39

It's not hard to prove that an unsolvable start exists. Just imagine a start where the only possible first moves would be moving cards to the extra cells. In some versions, -1 and -2 are examples of this though the only way to play them is to choose that seed. If you only count setups which can exist in normal play, seed 11982 in the Windows version is an ...


11

The key change in reversing the direction of movement is the fact that players now leave Jail in the opposite direction. The oranges and reds are particularly profitable because they are within 1-2 rolls of Jail, among other reasons. When moving counterclockwise, the dark purples and dark blues are now in a more often visited area, so I would expect their ...


11

Linked in Probabilities in the Game of Monopoly® by Truman Collins, are C source code files written to calculate the probabilities of normal Monopoly. We can just roll up our sleeves and tweak the program ourselves to see what kind of changes we get. Choices There are two separate programs linked: one that calculates the probabilities based on simulated ...


9

Here are the (quite extensive!) results: http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml The first part of that page is the long-term probabilities for ending up on a particular square. The last column tells you the ranking: you will end up in Jail most often, Illinois second-most-often, then Go, then the B&O Railroad, etc. This is neat, but ...


8

Instead of modeling you can compute these results exactly. If you roll n dice at difficulty d, the variance will be [d * n * (d-1)/6 * (7-d)/6], and the mean net gain will be [d * n * (7-d)/6 - 1]. Both scale linearly with n, so here are the mean (measured in Net Gain Per Die) and variance for each value of d: ----------------------- | d | Mean | Variance | ...


8

The short answer is "Yes, but...". The longer answer is, as per the paper in question, that a team of researchers did some calculations on what would happen in a 2-player game of Monopoly where both players follow very simple strategies (and a couple of things that aren't 100% by the rules), notably: Always try to keep a small reserve of cash on hand to ...


7

I know the results. Red and Orange properties are places where players most often lands on. Most often visited places are the Jail and the 3rd red property ("Illinois Avenue" in the American version and "Avenue Henri-Martin" in the French version). I found a table here (fr). The table contains the French names so I join a french Monopoly board to this ...


7

According to the accepted answer on the post containing that number, it originates in the book How to Win at Gin Rummy: Playing for Fun and Profit by Pramod Shankar. Unfortunately, the book doesn't seem to have a source or proof for it. Thankfully, though, a comment on that post does give an answer. A blog called Entropy Clay steps through the calculations, ...


6

I highly recommend Winning Monopoly if you are interested in such analysis. As other answers point out, payback period (combining rent amount and frequecy) is key for making winning decisions. One of the point from this book that I haven't seen else where is determining what version of Monopoly you are playing. Are you really playing until all others are ...


5

You're trying to run out of cards, and the opportunities to change colors are somewhat limited. Your goal, therefore, should be to play the last card of one of your colors, then be able to switch to another color you have on the next play. This doesn't always work, of course. When changing colors (via wild or matching the card), you should switch to the ...


5

I am not sure which particular site you are referencing, but How to Win at Monopoly calculated the Return On Investment (ROI) of all the properties based on the liklihood of landing on them. They concluded that Railroads (especially 4) had the fastest most consistent ROI, followed by a Monopoly with 3 Houses, utilities were the worst ROI.


5

Accordion According to one of the biggest player on the solitaire market (SolSuite), the game of Accordion (one card at a time version) has a chance of winning in about 1 of 200 games, i.e. 0,5% But I would actually say that there is no difference in the winning percentage (if played right) between the two versions you are talking about, since (in the ...


5

The reason that equity is used instead of winning probability is because it is possible to win a single game, a double game (gammon) or triple game (backgammon). Let's say that the value of the game, or bet, is $1. (That would occur if the cube is in the middle. If it has been turned, you multiply by 2, 4, or whatever the number is on the cube.) Let's ...


5

My original answer assumed that there was no penalty for guessing incorrectly. This answer assumes that you are playing with the rule that incorrect guesses cause a game loss. My original answer is provided below this one Never guess, unless a player has only a single character left If your opponent guesses, then your odds of winning are 50% if they have ...


4

So looking online I found this from 2015. It says More are sold per capita in Germany than anywhere else on earth Magic the Gathering is big, with something like 20 million players worldwide, however that will pale in comparison to board game sales so I'd be likely to ignore card games as they won't add a huge amount overall compared to board games. ...


