[Viberbi Algirothm Example: Fair dice vs. Loaded dice]

observed numbers: 23653245666

[Emission probability]
Fair:   1/6 1/6 1/6 1/6 1/6 1/6
Loaded: 0.1 0.1 0.1 0.1 0.1 0.5

[Transition probability]
F -> F : 0.95
F -> L : 0.05
L -> L : 0.90
L -> F : 0.10

           2   2   6   5   3   2   4   5   6   6   6
BEGIN 1  
FAIR  0  F01 F02 F03 F04 F05 F06 F07 F08 F09 F10 F11
LOAD  0  L01 L02 L03 L04 L05 L06 L07 L08 L09 L10 L11

[1]F -> F: 0.167 * 0.95 * 1.66667e-01 = 2.63889e-02
[1]L -> F: 0.167 * 0.10 * 1.00000e-01 = 1.66667e-03
MAX PATH to F: FF, F2 = 2.63889e-02
[1]F -> L: 0.100 * 0.05 * 1.66667e-01 = 8.33333e-04
[1]L -> L: 0.100 * 0.90 * 1.00000e-01 = 9.00000e-03
MAX PATH to L: LL, L2 = 9.00000e-03

[2]F -> F: 0.167 * 0.95 * 2.63889e-02 = 4.17824e-03
[2]L -> F: 0.167 * 0.10 * 9.00000e-03 = 1.50000e-04
MAX PATH to F: FF, F3 = 4.17824e-03
[2]F -> L: 0.100 * 0.05 * 2.63889e-02 = 1.31944e-04
[2]L -> L: 0.100 * 0.90 * 9.00000e-03 = 8.10000e-04
MAX PATH to L: LL, L3 = 8.10000e-04

[3]F -> F: 0.167 * 0.95 * 4.17824e-03 = 6.61555e-04
[3]L -> F: 0.167 * 0.10 * 8.10000e-04 = 1.35000e-05
MAX PATH to F: FF, F4 = 6.61555e-04
[3]F -> L: 0.500 * 0.05 * 4.17824e-03 = 1.04456e-04
[3]L -> L: 0.500 * 0.90 * 8.10000e-04 = 3.64500e-04
MAX PATH to L: LL, L4 = 3.64500e-04

[4]F -> F: 0.167 * 0.95 * 6.61555e-04 = 1.04746e-04
[4]L -> F: 0.167 * 0.10 * 3.64500e-04 = 6.07500e-06
MAX PATH to F: FF, F5 = 1.04746e-04
[4]F -> L: 0.100 * 0.05 * 6.61555e-04 = 3.30777e-06
[4]L -> L: 0.100 * 0.90 * 3.64500e-04 = 3.28050e-05
MAX PATH to L: LL, L5 = 3.28050e-05

[5]F -> F: 0.167 * 0.95 * 1.04746e-04 = 1.65848e-05
[5]L -> F: 0.167 * 0.10 * 3.28050e-05 = 5.46750e-07
MAX PATH to F: FF, F6 = 1.65848e-05
[5]F -> L: 0.100 * 0.05 * 1.04746e-04 = 5.23731e-07
[5]L -> L: 0.100 * 0.90 * 3.28050e-05 = 2.95245e-06
MAX PATH to L: LL, L6 = 2.95245e-06

[6]F -> F: 0.167 * 0.95 * 1.65848e-05 = 2.62593e-06
[6]L -> F: 0.167 * 0.10 * 2.95245e-06 = 4.92075e-08
MAX PATH to F: FF, F7 = 2.62593e-06
[6]F -> L: 0.100 * 0.05 * 1.65848e-05 = 8.29241e-08
[6]L -> L: 0.100 * 0.90 * 2.95245e-06 = 2.65721e-07
MAX PATH to L: LL, L7 = 2.65721e-07

[7]F -> F: 0.167 * 0.95 * 2.62593e-06 = 4.15772e-07
[7]L -> F: 0.167 * 0.10 * 2.65721e-07 = 4.42868e-09
MAX PATH to F: FF, F8 = 4.15772e-07
[7]F -> L: 0.100 * 0.05 * 2.62593e-06 = 1.31296e-08
[7]L -> L: 0.100 * 0.90 * 2.65721e-07 = 2.39148e-08
MAX PATH to L: LL, L8 = 2.39148e-08

[8]F -> F: 0.167 * 0.95 * 4.15772e-07 = 6.58306e-08
[8]L -> F: 0.167 * 0.10 * 2.39148e-08 = 3.98581e-10
MAX PATH to F: FF, F9 = 6.58306e-08
[8]F -> L: 0.100 * 0.05 * 4.15772e-07 = 2.07886e-09
[8]L -> L: 0.100 * 0.90 * 2.39148e-08 = 2.15234e-09
MAX PATH to L: LL, L9 = 2.15234e-09

[9]F -> F: 0.167 * 0.95 * 6.58306e-08 = 1.04232e-08
[9]L -> F: 0.167 * 0.10 * 2.15234e-09 = 3.58723e-11
MAX PATH to F: FF, F10 = 1.04232e-08
[9]F -> L: 0.500 * 0.05 * 6.58306e-08 = 1.64576e-09
[9]L -> L: 0.500 * 0.90 * 2.15234e-09 = 9.68551e-10
MAX PATH to L: FL, L10 = 1.64576e-09

[10]F -> F: 0.167 * 0.95 * 1.04232e-08 = 1.65034e-09
[10]L -> F: 0.167 * 0.10 * 1.64576e-09 = 2.74294e-11
MAX PATH to F: FF, F11 = 1.65034e-09
[10]F -> L: 0.500 * 0.05 * 1.04232e-08 = 2.60579e-10
[10]L -> L: 0.500 * 0.90 * 1.64576e-09 = 7.40594e-10
MAX PATH to L: LL, L11 = 7.40594e-10

[11]F -> F: 0.167 * 0.95 * 1.65034e-09 = 2.61303e-10
[11]L -> F: 0.167 * 0.10 * 7.40594e-10 = 1.23432e-11
MAX PATH to F: FF, F12 = 2.61303e-10
[11]F -> L: 0.500 * 0.05 * 1.65034e-09 = 4.12584e-11
[11]L -> L: 0.500 * 0.90 * 7.40594e-10 = 3.33267e-10
MAX PATH to L: LL, L12 = 3.33267e-10

MAX VALUE : L12
Backtracking MAX PATH: 
L12 -(LL)-> L11 -(LL)-> L10 -(FL)-> F9 -(FF)-> F8 -(FF)-> F7
-(FF)-> F6 -(FF)-> F5 -(FF)-> F4 -(FF)-> F3 -(FF)-> F2 -(FF)-> F1

So, the most probable state sequence is 
observed numbers: 22653245666
state sequence  : FFFFFFFFFLL