This is not correct. The scale is the same both at the lower and the higher end. A 200-point difference in rating predicts that the weaker player will score a proportion of points equal to 1/(1+10^(200/400)) = 1/(1+sqrt(10)) = 1/4.16 = 24%.

The difference between lower and higher ratings is mostly the percentage of draws, which are considered half a win for each player. So a 1200 player against a 1000 player might have

75% wins
2% draws
23% losses

whereas a 2800 player against a 2600 player might have

54% wins
44% draws
2% losses

but in either case the 200-point rating gap says the same thing about the split of total points. If the weaker player scores 24% of the points, is it an "almost sure win"? You need to quantify what you mean.

No, the OP is correct; or at least he used to be. They've changed the rating formulas to be much more complex and now it is difficult to explain without a background in mathematics. However, I think the new system is close enough that the basic aspect of tightening the ratings bands still holds.

Under the older system, for ratings that had achieved the 2200-point threshold the k-value was halved. Thus it took longer to move up to higher rating thresholds. A 400 point difference at a full K value was equivalent to a 200 point difference at half-K.

As the for the "sure win" part of it. At 400 points, the higher rated player is expected to earn 91 points out of 100 (assuming they were to play 100 games.) Any result that does not equate to that will result in a rating change; and there will be one over a single game, because the possible results are only 0, 1/2, and 1.

Edit: A personal anecdote: I played in the 1989 US Action Championship (G:30 time control) where I achieved the upset of the tournament - or at least it would have been had I submitted the game score - by defeating IM Eugene Meyer, Virginia State Champion. Eugene was rated FIDE Action 2625. I was unrated, but held a USCF rating of about 1800. Over an 800 point difference!

Obviously my knowledge of the rating system of chess is out of date. And in chess (as in many of the other games) I may have missed a level or two by making my "novice" player reasonably competent, but just new to the game.

It is true that the K-value is different for higher-rated players than for lower-rated players, but the K-value only affects the speed at which ratings are adjusted. It does not affect the expected score for a given difference of points.

Yes, a 2800 player will gain fewer points for beating a 2600 player than a 1200 player will gain for beating a 1000 player. In both cases, however, the higher-rated player is expected to win 76% of the points, and will lose rating points on average if he doesn't win that much. To put it another way, the K-value has no impact on whether it is an "almost sure" win. The surety of winning is determined only by the difference in rating.

I guess you are right.

Well, probably a few more than 8. A 4d will almost never beat a 7d. If it's a "good" 7d, even a 5d won't have any chance. In the higher kyu ranges, 4 stones is about the threshold.

I'd estimate, once you include the pros, probably more like 10 or 11 levels of "A has really no chance of beating B."

There was a scientific paper written on a similar subject describing Go as having something like 26 levels of skill and chess having about half as many. But then I would say that as I love Go.

In Go, the handicapping system allows players of different ability to play together. The handicapping system in chess is much clumsier.

I could be talked into 11 levels, but 26 probably uses a different assumption of 'level.' After all, there are only 56 or so skill levels, and I doubt you'd say that every two levels will "almost always" beat two lower. At the very high levels that's probably true, but at the lower levels you undoubtedly need 4-5 kyu difference.

If I recall correctly (and I may not), a player of one higher skill level would win at a 75% rate for the study in question.

The gap in true backgammon is determined by how many times you can survive paying the doubling die bill. Call it "tuition."

Truly, the great players can not only play this, but gamble as well. Much like in poker, there is an art to knowing when to double. In fact, this game is loads more interesting when played for money - when the stakes can quickly double, a slight losing position can be a winner if you know the other guy will drop out...

Thinking about it more, six levels seems like too many. But the average 32-board K.O. match is probably too short to be certain, and the stronger team wins that fairly often.

I also think 5 is appropriate. Using bridge terminology, these correspond to Flight C, Flight B, Flight A-, Flight A+, and World-Class. I think a team of 4 players in the same flight will average around 1.0 IMP/board in a team game against a team of 4 players in the next lower flight.

I did a study on this once. It turns out that the standard deviation is roughly 5.7 IMPs/board. That means that it takes a very long match for a team that's 1 IMP/board better than another to be "sure" of winning. But we have 64-board matches, which is about what it takes.

