Powerball Nears Best EV (Updated)

This is a quick post that is the exact same as the Mega Millions post I did. I break down the Powerball odds, use some sales data, and look at the EV over various jackpots.

The quick takeaway, as the Powerball is up to $450 million for Wednesday, is that either this drawing (or the next if no one wins) is as near to the possible expected value for this lottery. The other takeaway? Don’t buy lottery tickets!

UPDATE: Going back I found an error in my code. I’ll update it at some point, but for now, take it with a grain of salt (except the historical data part, that part was fine).

Continue reading →

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.

Continue reading →

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!

Continue reading →

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.

Continue reading →