3

Playing online against 3 computer opponents, one of my games would typically last 30-45 turns. I used the standard rules (i.e., no money on Free Parking, limited number of houses and hotels). Because it was me against computers, the games would take ~15 minutes to play. Playing against human opponents would certainly extend the actual playing time, and may ...


3

This question's been unanswered for a while, so I thought I'd take a crack at it. First up, I should say that I haven't looked at the four player case, just the two player game. The main reason for this is that it makes presenting the data a lot easier. I've put some graphs later, and you can see that they're already hard enough to understand for the two ...


3

A couple of pointers from the rules. Keep your score low: The winner is determined by whomever scores 500 points first, or in the variation Running Player Totals, by whomever has the lowest total points when someone reaches 500. A good strategy is always try to play your highest value card if you can (other than a Wild/Wild-Draw-4, since at least one of ...


3

For me, I would divide the deck into smaller parts that you can handle. Riffle shuffle (or any way you like) those and mix the small decks together, one group at a time.


2

The chance of getting a total of x on the two dice is simply (6-|7-x|)/36 where |7-x| is the absolute value of 7-x.


2

You can "translate" the word "equity" as a value of the particular position. Lets imagine we are one roll away from ending the match and we only have two checkers on deuce point. We will win with the probabilty of 26/36 and we will lose with the probability of 10/36. Lets also imagine that there is a friend who offers us some money and asks us to abandon ...


2

I would suggest checking out the Board Game Geek Avalon community. People regularly record their play sessions and the users on the forums are usually willing to go into in-depth analysis and discussion on game setup and configuration. For instance, even one of the most recent forum discussions is about statistical anomalies in Avalon games.


2

You would usually not skip the Go square (and the chance to collect $200) before going to Jail. The exceptions would be the Chance square between Oriental and Vermont (light blues), and the community chest square between the two dark purples. Even so, you would collect your $200 on the tenth square after leaving Jail instead of the 30th, and you would not ...


2

I haven't heard of this variation. Nuclear Wang's analysis is correct. Note the Dark Blues getting a frequency boost along with their high rent would cause ownership of that color group be key to winning a reverse game. To take the analysis further, take a look at the following site: http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml This site ...


2

The answer to this question will be very heavily dependent on your group, and their groupthink. In my experience, often bidding 3 on the blade would not result in getting it (I would probably be 2nd or 3rd, with someoen else going all in on the sword), while a bid of 2 on the Raven would probably be enough to get me at least one star (with someone else ...


2

Three Independent sources counted about 136,694 Gin hands, out of 15.8B possible 10-cards hands. 2+2 forum post: 1 in ~118,000. Using brute force which checked for Gin each of the 15.8B hands. Rulemonger's analysis: 136,694 in 15,820,024,220 or 1 in ~115733 How to Win at Gin Rummy: 1 in ~117,000, according to the book How to Win at Gin Rummy: Playing for ...


2

Wizards of the Coast deliberately obscures this data. Several years ago, some fans created a website that used bots to automatically crawl Magic the Gathering Online's matches to construct a table containing the meta percentages and the win/loss rates of each deck. However, Wizards later changed how MtGO's systems worked with the specific goal of preventing ...


2

Someone one the FB page where this question was originally posted found this answer from the School of Operations Research and Information Engineering Cornell University Ithaca NY 14853, USA ESTIMATING THE PROBABILITY THAT THE GAME OF MONOPOLY NEVER ENDS At the end of the 10-page report, the following is stated : All four of our estimators yield ...


1

According to a Ted-Ed article entitled Here's how to win at Monopoly, according to math experts ... the average game of Monopoly takes about 30 turns per competitor... Reference https://blog.ed.ted.com/2017/12/01/heres-how-to-win-at-monopoly-according-to-math-experts/ So the answer to your question is 120 turns (4 players times 30 turns/player) By ...


1

In The Backgammon Book, World Champions Oswald Jacoby and John Crawford recommend with both 6-2 and 6-3 moving one runner to the bar point and one man from the 12-point into your own outer table; though they concede that there another move almost as good: The modern play [written in 1970] is to use the six to move one back man to the black bar point and ...


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