## Dice Mania or How I am exploring dice games and their probabilities.

Ahh, the humble die. A simple cube with numbers from 1 to 6 etched on all sides as pips has generated innumerable games. Involve money in those games, and you got a casino in your hands.

Of course, when it comes to gambling dice games, Craps comes to mind instantly, and is a staple in all casinos all around the world. However, I want to showcase other gambling dice games and simulate them in a program.

## A primer on dice probabilities

Before I showcase the games, I want to give you a quick crash course of probabilities involving dice. Take a coin, for example, and flip it. You declare either heads or tails. The probability of landing a desired side is 50% or 1/2, where 1 represents the outcome you want the coin to land on and 2 representing the total number of outcomes a coin has. With that in mind, say you want to roll a die and have it land on 6. The probabilities of that happening are 16.67% or 1/6.

OK, but what happens if you add another die? Then you would have to multiply the probabilities. For example, you want to roll the illustrious Snake Eyes, two 1’s. The probability of that combination is 16.67% times 16.67%: 2.78% or 1/36.

## Odd-Even

Now that we got the probabilities in mind, let me start showcasing a classic Japanese gambling game: Odd-Even (Chou-Han). The rules are simple: two dice are rolled in a cup and overturned, covering the outcome. The players can then bet what will be the outcome of the sum total of the dice: Odd (Chou), which cannot be divided by 2 evenly, or Even (Han). After the bets are made, the dealer reveals the dice, shouts out the outcome and the winners collect their cash. Pretty simple, right? This dice game is popular with the yakuza for obvious reasons.

Now let’s take inventory: the goal of the game is to guess right the total sum of the dice before the reveal. Out of the 36 outcomes from two dice, we need to separate the Odd and Even outcomes. For that I created the following chart: