Years ago, once a week, I used to leaf through the pages of Merriam - Webster's Collegiate Dictionary and randomly grab a new word. I would learn the spelling, pronunciation and it's meaning. I would then try to use that word as often as I could (without being too irritating to others) for the rest of the week. And yet, with all the distractions in life and numerous reasons to put it off, my word searches didn't last long.

Today I have decided to give it another try. Better yet, I thought I would post and share my word finds. Therefore, I have decided to take this day, Wednesday, as my regularly posted word day and title it Wednesday Words.

So as I flip through the pages of Merriam Webster's Dictionary, my eye comes to rest on the word.....or I should say words....

**Markov Chain**

**Mar·kov chain**\mär-,kof, -,kov\ chān

noun "[A. A. Markov - a Russian mathematician] (1942) : a usu. discrete stochastic process (as a random walk) in which the probabilities of occurrence of various future states depend only on the present state of the system or on the immediately preceding state and not on the path by which the present state was achieved. -- called also the Markoff chain"^{1}

It is a mathematical system that goes through changes in a chain like manner whereas the next state depends only on the current state, not on it's entire past changes.

^{image from Wikimedia Commons}

** **

**Markov chain as applied to board games played with dice:**

"A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game. In the above mentioned dice games, the only thing that matters is the current state of the board. The next state of the board depends on the current state, and the next roll of the dice. It doesn't depend on how things got to their current state. In a game such as blackjack, a player can gain an advantage by remembering which cards have already been shown (and hence which cards are no longer in the deck), so the next state (or hand) of the game is not independent of the past states."^{2}

You can read more about Markov chain at Britannica.com

To learn more about Andrei A. Markov and his work:

https://netfiles.uiuc.edu/meyn/www/spm_files/Markov-Work-and-life.pdf

Thank you for stopping by

and

Have a beautiful day