At 1 IMP/board, the levels are roughly "total novice," "club player," "Flight C," "Flight B," "Flight A", and "World Champion." I think the difference between the levels decreases a little as you go up; a World Champ is less than a full IMP/board better than a Flight A player, but a club player is well more than an IMP/board better than a total novice.

The flights (and bridge ratings in general) do not measure skill so much as experience. Because ratings only go up, never down, they only provide bare hints as to ability.

Somewhat true, but irrelevant, since that's not what we are talking about. And it's only somewhat true. If you play 10,000 matches between teams of Flight C players and teams of Flight B players, the Flight B teams will win most of them with an average score difference of roughly 1 IMP per board. Yes, it's easy to construct a team of Flight C players who'll beat the pants off most Flight B teams, but that's not the point---we are talking about levels, not individuals.

The definitions of the flights change over time, of course, and the meaning of the ratings changes (American bridge ratings suffer from long-term inflation, so it's very hard to compare records across different eras), but pretty much there's always been some sort of distinction of this sort, and the goal of tournament organizers is to create distinctions so that most of the contestants within a level/flight/stratum/whatever feel that they aren't grossly outclassed when playing within their level. Since this is achieved by adjusting level boundaries with the knowledge of who is competing, the flight boundaries, while ever changing, reflect roughly one level of ability, or at least are intended to. In practice, they work OK for this purpose. For example, when a stratified swiss is held, most of the A teams end up ahead of the B teams and most of the B teams end up ahead of the C teams. Not all, of course, because 7-board matches are not close to sufficient to be a contest in which a team a level stronger than its opponents will nearly always win. IMO, that takes at least a 64-board match.

In other words, the ACBL has flights simply because they are cognizant of what Brian is talking about: there are contestants who will nearly always beat other ones, because they are substantially more skilled. The flighting structure aims to make the range of a flight roughly one level---the strongest contestant within a flight will nearly always beat the weakest. Obviously, that cannot work with the highest and lowest flights, and the flighting structure isn't always built like that, but the basic core of the system is to differentiate levels just as Brian discusses. It therefore makes lots of sense to call levels "Flight A," "Flight B," etc., even though we know that there are some B teams stronger than some A teams, because the rating system doesn't work all that great for individuals. It works pretty well for large groups.

If you've read the article called I believe "the Large Wharehouse of knowledge" you'd see there is a lot to this game and then applying all that to all the players at the table simultaneously this game would have at least 4 levels.

If you then decided you would counsider negotiation skills table talk being allowed and then on top of that reading the other players thoughts which would be a developed skill similar to good poker reading you might have 5 levels.

If there were 5 real experts at the table I could well imagine they would be able to predict the next 3 complete rounds every pick for every player including builds. With the exception of the settlers random factor. Again a rookie is going to throw the whole thing off but even then their play might be even more predictable.

I am not an expert but with some effort I can see the whold current round and into the next round if given the time. I think what we are forgetting is that these games seem limited because we don't give people 15 minutes to make one move. Like in chess.

If you are comparing this to Caylus, I think Caylus has a lot more than 3 levels.

I play regularly with a player in my group. I have won about 90% of those games, yet she is a fairly strong player when not playing me. On the hand, there are several BSW players that stomp me (and I have a 70% win rate). And ones that stomp even them. Throw in novices, and you have at least 5 or 6.

Caylus is probably closer to chess than Puerto Rico. For one, it functions well as a 2-player game, like chess, so the multiplayer aspect is not as prevalent, and it also is less dependent on player order "binding."

I'm no expert but every game has at least 3 levels Beginner, Intermediate and Advanced. Even Tic Tac Toe probably has 3 levels.

although most people are advanced after 2 games. Both of those occuring around age 5.

Beginner - No Idea what to do

Intermediate - Learn the "3 corners" strategy

Advanced - Play to win or draw every time

Amongst my colleagues at work, Race clearly has at least 4 levels. I'd label them:

"1st game": Most people pass this level after their first or second game, but some people don't "get it" until 3 or more games.

