I am trying to learn some probabilities in the game of monopoly. I am using one die with four sides and one die with six sides instead of using two dice each with six sides. There are links below to show you what the game of monopoly is. Again I do not have two dice with six sides.

Monopolyis aboard gamecurrently published byHasbro. In the game, players roll two six-sided dice to move around the game board, buying and trading properties, and developing them with houses and hotels. Players collect rent from their opponents, with the goal being to drive them intobankruptcy. Money can also be gained or lost through Chance and Community Chest cards, and tax squares; players can end up in jail, which they cannot move from until they have met one of several conditions. The game has numeroushouse rules, and hundreds of different editions exist, as well as many spin-offs and related media.Monopolyhas become a part of international popular culture, having been licensed locally in more than 103 countries and printed in more than 37 languages.

Monopolyis derived fromThe Landlord's Gamecreated byLizzie Magiein the United States in 1903 as a way to demonstrate that an economy which rewards wealth creation is better than one where monopolists work under few constraints,^[1]and to promote the economic theories ofHenry Georgein particular hisideas about taxation.^[3]It was first published byParker Brothersin 1935 until that firm was eventually absorbed into Hasbro in 1991. The game is named after the economic concept ofmonopolythe domination of a market by a single entity.

I desire to construct the payout distribution according to the value rolled in four columns:(a) the value rolled - values 2 to 10, (not 2-12) (b) the name of the outcome square ("Park Place," "Go"), (c) probability of the outcome, and (d) the payout (or "rent").

Id like to show the computation of the expected value and the variance of the payout from the payout distribution in payout distribution according to the value rolled in four columns:(a) the value rolled - values 2 to 10, (not 2-12) (b) the name of the outcome square ("Park Place," "Go"), (c) probability of the outcome, and (d) the payout (or "rent").

If i wanted to buy insurance for the payout of the above next roll.Whats the expected related to the pricing of that insurance.

Examples of previous answers below:

(a) In Monopoly, moves are determined by the sum of the roll of two six-sided dice.State the probability of landing on Boardwalk on the next roll when starting on Pacific Avenue.

Boardwalk is 8 steps from Pacific Avenue.There are five sample points (or "sequences") that yield a sum of 8:those are (2,6), (6,2), (3,5), (5,3), and (4,4).It may help you to imagine, as I have done, that the first roll is done with a purple die and the second roll with a red die; thus, the sample points are color-coded above.Note that as long as you keep the colors in that order, you have exactly five different unique arrangements that sum to 8.Think about it.

There is a total of 36 sample points ("sequences of die rolls").We can manually count them, {(1,1), (1,2), ... (6,6)} or we can recognize that a box measuring six by six has area 36.

Cardano tells us to compute the probability of the event of getting a sum of 8 by taking the ratio in which the numerator is the number of sample points that yield a sum of 8 and the denominator is the total number of possible sample points.That is 5/36.

(b) You are on Pacific Avenue.There are hotels on Park Place and Boardwalk.Look up the rental prices for those two properties on the Property Deed page.Construct the probability distribution of next roll assuming that only Park Place and Boardwalk have non-zero monetary value.

For a discrete random variable, the "probability distribution" is best defined as a simple table of outcomes and probabilities.There are three monetary outcomes defined above:$2000, $1500, and $0.Those probabilities are 5/36, 5/36, and 1-(5/36+5/36) = (36-10)/36 = 26/36.

Probability Distribution Payout for Next Roll

Outcome.Probability

20005/36

15005/36

026/36

(c)Find the expected value of the your next roll.That amount would be the "fair price" of insurance that would cover your stay at Park Place or Boardwalk if you were to land there on the next roll!Of course, the insurer would have to add overhead to that theoretical fair price to stay in business.

Expected value = (2000*5/36) + (1500*5/36) + (0*26/36)

= (10,000 + 7,500)/36

= 17,500/36

= $486.11

(d)Find the variance of your next roll.

Variance = ((2000-486.11)^2)*5/36 + ((1500-486.11)^2)*5/36 + ((0-486.11)^2)*26/36

=$$631,751.54

Taking the square root of the variance of the gamble, we get the standard deviation:s

Standard Deviation = $794.83

(e)One of the Chance cards says, "Take a Walk on Boardwalk."If we include thatpathto Boardwalk, what is the probability of ending up on Boardwalk on your next roll, starting at Pacific?

It is five steps to Chance from Pacific; the sample points that yield a sum of five are (1,4), (4,1), (2,3), and (3,2), a total of four.Therefore, the probability of landing on Chance is 4/36.So,

P(Chance) = 4/36.

There are 16 Chance cards.Therefore, the probability is 1/16 of drawing the Take a Walk on Boardwalk card conditional on landing on Chance, so

P(Boardwalk|Chance)=1/16.

Since

P(Boardwalk|Chance) = P(Boardwalk and Chance) / P(Chance),

so,

P(Boardwalk and Chance) = P(Boardwalk|Chance) P(Chance)

= (1/16) (4/36)

= (4/576)

= 1/144.

Therefore, the probability of ending up on Boardwalk either from a direct roll or indirectly via the Chance card is

P(Boardwalk) = 5/36 + 1/144

= 20/144 + 1/144 =

= 21/144

(f) If we include the Chance-card route to Boardwalk, how would the expected value change?

Expected value = (2000*(5/36 +1/144)) + (1500*5/36) + (0*26/36)

= (2000*(21/144)) + (1500*5/36)

= (500*(21/36)) + (1500*5/36)

= 10500/36 + 7500/36

= 18000/36

= $500

Thus, adding "insurance" against the Chance-Card-to-Boardwalk path increases the fair price of the insurance by a little less than $14.