Arnab Chakraborty did his BStat (Hons.) and MStat degrees from the Indian Statistical Institute (Calcutta). He is now a PhD student in the Department of Statistics at Stanford University, California. His research interest lies in areas of statistics and computational algebra. Apart from that he is interested in playing the piano and wishes he could really play well.

In Part 1 of this two-part article, we give two examples -- one to illustrate the Markov chain, and the other to illustrate sampling of units in a Markovian dependent manner and explain how it can be used in a Monte Carlo sampling procedure.

The Game of Ludo

Have you ever played a game of Ludo? There are many different
versions of the game -- the one I liked playing may be called the
Snake-n-Ladder Ludo. Some people call it as Chutes-n-Ladders,
though. The game consists of a square board 10 by 10 in size, two
differently coloured counters (one for each player) and a die.

The 100 small squares are numbered from 1 to 100 as shown, and the game starts with both the counters on square 1. The players take turns at rolling the die, and advance their counters accordingly.
In case the counter lands on a square with a snake's mouth in it,
the counter has to move down to the tail of the snake. The reverse
is the case for a ladder, which takes your counter up from the
bottom to the top. The aim is to arrive at square 100 before your
opponent. Obviously, this is not a game of strategy. You are
simply a mute spectator to what chance does to your counter.
Nevertheless, this simple game has a potential that can really do
wonders to your mathematical mind and make you ask very
interesting questions. We shall learn about this in this article.

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Address for Correspondence
Arnab Chakraborty
Department of Statistics
Stanford University California, USA.