nipunbatra · October 13, 2025 19:01 · Henry3461 · Sep 24, 2025 · milkesilo-lang · Oct 13, 2025
diff --git a/unfair_casino_viterbi.py b/unfair_casino_viterbi.py
 """
 ========================================
 Unfair Casino Problem using Discrete HMM
 ========================================

 This script shows how to use Decoding in a Discrete(Multinomial) HMM, which means
 given the model parameters and an observed sequence we wish to find the most likely hidden state sequence
 generating the same.
 It uses the model given in http://www.rose-hulman.edu/~shibberu/MA490/MA490HMM.html#Example_Dishonest_Casino_
 One may also refer to a great lecture series at http://vimeo.com/7175217

 """
 print __doc__
 import datetime
 import numpy as np
 import pylab as pl
 from sklearn.hmm import MultinomialHMM
 import random

 ###############################################################################
 ################################################################################
 #Specifying HMM parameters

 #We can obtain the starting probability by finding the stationary distribution from the transition matrix
 #This denotes that the probabilities of starting in Fair state and Biased state are 2/3 and 1/3 respectively
 start_prob = np.array([.67, 0.33])

 #The Transition Matrix
 #This means that given that current state is Fair, probability of remaining in fair state is .95 and transitioning to
 #Biased state is .05. Similarly, given that current state is Biased, probability of transitioning to fair state is .1
 #and remaining in the same state is .9
 trans_mat = np.array([[0.95, 0.05],
                      [.1, 0.9]])

 #The Emission Matrix
 #This means that if the dice is fair, all 6 outcomes (1 to 6) have same probability,
 #whereas, for the biased dice, 6 is observed with probability 0.5 and the remaining 
 #with a probability 0.1 each                  
 emiss_prob=np.array([[1.0/6,1.0/6,1.0/6,1.0/6,1.0/6,1.0/6],[.1,.1,.1,.1,.1,.5]])

 #Initializing the model with 2 state(n_components) and specifying the transition matrix and number of iterations
 model = MultinomialHMM(n_components=2,transmat=trans_mat,n_iter=10)

 #Number of emitted symbols
 model.n_symbols=6
 #Assigning emission probability, start probabilty and random seed
 model.emissionprob_=emiss_prob
 model.startprob_=start_prob
 model.prng=np.random.RandomState(10)

 #dice_obs is a random sequence of observations. Note that some extra 6's have been added in middle of the sequence
 #which might correspond to use of Biased Dice 
 dice_obs=[random.randint(1,6) for i in range(0,20)]+[6,6,6,6,6,6]+[random.randint(1,6) for i in range(0,20)]
 print "Dice Observations\n",dice_obs

 #Note that the emitted symobols must vary from 0 through 5. Thus we subtract 1 from each element of dice_obs
 obs=[x-1 for x in dice_obs]

 #Finding the likely state sequence and log probabilty of the path using Viterbi algorithm and parameters specified in the model
 logprob, state_sequence = model.decode(obs)
 print "\nExpected State Sequence- F for fair and B for Biased"
 state_sequence_symbols=['F' if x==0 else 'B' for x in state_sequence]
 print state_sequence_symbols

 print "Log probability of this most likely path is: ",logprob
 print "Probability of this most likely path is    : ",np.exp(logprob)
	"""
	========================================
	Unfair Casino Problem using Discrete HMM
	========================================

	This script shows how to use Decoding in a Discrete(Multinomial) HMM, which means
	given the model parameters and an observed sequence we wish to find the most likely hidden state sequence
	generating the same.
	It uses the model given in http://www.rose-hulman.edu/~shibberu/MA490/MA490HMM.html#Example_Dishonest_Casino_
	One may also refer to a great lecture series at http://vimeo.com/7175217

	"""
	print __doc__
	import datetime
	import numpy as np
	import pylab as pl
	from sklearn.hmm import MultinomialHMM
	import random

	###############################################################################
	################################################################################
	#Specifying HMM parameters

	#We can obtain the starting probability by finding the stationary distribution from the transition matrix
	#This denotes that the probabilities of starting in Fair state and Biased state are 2/3 and 1/3 respectively
	start_prob = np.array([.67, 0.33])

	#The Transition Matrix
	#This means that given that current state is Fair, probability of remaining in fair state is .95 and transitioning to
	#Biased state is .05. Similarly, given that current state is Biased, probability of transitioning to fair state is .1
	#and remaining in the same state is .9
	trans_mat = np.array([[0.95, 0.05],
	[.1, 0.9]])

	#The Emission Matrix
	#This means that if the dice is fair, all 6 outcomes (1 to 6) have same probability,
	#whereas, for the biased dice, 6 is observed with probability 0.5 and the remaining
	#with a probability 0.1 each
	emiss_prob=np.array([[1.0/6,1.0/6,1.0/6,1.0/6,1.0/6,1.0/6],[.1,.1,.1,.1,.1,.5]])

	#Initializing the model with 2 state(n_components) and specifying the transition matrix and number of iterations
	model = MultinomialHMM(n_components=2,transmat=trans_mat,n_iter=10)

	#Number of emitted symbols
	model.n_symbols=6
	#Assigning emission probability, start probabilty and random seed
	model.emissionprob_=emiss_prob
	model.startprob_=start_prob
	model.prng=np.random.RandomState(10)

	#dice_obs is a random sequence of observations. Note that some extra 6's have been added in middle of the sequence
	#which might correspond to use of Biased Dice
	dice_obs=[random.randint(1,6) for i in range(0,20)]+[6,6,6,6,6,6]+[random.randint(1,6) for i in range(0,20)]
	print "Dice Observations\n",dice_obs

	#Note that the emitted symobols must vary from 0 through 5. Thus we subtract 1 from each element of dice_obs
	obs=[x-1 for x in dice_obs]

	#Finding the likely state sequence and log probabilty of the path using Viterbi algorithm and parameters specified in the model
	logprob, state_sequence = model.decode(obs)
	print "\nExpected State Sequence- F for fair and B for Biased"
	state_sequence_symbols=['F' if x==0 else 'B' for x in state_sequence]
	print state_sequence_symbols

	print "Log probability of this most likely path is: ",logprob
	print "Probability of this most likely path is : ",np.exp(logprob)