"Novice": Understanding of the simpler strategies; military rush & simple produce/consume. Doesn't pay attention to other players very much.

"Intermediate": Nearly complete knowledge of the deck, plays many strategies depending on their cards, understand the big 6-strategies, as well as many of the power combos. Pays attention to other players for game pacing and leeching. Tends to play produce/consume a lot.

"Advanced": Knows all the cards, changes strategies fast, controls pacing of the game and understands all the 6-strategies as well as several alternate "overall" strategies other than produce/consume and is extremely engaged with other player actions and effectively leeches as well as successfully taking actions dependent on other player actions (eg, speculative consume).

I suspect there's a level above that, but the players I know at that level don't play with the same population of players, so it's hard to be sure.

Between levels I'd say the win rate is 75%.

I'd be tempted to say you were wrong, I've played a bit online and there are certainly at least three levels of skill with this game though as you point out with luck in the game it's hard to define as easily as 2 player zero sums.

With the Cities and Knights expansion, I would say there is at least three skill levels. The online site I play at gives ratings each month and some players are consistently ranked very high each month while others are ranked consistently low, and yet others oscillate each month.

I have to say that having played this game literally thousands of times there are definite skill gaps.

I would put at least 4 levels of expertise here: Beginner, Intermediate, Expert, Master. These differences are going to be apparent in winning percentage and average points per game.

At the master level I would expect to see someone who wins an average of 45-50% of their games and scores and average of 8.5+ points per game.

There are very few people who can match these statistics. And if you claim that you CAN match these statistics then I hope you're not just talking about games with your local gaming group.

As to the luck in Settlers, it is definitely true that in any given game a Beginner could beat a Master. Unlike Chess, Go, and other games like that, there is no such thing as a definite win in Settlers.

What would you expect if four masters play? Would they all win 50%?

Clearly winning percentage only makes sense relative to the opposition. In two-player games, a winning percentage of 75% to 25% is often called a level, and it corresponds to a winning ratio of 3:1. Extending this notion to Settlers, if one player is a level higher than the others (who are equal) the winning chances would be 3:1:1:1, i.e. the higher-level player would win 50% while the others each win 16.66%.

The number of levels in Settlers could then be determined recursively.
Level 0 = Novice
Level 1 = Wins 50% against three Novices
Level 2 = Wins 50% against three Level 1 players
Level 3 = Wins 50% against three Level 2 players

and so on until the players are so good that nobody is good enough to win 50% against three of them.

If you use Brian's original scale where there are six levels above novice in chess, then a level is more like a 90% winning chance, i.e. a 9:1 win ratio. A game of Settlers with 9:1:1:1 winning ratio gives the master player a 75% winning chance, while the other players each have 8.33% to win. This would tend to back up Brian's idea of only a novice/experienced distinction. If the ladder were like this:

Level 0 = Novice
Level 1 = Wins 75% against three Novices
Level 2 = Wins 75% against three Level 1 players,

would we even get to Level 2?

This has at least 3 -- Last tourney I was in I thought I knew what I was doing, but the winner seemed like he was on a whole different plane.

I wonder if, sort of like Puerto Rico and Caylus, this one has three levels but they should be named differently: novice, expert, and solved. Novices will lose to experts, and experts will lose to people who have "solved" the game. But having solved the game doesn't really (to me) imply a higher level of skill, just that they've played enough to find or figure out the weaknesses of the game and exploit them. And with games that can be solved, we can say with some confidence that there is no level beyond that.

I think probably a lot of the highly-tactical, constrained, and minimally random games of ours are amenable to being ultimately solved. It seems like the nature of the thing.

I have had the opportunity to play several 18xx games with a group of guys who have probably played together several hundred times, including a stretch of several years when they played 18xx exclusively.

I have seen 18xx from an entirely new perspective. I don't believe it is ever solved. These guys will tell you that every game is different, each is a rich gaming experience, and as soon as you think you have the winning combination figured out someone pulls the rug out from under you.

Should also note that this is a sharp bunch of gamers. They always do well no matter what game they are playing.

A game played with true sharks can be likened to a knife fight. The game goes so fast, its likely someone will go bankrupt.

