Draft:Fair game (statistics)

Submission declined on 12 December 2023 by NoobThreePointOh (talk).

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Declined by NoobThreePointOh 5 months ago. Last edited by Citation bot 3 months ago. Reviewer: Inform author.

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A fair game is in probability theory defined as a game of chance where each player’s expected payoff is equal to zero, in other words the expected value of the game is zero.^[1]^[2]

Let $X_{n}$ be the fortune of a gambler after the n'th game, then the game is defined as fair if:^[3]

$E{\bigl (}X_{n+1}\mid X_{1},....,X_{n}{\bigr )}=X_{n}\forall n$

Example of fair game: a player roll a die and receive 4 units if the die lands 5 or 6 and looses 2 units if the die lands 1-4.

An unfair game by contrast is defined as a game with expected value different from zero. Most lotteries and casino games are designed as unfair games with expected value for the players being negative and hence the players can expect to loose money as they play.

References edit

^ "Expected Value". Libre Texts Mathematics. 8 July 2022. Retrieved 10 December 2023.
^ "Fair Game". NumWorks. Retrieved 10 December 2023.
^ Breiman, Leo (1968). Probability. Addison-Wesley Publishing.

[1] "Expected Value". Libre Texts Mathematics. 8 July 2022. Retrieved 10 December 2023.

[2] "Fair Game". NumWorks. Retrieved 10 December 2023.

[3] Breiman, Leo (1968). Probability. Addison-Wesley Publishing.

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