Questions which are rarely asked

by on January 16, 2013 at 2:18 pm in Games, Science | Permalink

All Scrabble players know that Q and Z are the highest scoring tiles. You can get 10 points for each, in the English language version of the game.

But according to one American researcher, Z really only deserves six points.

And it’s not just Z that’s under fire. After 75 years of Scrabble, some argue that the current tile values are out of date as certain letters have become more common than they used to be.

“The dictionary of legal words in Scrabble has changed,” says Joshua Lewis, researcher and creator of a software programme which allocates new, up-to-date values to Scrabble tiles.

“Among the notable additions are all of these short words which make it easier to play Z, Q and X, so even though Q and Z are the highest value letters in Scrabble, they are now much easier to play.”

Here are some details on the reforms:

According to Lewis’s system, X (worth eight points in the current game) is worth only five points and Z (worth 10 points now) is worth six points.

Other letter values change too, but less radically. For example, U (one point currently) is worth two in the new version, G (two points) becomes three and M (three points) becomes two.

Here is more, via @timharford, and here is further information.

craig January 16, 2013 at 2:25 pm

We could largely eliminate the Z problem if we made the word “ZA” worth minus eleven points.

Urso January 16, 2013 at 3:58 pm

One problem with words with friends is that it allows all these little two letter words that don’t actually exist. No real life scrabble player would ever allow someone to play “xi” or “za.” So winning words with friends is unduly tilted towards knowing these little tricks and loopholes.

Paul F January 16, 2013 at 4:13 pm

You’re wrong, as XI, XU, ZA, QI and many other words that “don’t actually exist” do actually exist and are acceptable Scrabble words. WWF word list is based on Scrabble word lists. These are not tricks and loopholes, but words. Your Scrabble board in fact came with a set of instructions that lists all the 101 2-letter words for you.

Doug M January 16, 2013 at 4:42 pm

The value of the letters in a scrabble game is based upon the frequency of their appearance in common language. Alfred Butts, the inventor or scrabble, sampled articles from the New York Times to derive his point system.

The problem is the official scrabble dictionary. There is a greater frequency of X and Z words in the scrabble dictionary than there are X and Z word is common usage. The scoring system is great for casual scrabble players, but is ‘broken’ for the scrabble enthusiast. Of course, the enthusiast is the one who will argue most vociferously to scoring unchanged.

David Wright January 16, 2013 at 6:01 pm

+1. The Official Scrabble Dictionary has had an enormously negative impact on the game.

If you want to play a fun game for which a good vocabulary is a helpful skill, grab a paperback college dictionary and agree to use it as your reference dictionary.

If you want to engage in obscure machinations dominated by people who memorize and employ random strings of characters that bear only passing resemblence to words, grab your Official Scrable Dictionary and head off to a tournament.

Urso January 16, 2013 at 6:14 pm

No, I’m right, at least among the non-autists I have played Scrabble with. YMMV, and I bet Scrabble games with you are a blast.

byomtov January 16, 2013 at 6:55 pm

I don’t know about “za,” but “xi” is a Greek letter. It’s as legitimate as “alpha,” or any other. Unlike “za” it’s right there in my 1963 Webster’s New Collegiate.

Steve January 16, 2013 at 10:42 pm

I play Words with Friends against a “real” Scrabble player and often have to apologize for some of the stupid words I play. But it does let me compete with someone who would easily outclass me in real Scrabble.

derek January 16, 2013 at 11:57 pm

I disallow other Greek letters as well! Some are okay, such as pi, which is a mathematical concept, or alpha, as in male, but no one is ever getting with spelling out their sorority on my board,

byomtov January 17, 2013 at 4:22 pm

Virtually all Greek letters are used in fairly standard ways in math and statistics, and probably elsewhere as well. There’s also “beta testing,” “alpha and omega,” “not an iota,” “gamma rays,” various meanings of “delta,” and no doubt others I’ve overlooked.

I think arguing that Greek letters are not English words is quite a stretch.

brad January 17, 2013 at 12:41 pm

Long live the third edition! Down with qi and za!

Bill January 16, 2013 at 2:25 pm

That’s what you get when some heavy handed bureaucratic game manager assigns points.

Foobarista January 16, 2013 at 2:59 pm

As for the over-the-top decor, there are actually several San Francisco Chinatown restaurants which would fit the bill. Monterey Park in LA has a few also, although the decor is more modern – and typically black laquor with gold trim.

My guess is they survived in SF since they were built a long time ago and the over-the-top decor evolved into a sort of institution in itself.

Luke January 16, 2013 at 3:02 pm

Does anyone else feel that the distribution of letters in Scramble with Friends (the Zynga Boggle clone) is also statistically flawed? It’s just an impression, but I think it has to do with high-frequency letters being over-represented due to the uneven topology of the gameboard.

Paul F January 16, 2013 at 3:50 pm

Individual tile values are only part of the story, though. The blank is worth 0 points and is arguably the most valuable tile. There are only four S’s (worth 1 point), and they are all more valuable than a Q.

