# MLB Call Challenges: Who Wins the Reviews? (Updated)

Back at the start of the 2014 Major League Baseball season, new rules were implemented for making plays reviewable. Managers are now allowed to have certain plays reviewed and potentially overturned. There’s only 1 full season and a couple months of data, but let’s dig in and see what we can learn.

I’m interested in finding out several things: Which teams ask for reviews the most? Which teams are the most successful? Are there any umpires who find their calls being reviewed and overturned more than others? Also, how long do reviews take, and does the length of the review time hint at the ruling for the review?

# Computational Methods for Games 2: Markov Chains

In many games, tabletop or otherwise, there are a series of positions, board states, or other features that occur in some kind of order. In monopoly, for example, you travel in a circle. Each property is a ‘state’ that your piece (battleship!) can be in. In something like Candyland, Chutes and Ladders, or Mr. Bacon’s Big Adventure, there is a goal state to reach, and you do things (roll die, draw cards, etc.) to try to get there.

What makes these more complicated than say, just figuring the combined probability of rolling a certain sum for many die, is that the game states branch. Branching just means that you can reach more than 1 state after your current one. Markov Chains are a powerful tool for analyzing a game’s progress through it states, and this post will show you an example of that, using the game Betrayal at House on the Hill.

# Zombie Dice Strategy Evaluation

In the last post, we took a quick look at the basics of Monte Carlo simulation, and used a simple simulation to get the probabilities of various outcomes in the first roll of Zombie Dice. In this post, we’ll extend our simulation to play turns for us, based on a strategy that we can define. We’ll try several different strategies of varying complexities and see how well we do!

# Computational Methods for Tabletop Games 1: Zombie Dice and Monte Carlo Simulation

Many board and tabletop games rely on the randomness of dice rolls (or card order) to create uncertainty in the game. This will lead many frustrated players to ask “What are the odds of that happening?”. Catan is a good example of this, as a run of not getting any of your numbers will quickly lead to frustration! Catan’s odds are easy to calculate, though. The die rolls are independent from one turn to the next, and the state space of outcomes never changes.

When the games get more complex, the odds may not be possible to compute analytically, or they may just be complicated to compute by hand. Zombie Dice is an example of just such a game. Zombie dice has many stages within a turn, and while each stage is analytically calculable, the overall odds of getting some number of brains is dependent on the player’s strategy. Using a general method called Monte Carlo Simulation, we can easily play thousands of turns and calculate odds, all without needing more than a simple random number generator.