This game has three axis of skill: giving clues, guessing clues, and memory & general knowledge. I'd put it at 5 levels - novice, good at one thing, good at two things, good at three things, and Kevin.

The levels here pertain to knowledge outside the game, and not the gameplay at all. I'm not certain that Trivial Pursuit (or any of the trivia games) belongs on this list.

Trivial pursuit is a game where certain people will almost never lose to certain other people. It therefor has levels of expertise. You may think that the skill isn't particularly important, but it certainly belongs. The 100 yard dash has levels of expertise, too (but it's not a game in the BGG database).

Another thing to think about is that certain people only have expertise in certain areas of the game's questions. I know just about every science/tech/history question. But I get stumped sometimes on Pop Culture, and stumped very easily on Sports (because they usually don't include Motorsports as part of it)

I don't think Trivial Pursuit has discrete levels. Consider a person who knows the answer to all the questions. As soon as they get a turn, they'll win, because they can't possibly lose the turn. A person who knows the answer to 90% of the questions, though, will get about 10 die rolls before they stop, and we can calculate about how many expected turns they'll need to win.

Everyone in between 90% and 100%? Two levels? Three levels? Where does the line get drawn?

Usually when a game has levels of expertise, it means that there are techniques that one can acquire (through learning or insight) that give one a significant advantage over other players. Trivial Pursuit's main skill set is continuous over a wide range.

There are those that have memorized all of the 2 letter words, and those that haven't.

Neither group is required to know the meaning of those words.

Some of the tricks in Scrabble involve learning how to play the game as a game and not just memorizing words. The levels can be confusing because of differences between skills in board play and pure knowledge. I am guessing there is a rough limit to how well you can play the game, but simple rack management skills and knowing how to lock down the board is useful against people who have never thought about it.

I stopped learning after memorizing the two-letter lists and beginning to learn which two-letter words can be made into three-letter words, so I can say I know of at least three levels: novice, whatever I was, and whatever can beat me. I wouldn't be surprised to find out that there were at least two levels above me because of references to changing how to play the board once people's vocabularies get good enough to avoid blocking.

As a tournament scrabble player, I can verify that four-ish is about right. Roughly the levels are Beginner, Intermediate, Expert and (this is an unofficial title) Master. There is a rating system for tournament play which breaks down approximately like this:

0-1200 Beginner
1200-1600 Intermediate
1600-1800 Expert
1800-2000 Master

The rating system is based on Chess, but of course Scrabble is a different game because of the luck factor. I am currently rated 1658, so in the expert class, but I’ve beaten Brian Cappelletto, one of the best Scrabble players ever (currently ranked 2009 and #1 in North America) in club play due to an extremely favorable draw. This would almost never happen in Chess. However, Brian will probably beat me 8 or 9 times out of 10.

Even most beginners know all the 2 and 3 letter words.

The move from Beginner to Intermediate involves increased word knowledge (memorizing 4 and 5 letter words and, crucially, the most common seven and eight letter Bingos) and more sophisticated board vision (seeing scoring opportunities, weighing whether a board should be open or closed to maximize possibilities of winning).

Expert players have memorized almost all of the seven and eight letter words and play a more fluid and open game, as Mr. Hen has alluded to. Intermediate boards are often cramped and defensive, while Expert boards are open, with long words forking across the board like lightning.

There is a significant gap between Expert and Master players. Masters will have memorized all the words from 2-8 letters (about 70,000 words!) and often the 9 and 10 letter words (another 50,000). Masters think about probabilities in much more detail than Experts (knowing whether to keep an ‘A’ or ‘E’ on the rack in a given situation based on the remaining pool of tiles to maximize bingo possibilities) and have incredible board vision. A famous play in scrabble circles is WATERZOOI (a 9 letter word) through two disconnected letters on the board to win a game. While all tournament scrabblers need to be able to anagram (switch letters around in their head to find words that fit the board situation), Master players can do this effortlessly with 9, 10 and 11 letter words.

To me this is a critical skill that average players probably don't even know exists. I don't calculate probabilities, I just have an intuition for what to keep. I would be on an expert level in that sense, although I don't play tournaments and not having a good word list memorized might hold me back from expert level in tournaments. I guess masters, on the other hand, calculate actual probabilities instead of just using intuition, in a similar way to how good poker players know exactly how many "outs" they and their opponent have.

