1/
Get a cup of coffee.
In this thread, I'll help you understand Markov Chains.
In life, and in investing, we often come across situations where luck/chance plays a major role.
And Markov Chains are often a great way to model and analyze such situations.
2/
Here's what prompted me to write this thread.
Earlier this week, I conducted a Twitter poll.
In the poll, I posed a question that required a bit of probabilistic reasoning.
The good news: over 10,000 people responded.
The bad news: ~87% got the answer wrong!
3/
Here's the question I asked.
Imagine we have 2 volunteers: Alice and Bob.
We give them each a fair coin.
We ask Alice to keep tossing her coin until she sees a Heads immediately followed by a Tails (ie, the pattern HT).
4/
We ask Bob to keep tossing his coin until he sees two consecutive Heads (ie, the pattern HH).
The question is: on average, who will take more tosses to get to their "target pattern" -- Alice or Bob?
Or will they both on average take the same number of tosses?
5/
More precisely:
Suppose Alice takes A tosses on average to get her HT.
And Bob takes B tosses on average to get his HH.
Then, which is the bigger number: A or B?
Or are they both the same number?