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 ...
The hardest part of computing the probability is determining the best strategy for the players. I have used a script to simulate games where players use a few simple tactics, and estimated the probability based on these strategies. Given that the strategies I implemented are not the optimal strategy, these figures provide an upper bound on the probability ...
Meaningful decisions per hour is one of several contributory factors, not the only one.
Other important components of "fun", at least for me, include:
high ratio of meaningful decisions to total decisions
Interesting choices to make in those decisions
link of setting/backstory/theme to mechanics.
interactivity of ...
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.
There are two separate programs linked: one that calculates the probabilities based on simulated ...
A friendly warning: This is a looong answer.
I've calculated the chances of Fools' Landing being lost immediately after the first turn with all players playing to prevent it and a random tile setup.
A few variables:
n = number of players
w = water level after rising once (2 for Novice, 3 for everything else)
First, of all,...
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 ...
Key assumption: Every player places both of their initial settlements according to what will get them the most resources (so we don't have people going for port combos, weird 12/2 superstitions, etc.)
I just downloaded the rules and have the Beginner's Setup in front of me. If you don't, then this won't make any sense!
We all agree that it suffices to add ...
councilroom.com hosts stats for millions of online games played at dominion.isotropic.org.
It's currently down but it should give you the most accurate answer when it goes back up again.
For example, here is a ranking of the best openings from google's cache
Greed (a.k.a. Farkle) has an extensive amount of statistical analysis done on the game.
Now that you have updated your question, here is my updated answer.
If you want to maximize your score, what you need to figure out is what is your expected score if you risk rolling, compared to your score if you choose not to roll. So, the first thing you need to know,...
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 ...
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 |
The answers to your questions depend on the details of how you score the game. For example, Facebook Farkle scores three pairs as 750 points, Gaby Vanhegan's Zilch implementation scores it as 1500 points, and Wikipedia's entry on Greed scores it as 800. These and other scoring differences affect the expected value of rolls and ultimately the optimal play ...
The probability of losing in the first turn due to Fool's Landing sinking, assuming all players try their hardest to avoid it, is dependent on the difficultly level and the number of players n:
Difficultly | n | Probability
Novice | 2 | 0.00199
Novice | 3 | 0.00122
Novice | 4 | 0.00071
Normal/Elite | 2 | 0.00291
Normal/Elite | 3 |...
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 ...
The card that immediately pops to mind:
Here's an article on dominionstrategy.com which outlines why this card is considered the best in the game. No other card allows you to shape your deck so quickly and early, ensuring you get useful and powerful draws to ramp up your deck.
If you look at the best openings ranking linked by Dor Shemer, you'll see many ...
These were all more or less directly copied from the source attributed at the bottom of the answer:
Directly rolling a particular number (e.g. 2) 30.55%
Rolling a particular double (e.g. 3-3) 2.77%
Rolling a particular non-double (e.g. 5-1) 5.54%
Rolling any double 16.66%
Chance of getting off the bar with one or two pieces and X open points:
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 ...
Try this, it's a system called Whole-History Rating. From the abstract:
Whole-History Rating (WHR) is a new method to estimate the
time-varying strengths of players involved in paired comparisons. Like
many variations of the Elo rating system, the whole-history approach
is based on the dynamic Bradley-Terry model. But, instead of using
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 ...
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.)
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 ...
(disclaimer: i haven't played button men seriously in ages, but i'll share my impressions from back in the day)
My feeling is that Lab Rats is the best button, as its 2-dice will allow skill-attacks on far better dice than it has to give away. Bunnies, with its 1-dice is also strong, but can too-often get trapped into not being able to make any attacks.
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.
So looking online I found this from 2015.
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.
As Eric Murray famously said in the case of Crown vs St. Clair Bridge Club:
"The game [rubber bridge] is only one of luck when played as the
justices of the Ontario Superior Court play it in closed chambers."
That is of course the same Eric Murray of the Canadian partnership Murray & Kehela that was widely ranked the third best in the world during ...
I'd learn the chances for the roll combinations. There are 36 possible rolls, (let's say of one red and one green die) as follows:
11: 2/36 (two 6-5s)
10: 2/36 (two 6-4s)
9: 4/36 (two 6-3s, two 5-4s)
8: 4/36 (two 6-2s, two 5-3s)
7: 6/36 (two 6-1s, two 5-2s, two 4-3s)
6: 4/36 (two 5-1s, two 4-2s)
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 ...
it is also easier to go for the longest road when you start in fourth or third. keep that in mind.
To me, it all depends on the board : like if there is one supreme location and players takes it... but that's kind of rare. There are usually 4 honestly good places and then it gets worse, so the advantage of being first is not that good to me.
I would estimate between 60%-70%. The best strategy to use when attempting to survive for 70 days, is to try to avoid wounds. If the wounds that the Barbarian Prince receives are ever 1 less than his Endurance (fall unconscious), or greater than or equal to his Endurance you lose the game. This basically means that we need to avoid combat at all costs. The ...