simplegame: Simple Game for Estimation of Expected Gain

In joemckean/mathstat: Introduction to Mathematical Statistics R Package

Description

Computes the estimation of expected gain for a game wherein the following rules apply: A player pays p_0 to play. The player then rolls a 6-sided die. If the roll is a 1 or a 2 then the game is over. Otherwise, the player flips a fair coin. If the coin toss results in a tail, they receive $1 and the game is over. Otherwise they draw 2 cards without replacement from the standard deck of 52 cards. If none of the cards is an ace they receive $2, while they receive $10 or $50 is they get 1 or 2 aces respectively. In both cases, the game is over. Let G denote the player's gain. To determine the expected gain, we need the distribution of G. The support of G is the set -p_0, 1-p_0, 2-p_0, 10-p_0, 50-p_0. For the associated probabilities we need the distribution of X where X is the number of aces in a draw of 2 cards. The distribution is P(X=x) = ( (4 choose x) * (48 choose (2-x)) ) / (52 choose 2) for x=0,1,2

See example 1.8.9 on page 65 of the book.

Usage

simplegame(amtpaid)

Arguments

amtpaid

Initial amount that a player pays (p_0 in description).

Value

Estimation of expected gain for player.

References

Hogg, R. McKean, J. Craig, A (2018) Introduction to Mathematical Statistics, 8th Ed. Boston: Pearson

Examples

player_winnings <- simplegame(1)
player_winnings <- simplegame(5)
player_winnings <- simplegame(10)

joemckean/mathstat documentation built on May 30, 2019, 2:01 p.m.