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Game of Ludo

Last week, my 7-year-old cousin Rommel, forced me to play Ludo with him. One reason Rommel hates playing with me is that I don’t allow him to cheat, which Ammi (our grandmother) graciously allows all the time.

Now, while playing with Rommel, I saw him making lots of rookie mistakes. It was then that I realized that back when I was a kid, I used to make the same kind of mistakes! Using the concept of probability, I’ll show you how to be a boss at Ludo. It isn’t really as much a game of chance as you’d like to think.

For people who are yet to study probability, it is the number of favourable events, divided by the total number of possible events. Classic (and practically improbable) example: Say you have a bag containing 8 pens: 2 of black ink, and 6 of blue. Without looking, you reach into your bag and draw out a pen. Chances that the pen has blue ink is 6/8 = 0.75. Chances that the pen has black ink is, you guessed it, 2/8 = 0.25. This is all the math you’re going to need for winning at Ludo.

First of all, remember all those people who told you to follow your heart? If you want to win this game, the first thing you need to do is to not follow your heart.

Consider the situation given below, and say your roll of the die gives 4. What’s your instinct? Do you move A or B?

Sit_2

Rommel was in a similar situation, and he decided to get the piece closer home (B), even closer. Gut instinct, right?

But here’s the thing: It was a stupid move.

At his initial position, his chance of getting a 5 was 1/6. When he moves up the piece closer home, his chance of getting a 1 is again 1/6. He gained no advantage by moving up that piece. Though mann-ki-shanti comes from moving your pieces as close home as possible, in effect, you waste a turn.

The second rookie mistake that Rommel made was when he had his pieces like this. He rolled the die and got a 2. Which piece do you think he moved?

Sit_1

Rommel decided to move the piece (C) that was closer to my piece. Because hey, the gut tells you to move your pieces as far away from the chasing piece as you can, right?

Wrong. In his initial position, my chances of landing on one of Rommel’s pieces was 2/6 = 0.33 (i.e. if I rolled a 1 or a 2, I would land on one of his pieces). However, when Rommel moved up the piece C, my chances of landing on him still remained 0.33 (i.e. if I rolled a 2 or a 3). If he had instead moved up B to safety, my chances of landing on him would have been a much lesser 1/6 = 0.17.

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So, all you need to do while playing Ludo is apply basic probability, and nothing (other than a really unlucky day) can stop you from winning.

I am glad you overcame all the math in this blogpost to reach its end. Here’s a small gift for you. Ping me up on Facebook or drop me an email at gmail@suryashekhar.com, and I’ll share with you the secret to modify your die so that you get 6 on it more frequently. :3

The really cool GoT themed graphics has been designed by Trenchant Rambler of Saintbrush. Apparently that’s supposed to make this blog look really hip.

By Surya

I am a student of Computer Science and Engineering at Vellore Institute of Technology. I like finding out about as many things in the world as possible!