Furthermore, what is the purpose of this revaluation? What conditions are satisfied by these new but not by the old ones? Isn’t it okay in a *game* that some tiles are *over-valued*? Doesn’t that make the game fun? If Z is worth too many points, pay attention to TLS spots next to As–play strategically. If we make the (tile value × frequency in playable words) equal for all letters, then it reduces Scrabble to a vocab quiz, and there is not as much strategic play. Scrabble is a hard (fun) game because you have to navigate these inconsistencies, not in spite of them.

Willitts January 16, 2013 at 4:16 pm

OK, so you make a very good point that inconsistency might make the game more interesting. But that’s begging the question of the values of the tiles in the original version. What was the rationale for it? Why not assign values at random? It appears to be the case that the game eas designed with relative scarcity in mind.

What about dipthongs? Shouldn’t a Q be valued slightly less because it will almost certainly be paired with a U? Should a TH or an NG or ING or ST or SH be valued at less than the sum of their individual components? It makes scoring harder, but accomplished players could easily remember the value of common two letter combinations.

Scrabble is, was, and always will be a vocabulary game. I don’t see how strategy would vanish if letter values changed. It would just create new strategies. It sounds like you are making an argument that there exists arbitrage opportunities because of point mismatches from intrinsic value. That’s not a bad argument. But removing arbitrage opportunities doesn’t make the game less enjoyable, and I’m not sure any expert Scrabble player understands arbitrage. On the other hand, you seem to understand it fairly well, so I could be wrong. Good thought provoking question.

Paul F January 16, 2013 at 4:33 pm

Yes, clearly I’m just arguing that the game is fun the way it is–and current players understand it the way it is–so I don’t see the value in changing. The only argument I can really offer in favor of keeping Z at 10 points rather than 6 is that 1) there is no “perfect” value, 2) 6 is not better than 10, and 3) right now it’s 10 points.

I think the Q+U combo is an argument for awarding more, not fewer, points for Qs. Even if you know all the Q-without-U words, the Q is a pain in the ass without a U. However, I think home players can (and do frequently) come up with new scoring schemes which change strategies in different ways. That’s totally fine.

Suggesting that a system that was never perfect should be improved, however, is weird to me. That’s like saying the colors in Twister today really should be green, purple, grey and red.

Finally, I’m not saying it isn’t a vocab game, but what I’m saying is that it’s a vocab + strategy + luck game.

Willitts January 16, 2013 at 5:00 pm

I don’t agree with your Twister comment because the colors were never meant to signify anything nor is there a rationale for placing a particular color. The game doesn’t change AT ALL if you change the colors.

Scrabble most definitely had some rationale for its letter values, and changing them changes the game.

For all the reasons you suggest, perhaps the game should stay the same. But games can and do change, often for rational reasons, to make them more fun, more fair, quicker, or longer. It’s not remarkable that someone should suggest a rule change for a game. This blog once had a post on the REAL rules of Monopoly that almost no one really uses.

JR makes a good argument that this is unnecessarily pedantic, and you are saying ‘leave well enough alone’ – two polar opposite views for keeping the status quo.

I would suggest that the chief source of conflict in games is not the competition but rather the interpretation, application, and abuse of rules. Rules make the game.

PKSully January 16, 2013 at 5:11 pm

I agree. It’s interesting to know that the tile values don’t represent the rareness of the letter absolutely, but that doesn’t mean they should change. A 3 pointer in basketball is worth 50% more than a shot taken with one toe on the line, it’s no more difficult, just more valuable. And we like it that way!

Willitts January 16, 2013 at 10:00 pm

Basketball could feasibly have a large number of scoring zones based on difficulty of the shot. As far as stepping on the border between one zone and another, that’s the same problem of discrete scoring rubrics that Scrabble has.

Whether fans “like” it the way it is lacks the counterfactual of alternatives, the sole exception being all field goals counting as two points.

Theoretically, you could score basketball by a computer that measures relative difficulty. In a sense, slam dunk competitions use subjective judgment to do just that.

At risk of being beaten up by JR, I’ll just shut up about that now.

Dashington January 17, 2013 at 11:07 am

Scrabble is NOT primarily a vocab game. In its purest form, it is effectively chess + luck. I mean that seriously. I believe that the endgame, for example, is a highly complex set of math and logic decision-making. Throughout the game, you must predict/handicap opponent moves several iterations into the future. It certainly helps to have a great vocab…but it helps a lot MORE to have a higher IQ. More explicitly: a person of average intelligence (IQ 100) with perfect knowledge of every single word in every single dictionary probably does not have an edge in Scrabble over a 145 IQ person with an average vocab knowledge.

byomtov January 16, 2013 at 7:05 pm

Correct.

All rules of games are arbitrary. They’re games, remember. Is a touchdown twice as hard as field goal? Or slightly less than 7/3 as hard?