I would say, besides word memorization, there are skill levels based on these tactics:

1. Plays for the maximum score from a single word
2. Plays defensively, not giving, e.g., triple-word score opportunities
3. Plays multiple words in a single turn (memorizing two-letter words becomes critical)
4. Anagrams for bingos
5. Uses hand management to maximize the chance for bingos. This involves playing suboptimal words and sometimes passing with perfectly good tiles just to very selectively exchange tiles.

There may be more but this is about as high as I go.

For specific word games, players with the same language/word skills will have varying levels of expertise.

For word games in general, a player's general literacy/reading level and vocabulary size effect their ability to play compeditively.

So really, there's Over 9000 levels here, depending on language literacy, and then experience and competence with individual game systems.

Playing this on the iPhone has made a much better player over the last few months!

There are rankings at yinsh.biskai.de and brettspielwelt, which I suppose could give people an indication.

Could be slightly more than three.

Novice players know basically how to play your cards in a climbing game (e.g., don't play your Ace over a 4 when you have a single 5 to get rid of). You could have an even lower level of people who don't even know this, but counting exactly how many levels there are at the bottom isn't very interesting. Novice players also might make mistakes like playing over their partner.

Intermediate players know when to call Tichu.

Advanced players know various tricks for when to deviate from the typical rules of how you play your cards in a climbing game. They therefore have more hands when they can successfully call Tichu and can break more of their opponent's Tichus.

There are numerous such tricks. Is someone who knows seven different tricks on a higher level than someone who knows three? I might say yes. In a game, there might be an average of one trick useful per round. That trick might have a 25% chance of being effective. Over the course of a game, that might be decisive. Over the course of a series, it has a pretty strong chance to. Would someone who knows half as many tricks consistently lose the series? I'd say it's borderline.

Perhaps.

A pair of newbies has little chance against one experienced player and a newbie, who will themselves be beaten by two experienced players. Four levels is not out of the question here, if you look at pairs.

I'm not convinced that Tichu has more than 2 levels in the sense of levels being used for the other games on this list. There certainly are a lot of different skill levels, but there is so much luck involved in the deal, and no mechanism to even out the luck from one hand to the next. There are hands that are so one-sided that any experienced partnership should be expected to score 400 points, i.e. 40% of the winning score.

It would be very interesting to see the spread of skill levels if one was to set up a 'duplicate Tichu' play format.

One skill that definitely develops in this game is being able to estimate what your partner and your opponents have left in their hand based on how they've played the hand thus far. And as this skill develops, a bluffing element comes in where you play your cards in a non-intuitive order as a way of throwing off your opponents ability to estimate what you have left.

The original poster made some allowance for games with a lot of luck by saying the criteria could be based on a series of games. I guess Tichu is already played as a series of independent rounds, but I interpreted it as a series of several 1000-point games.

Yes, I'd imagine a series. And we can consider partnerships, instead of individuals.

New players don't much to worry about with this title. They just need to have 200 pages of rules memorized with a working knowledge of when to apply every rule to maximize them to their advantage.

They also only need to be able to 'see' things like choke points, rally points, fields of fire and optimial defensive locations. Also to see probable strategies of their opponent beforehand to not have vital units out of position the entire game.

Then you need to be able to see a scenario card for balance and which side has the better chance of victory.

If you get all that, you still don't have much of a chance against an experienced opponent.

This is a tough one, because we have to ask, is "knowing the rules" a skill? i.e., can you really say that a player is "intermediate" instead of a "novice" because he is more thoroughly familiar with the rules? It's not obvious to me one way or the other.

Clearly there are at least three levels here. Four if you want to count "still figuring the game out", "novice", "experienced", and "master". There is a lot of skill to ASL, but if you factor out simple rules knowledge and luck, it might be less than you would expect. I would think Scrabble has more, for example. You can imagine essentially unlimited scope for effort improving play in Scrabble (in memorizing words if nothing else). After you've learned all the rules to ASL, I can't see the same sort of return on effort investment.