Timothy R. Sumner

This initial game illustrates the classic Gambler's Ruin problem, a concept first introduced in 1656 by Blaise Pascal in a letter to Pierre Fermat. For a detailed history of this problem, see Song and Song (2013). Basically, Gambler A and Opponent B each start with a specified number of units. The game continues until one player loses their entire initial stake. The question is: what is the probability that the gambler will either lose all their money or win all of the opponent's money, assuming an unlimited number of plays are possible?

In the variation you can play here, the game is completely fair—the probability of winning each round is 50%. However, your opponent has an unlimited initial stake, which is often the case when playing against large institutions like casinos.

The outcome of this variation is that you are guaranteed to eventually lose if you continue playing indefinitely, even though the game is fair. A similar result is observed when any species has birth and death rates that are in balance. When this occurs, it can be proven that extinction is certain. Here, you can set your initial stake and choose how much you want to wager each round. Try to see how much you can win before losing.

The Game of Life, devised by mathematician John Conway in 1970 , is a cellular automaton that simulates the evolution of simple organisms. Played on an infinite grid of square cells, each cell can be alive or dead. Despite its simple rules, the Game of Life produces complex and often surprising patterns, illustrating how complexity can emerge from simplicity.

To play, you start with an initial configuration of live and dead cells. Each cell's state in the next generation is determined by its eight neighbors: a live cell with two or three live neighbors survives, while all others die. A dead cell with exactly three live neighbors becomes alive. These rules are applied simultaneously to all cells, and the process is repeated for as many generations as desired, revealing the intricate dynamics of the system.

The random walk model is not only easy to grasp but also widely applicable in real-world scenarios. Essentially, it posits that the next point is determined by adding a random value to the current point, resulting in each new value being both random and influenced solely by the preceding one.

The interactive game here offers a personalized twist on this model by introducing a maximum limit, ensuring that the random walk remains bounded. It's worth noting that this version holds significance as it has been proven that when a random walk is constrained from above, it will eventually reach zero. Here, you have the freedom to choose your initial starting point, adjust the probability of moving upward, and set the maximum value threshold.

Craps is one of the oldest games in modern casinos, with dice games being among the earliest forms of gambling. While there are numerous ways to bet at a craps table, the standard gameplay proceeds as follows:

First, an initial wager is placed, and two dice are rolled. If the dice show a 7 or 11, the player wins and is paid out at 1 to 1. If a 2, 3, or 12 is rolled, the player loses, and the initial wager is forfeited. If any other number is rolled, that number becomes the "point." The player then continues to roll the dice until either the point number is rolled again, resulting in a win, or a 7 is rolled, resulting in a loss. Once a point is established, the player cannot alter or reclaim the initial wager.

This game, like all dice games, is played with two standard dice. However, to mix things up, you have the unique opportunity to play with Sicherman's Dice—an experience you won't find in a casino. The famous Sicherman dice puzzle poses the question: Is it possible to number the faces of two cubes in a completely different way from standard dice, while maintaining the same probabilities as standard dice in any dice game? The answer is yes. More specifically, there is exactly one other way to number the dice to achieve this result. These dice can be seen here.