# Descartes Game

Learn how to have a good fortune at games of chance.## Rules

This game allows you to bet on the throw of dices. Thanks to your intuition, perceive which sides will be shown. The dice are thrown randomly, hence the winning faces are completely unpredictable.

The game is played with traditional 6-face, balanced dice. The game offers you two options :

- one die : you must guess the face that will appear (from 1 to 6)
- two dice : you must guess the sum of the two faces that will appear (from 2 to 12)

The principle is simple : make a bet on then throw the die (or dice). Then observe whether you made the right choice – i.e., whether you’ve been aware of your intuition and followed its guidance.

At each trial, you may bet a certain amount, selected using the « + » and « – » buttons. You may also enter more than only one guess (in one-die mode, up to 5 ; in two-dice mode, up to 10). Your gains and losses reflect the risks you’ve taken.

Your scoring depends on your hit rate, on the amount of your bet, and on which faces you have chosen.

In the one-die mode, if your score exceeds 4000, you switch to the two-dice mode.

In the two-dice mode, if your score dives under -1000, you switch to the one-die mode.

Now follow your intuition… the die is cast !

## The little twist of the game

When you play with one die, all 6 faces have the same occurrence probability : 1/6 = 16,66 %. However, when you play with two dice, the 11 possibilities for the sum of the two faces don’t share the same probability, because some can be obtained through different face configurations. For instance, the number 2 has only a 1/36 probability to occur, corresponding to the sole (1,1) pair among 36 pair possibilities ; the number 10 has a larger, 1/12 probability, because it is associated to three pairs (6,4),(5,5),(4,6) ; the most probable option, 7, has a 1/6 chance of turning up when adding the two faces, since it can be obtained in 6 different ways.

When you bet with two dice, you choose among the 11 sum options, but since these choices aren’t equivalent this will inevitably prompt your intellect. More or less consciously, your mind can’t help doing calculations, clouding the intuitive information. So beware, this represents the biggest challenge of this game.

## Why Descartes ?

French philosopher René Descartes (1596-1650) once confessed in a letter to Princess Elizabeth of Bohemia – a philosopher herself – that he had observed that our inner state of mind could influence our luck, even in games of chance. He noticed in particular that a joyful spirit would make him more fortunate. Such a claim from the apostle of rational thinking and mind-body separation, is a stunning notion.

Yet, a few decades later, his contemporary Blaise Pascal (1623-1662) founded a new branch of mathematics in order to solve certain well-known problems encountered by gamblers. This *géométrie du hasard* (chance geometry) or game theory, evolved into probability theory, is everywhere in our sciences and our way of thinking. And it has allowed, four centuries after Descartes, to scientifically demonstrate that his observation or intuition was indeed correct : the mind can influence, consciously or subconsciouscly, random events. But this is another story…