- —Jesse's Pandemonium is a game of chaos.
- By: Jesse Riggs

There are 105 players in a population. Each player's actions are decided by the roll of a die.

**Rules:**

- Each player is given either two or three coins. Each player must hold their coins until it is their turn. A player who still has their coins is called
.**susceptible** - It becomes a players turn when a coin is transmitted to them by another player, except when the player is chosen to be first ( Player Zero ).
- When it is a players turn, they must transmit each of their coins to a different player via connection. A player who is taking their turn is called
.**infectious** - After a player has taken their one and only turn, they are no longer in the game. Any further transmissions must be blocked. A player who is no longer in the game is called
.**immune** - The game is over when the last transmission has been blocked. The winners of the game are those who remain susceptible.

Three buttons control Pandemonium. ** Full Screen** causes Pandemonium to be displayed in full screen mode.

When a player successfully transmits their coins, they have reproduced that turn — that is, thier turn has been given to at least one other player. The number of coins that a player is given is proportional to the number of times that player can reproduce that turn. The average number of coins that a player has is called the * effective reproduction number* — or R. The graph below shows the number of infected players, over time, given value R.

As the number of immune players grows, the more likely it is that a transmission will fail — the transmission of a coin will be blocked by an immune player. Eventually, the number of susceptible players will drop to a point where it's very difficult to transmit coins and then the number of infected players drops to zero.

We can see in the graph below, that the number of infected players increases for R values above 1. But then levels off when R=1. As R drops below 1, the number of infectious players drops to 0.

If we want to find the reproduction number at any given time, we will need to know what R was in the very beggining, and the proportion of the polulation that is susceptible. The average number of coins that each player has, at the beggining of the game is a special reproduction number called R_{0}

Here, the * susceptibility* of the population is measured by ( 1 -

It would be useful to know when R = 1, because this is when the number of infections level off. This point is known as the * herd immunity threshold*. If we could find the correct proportion of the population that would need to have immunity to reach this threshold, we could estimate when the infections will taper off. This critical proportion is called

I hope this demonstration has been informative. :)