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20

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 ...


14

Statistically, I think the Axis get the short end. I tried finding some web site specifically discussing stats on various countries, but came up empty, so you'll have to settle for qualitative data from me at least. I havn't played this game in years, but I always like playing Russia. I would say Russia is the best in terms of fun to play, but it's not ...


12

Answering the question with AAMC bid statistics Others have explained why the Axis have a significant disadvantage in the 2nd Edition rules. I'll attempt to provide hard evidence and quantify this advantage. The popular play-by-email (PBEM) site Axis and Allies Members Club (which I have no affiliation with and which I hadn't logged onto in years until I ...


8

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


8

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 ...


8

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) Special abilities/actions First, ...


7

At the start of the game, the Allies have a significant advantage over the Axis due a variety of reasons, including: Their combined economic power The fact that there are three Allies playing against two Axis US's economic strength and the fact that its richest territories are virtually safe from attack due to their distance from the European and Asian ...


7

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 ...


6

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 Interesting setting/backstory visual appeal link of setting/backstory/theme to mechanics. It's ...


6

Summary 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 ...


5

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: ...


5

The article on Shuffling at the Wikipedia discusses the famous paper by Persi Diaconis and Dave Bayer which shows that a 52 card deck of cards doesn't become random until the fifth shuffle, and requires seven shuffles to become "truly" random. Your question "Are there any other methods of cuttings of the deck or shuffle types that create a more random ...


5

I have a couple of friends who used to play a lot of settlers online. Apparently there was once a site that had a lot of settlers data, but it went down. You can see some of the archived data at the settlers 3d web.archive.org page. There is now a forum in its place. Maybe some of the posters there have a backup of the data?


4

With Ticket to ride, 3-5 riffle shuffles should be sufficient to randomize the deck sufficiently for play. As long as the runs of matched cards aren't 5-6 cards long, it's not a big issue. I'll note that japanese style block shuffling is inadequate for TTR until about the 9th or time through the deck, which I discovered due to using sleeved cards in ...


4

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 ...


4

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 ...


3

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.


3

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 ...


3

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 ...


3

There are a few problems with finding data. The first is finding any data. I would recommending emailing/contacting sites that offer Catan or Catan-esque games for play to see if they keep records of games played. I found a short list of potential sites with a little searching via Google. (Do note that I have not verified any of those sites.) The second ...


3

(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. ...


3

With every card game I play I do a mix of Riffle, Stripping, and Mongean-Stripping Combo. I generally intermix these in a random order with a random number of times, usually at least 3. I've found that mixing shuffling techniques, especially in a random order, will result in a fairly nice card distribution and randomization.


3

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 ...


3

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 ...


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 ...


2

There was a "Button Men Online" website until recently that had amassed HUGE quantities of statistics on different Button Men competing (albeit being controlled by people users on the site). If you could get a hold of that data, that might answer your questions. I've messaged @cheapassjames on twitter, he might have the data. Possibly, you could contact the ...


2

It depends on how you define "best" country. If you mean, "easiest country to play," probably U.S.A. If you mean "most multifacted," perhaps Japan. If you mean "most vulnerable," and like the adrenalin of an early brush with "death," before coming back from behind, then Russia. If you mean "most challenging" (in terms of difficulty of finding a clear ...


2

With the implied restriction on time combined with the explicit restriction to keep the cards pristine, I'd suggest using extra space to shuffle. Here's what I do with large decks of cards: Divide the large deck into several smaller piles. For 80 cards, I'd make about 8 piles of 7-15 cards Select two piles at random and combine them using a hindu shuffle ...


2

For Ticket to Ride, as cards are turned in I distribute them across up to six stacks, trying to not place cards on top of like cards (orange does not go on top of orange). Sometimes a card gets tucked to the bottom of a stack. When it comes time to shuffle, the stacks get shuffled together pair by pair (stack 1 with 2, then 3 with 4, etc.), ultimately ...


2

Generally speaking, I shuffle using a combination of overhand and Hindu shuffle. I start with the pack in my left hand, pluck out the middle half with my right, and then proceed to drop blocks of cards alternatively onto the top and then bottom of the pack, using a quick flick of fingers or thumb to swap between cards dropping onto the top or bottom of the ...



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