# de.Finetti.Game: de Finetti's Game In LaplacesDemon: Complete Environment for Bayesian Inference

## Description

The `de.Finetti.Game` function estimates the interval of a subjective probability regarding a possible event in the near future.

## Usage

 `1` ```de.Finetti.Game(width) ```

## Arguments

 `width` This is the maximum acceptable width of the interval for the returned subjective probability. The user must specify a width between 0 and 1.

## Details

This function is a variation on the game introduced by de Finetti, who is one of the main developers of subjective probability, along with Ramsey and Savage. In the original context, de Finetti proposed a gamble regarding life on Mars one billion years ago.

The frequentist interpretation of probability defines the probability of an event as the limit of its relative frequency in a large number of trials. Frequentist inference is undefined, for example, when there are no trials from which to calculate a probability. By defining probability relative to frequencies of physical events, frequentists attempt to objectify probability. However, de Finetti asserts that the frequentist (or objective) interpretation always reduces to a subjective interpretation of probability, because probability is a human construct and does not exist independently of humans in nature. Therefore, probability is a degree of belief, and is called subjective or personal probability.

## Value

The `de.Finetti.Game` function returns a vector of length two. The respective elements are the lower and upper bounds of the subjective probability of the participant regarding the possible event in the near future.

## Author(s)

Statisticat, LLC. software@bayesian-inference.com

`elicit`