2, exploring from this node :
State : M = 2, K = 3 and t = 0, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 27 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 10 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 1.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 10 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 1.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 13 different states...
For depth = 1, exploring from this node :
State : M = 2, K = 3 and t = 1, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
we saw 10 different states...
There are 144 unique leafs for depth 2...
Leaf with probability = mu_1*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_2**2*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = (mu_1**2*mu_2**2 - 2*mu_1**2*mu_2 + mu_1**2 - 2*mu_1*mu_2**2 + 4*mu_1*mu_2 - 2*mu_1 + mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = (mu_2**2*mu_3**2 - 2*mu_2**2*mu_3 + mu_2**2 - 2*mu_2*mu_3**2 + 4*mu_2*mu_3 - 2*mu_2 + mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_2**2*mu_3**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 1. 1.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_3**2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_2*(mu_2 - 1)*(mu_3 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)**2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_3 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_2**2*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = -mu_1*(mu_2 - 1)*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_1*mu_2**2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_2*mu_3**2*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_2 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_2*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_2**2*(mu_3 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_2**2*mu_3*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = (mu_2 - 1)*(mu_3 - 1)*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_3**2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_1**2*mu_2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_2 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_2*(mu_3 - 1)*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1**2*mu_2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)**2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_2*mu_3**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 1. 1.]] =: N
Leaf with probability = mu_1**2*mu_2*mu_3/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 1. 1. 0.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_3 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_2*(mu_2 - 1)*(mu_3 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_2**2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = (mu_2 - 1)*(mu_3 - 1)*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_2**2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = mu_2*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_3*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1**2*mu_2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_1**2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_1**2*mu_2*mu_3/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_3*(mu_2 - 1)**2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_3*(mu_2 - 1)*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)**2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_3*(mu_2 - 1)**2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_1*mu_3**2*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = mu_1*mu_2*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1**2*mu_3*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_3**2*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_1*(mu_3 - 1)*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1**2*mu_3**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 1. 0. 1.]] =: N
Leaf with probability = mu_1*mu_2**2*mu_3/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 1. 1. 0.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_1**2*mu_3*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_3*(mu_2 - 1)*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_3**2*(mu_2 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1**2*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 1. 0.]] =: N
Leaf with probability = mu_3**2*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)**2*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = (mu_1**2*mu_3**2 - 2*mu_1**2*mu_3 + mu_1**2 - 2*mu_1*mu_3**2 + 4*mu_1*mu_3 - 2*mu_1 + mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_2**2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = (mu_1 - 1)*(mu_3 - 1)*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = (mu_1 - 1)*(mu_3 - 1)*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_2*mu_3**2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 1.]] =: N
Leaf with probability = -mu_1**2*mu_2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2**2*mu_3/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = mu_1**2*(mu_2 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_2*mu_3**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 1. 0. 1.]] =: N
Leaf with probability = mu_3**2*(mu_1 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_1*(mu_2 - 1)*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_1*mu_2**2*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = (mu_1 - 1)*(mu_2 - 1)*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 1.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_3**2*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = mu_1*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_2*(mu_3 - 1)*(mu_1**2 - 2*mu_1 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_1*(mu_3 - 1)*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1**2*mu_2**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 1. 0.]
[ 1. 1. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 0. 0.]] =: N
Leaf with probability = (mu_1 - 1)*(mu_2 - 1)*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1**2*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_2**2*(mu_1 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_3*(mu_1 - 1)*(mu_2**2 - 2*mu_2 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_2*mu_3**2*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 1.]] =: N
Leaf with probability = -mu_1*mu_2*mu_3*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 1. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_1**2*(mu_3 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = mu_1*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_2*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 0. 0.]] =: N
Leaf with probability = -mu_2*mu_3**2*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 0. 1.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = -mu_1**2*mu_3*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 1. 0. 1.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_2**2*(mu_1 - 1)**2/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 0. 1. 0.]] =: N
Leaf with probability = -mu_2**2*mu_3*(mu_1 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 1.]
[ 0. 1. 0.]] =: N
Leaf with probability = mu_2*mu_3*(mu_1 - 1)*(mu_2 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 0. 1. 1.]] =: N
Leaf with probability = -mu_1*(mu_1 - 1)*(mu_2 - 1)*(mu_3 - 1)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 0. 0.]
[ 1. 0. 0.]] =: N
Leaf with probability = mu_1*mu_2*(mu_3**2 - 2*mu_3 + 2)/18:
State : M = 2, K = 3 and t = 3, depth = 0.
=: Stilde
[[ 0. 1. 0.]
[ 1. 0. 0.]] =: N
Done for exploring every transitions up-to depth 2 for this root state:
State : M = 2, K = 3 and t = 0, depth = 2.
=: Stilde
[[ 0. 0. 0.]
[ 0. 0. 0.]] =: N
Using these policies:
- Player #0/2 uses Selfish_UCB_Ubar (which is )...
- Player #1/2 uses Selfish_UCB_Ubar (which is )...
Using these arms:
- Arm #0/3 has mean mu_1 ...
- Arm #1/3 has mean mu_2 ...
- Arm #2/3 has mean mu_3 ...
There were 144 unique leafs for depth 2...
For depth 2, 0 leafs were found to be absorbing, and the probability of reaching any absorbing leaf is 0...
==> Numerically, for uniformly spanned means = [0.10000000000000001, 0.5, 0.90000000000000002], this probability is = 0 ...
Creating a dot graph from the state...
Saving the dot graph to 'plots/trees/Tree_exploration_K=3_M=2_depth=2__Selfish_UCB_Ubar.gv.svg'...
[Enter] to continue...[1;5C[1;5C[1;5C[1;5C