The multi-armed bandit (MAB) is a classic problem in probability theory and statistics that models exploitation-exploration trade-off, leveraging choices that have proven effective in the past versus choosing new options that might provide better-unexplored trade-offs. Imagine a row of slot machines, each with a different and unknown distribution of paying out a reward. The goal is to select the machine(or ‘arm’) at each time instance such that it maximizes the total reward over time. This article will discuss simulations for some known algorithms in MAB in stochastically chosen, adversarially chosen, and stochastically chosen but strategically corrupted reward scenarios and run simulations for the algorithms discussed.

The Monty Hall Problem is a classic puzzle in probability theory that may seem straightforward at first but is surprisingly tricky and confusing. This article will delve into the problem by examining how the host’s choice of door affects the game, to better understand the problem.

Let’s try to understand what insurance means from the hypothetical example of Alex.
Alex one day wakes to find a magic coin with the following instructions:

• You are only allowed to flip the coin once and it will vanish afterward.
• The coin has an equal probability of landing either ‘Heads’ or ‘Tails’.
• If the coin lands on ‘Heads’ you will be given 10 million.
• If the coin lands on ‘Tails’ you will be given nothing.