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:

From this chart we can count all the Odd and Even outcomes: 18 and 12, respectively from 30 pairings if you exclude the doubles which are always Even. With this we can calculate the probabilities for Odd and Even: 50%(18/36) and 33.33%(12/36), respectively. Now you might think you have better chances to always bet on Odd in your games. So I decided to test that hypothesis in a program I developed. I simulate 1,000 games for two scenarios: always bet on Odd and always bet on Even. Here are at least 3 results:

Well would you look at that, the chances of getting the right call are roughly equal, and not favored to the Odd sum results. This one of the wonders of programming: you can simulate events which would be humanly exhaustive. Aren’t computers dandy?

I also have another dice game set up, but will do that on a follow up post. Of course, I will leave a link to the source code of my program here.

Until then… *HACK TO THE FUTURE!!*