The point is not to reflect some exogenous fact. It’s to make the game interesting. As a game becomes widely played it will often be the case that someone will discover strategies that are “too effective,” in that they work too well. Then the rules have to change or the game dies. But there is no reason the changes have to follow some logical pattern, other than rendering those “too effective” strategies illegal or otherwise less useful. Is that happening in Scrabble? I don’t know. I’m a very casual player.

Willitts January 16, 2013 at 10:15 pm

A scoring system isn’t “arbitrary” just because it deviates from some theoretical ideal of relative difficulty. A touchdown (or first down) is indeed much harder to get on fourth down than a field goal, especially given the risk of giving the opponent good field position. We see this represented in the way calls are played. The scoring system need not be exact to reward game play based on relative difficulty. A scoring system must be RATIONAL, not perfect. The more scoring deviates from relative difficulty, the more perverse the incentives. You will see game play based on the most bang for the effort and thus final results more a matter of chance than skill.

It isn’t arbitrary that a field goal is 3 and a touchdown is 6. Consider how the game would be played if the points were reversed. I don’t think that game would be fun to watch.

Poker once suffered from a straight beating a flush. Over time, the game was necessarily and properly corrected. But I would have not wanted to be a player at the time shortly after that rule change. :)

Byomtov January 17, 2013 at 10:01 pm

No, a scoring system need not be rational, or even RATIONAL.

Scoring systems define games. They tell the contestants what the objectives are, and lead the contestants to devise strategies to maximize their chances of outscoring their opponents. It’s a mistake to assume that under a different scoring system the game would remain the same.

Suppose field goals counted six and touchdowns three. Strategies would change. No long passes – why bother? We’d see offenses designed to get into field goal range, not to rack up a big gain. We’d see defenses that had more players close to the line, especially when the offense was at, say, the fifty-yard line.

Would that be as popular, as commercially successful, as interesting, as football is now? I doubt it, so it would change. But it would be no less “arbitrary” than the scoring system being used now.

The key is that changing the scoring changes the game. If baseball teams scored a point for every base, rather than for getting a runner all the way around to home, you’d see different tactics, different “stars,” etc.

vlad January 17, 2013 at 8:59 am

If the letters are not valued properly, luck plays a bigger role – you get a random advantage if you happen to get a high valued letter that is actually easy to use. They want it to be a game of skill.

j r January 16, 2013 at 4:12 pm

And there are reasons why questions like this are never asked. Pedantic articles like this remind me why nerds got beat up in the 80s. It’s like the internet turns everyone into The Simpson’s comic shop guy?

Willitts January 16, 2013 at 4:46 pm

I think the people who would beat up these pendants would beat up Scrabble players, more generally. :)

It is pedantic, but that’s what makes it interesting. It’s not as far-fetched as you might think. People still debate the DH rule in baseball.

What if pawns could move backward in chess? Do you allow captures en peasant? Do you put cash under Free Parking in Monopoly, and do you follow the actual game rules of auctioning unpurchased properties?

In Eight Ball, does slop count and can you combine off the other player’s balls? Every game has pedants and every game has informal rules that deviate from published rules.

But I will say that “pedantic” was the first word that came to mind when I read this, so I’m not too critical of your feelings.

Mr. Beefy January 16, 2013 at 5:25 pm

LOL on the 8-ball – seen more bar fights over those nuances in rules; :).

dead serious January 16, 2013 at 7:52 pm

“En peasant?” I challenge that.

willitts January 16, 2013 at 10:17 pm

I blame all spelling errors on my spell checker.

But now that you mention it, en peasant isn’t too far from truth.

Rahul January 17, 2013 at 1:29 am

I’d like to beat a pedant with a pendant.

Willitts January 17, 2013 at 10:58 am

@Rahul

Good one.

Paul F January 17, 2013 at 10:49 am

No money on Free Parking ever! We used to put cigarettes there when I was in college, however.

Jeff Albertson January 16, 2013 at 5:29 pm

Worst. M-R. Comment. Ever.

Jason Hartley January 16, 2013 at 4:37 pm

I think value should be given to the combination of letters, not just the letters themselves. For instance, you could have a multiplying effect for rarely used words (the data would be collected through the Scrabble app). So “za” or “qi” would be worth less than “muntin.” This way you get credit for knowing more words, which seems like a good thing.

Roy January 16, 2013 at 11:07 pm

It would completely destroy all transparency in scoring and make the game even more annoying when playing with scarbble experts.

Jevon Jaconi January 16, 2013 at 5:10 pm
Owen January 16, 2013 at 5:50 pm

Scrabble, more so than any other board game I can think of, is played completely differently by amateurs and enthusiasts, even under roughly the same rules. In Monopoly everyone seems to follow the same general heuristic of buying everything, and people learn pretty quickly that the second and third rows are where the value is at. In chess, beginners are obviously using terrible strategy, but they generally admit it, and when they see an expert, they want to emulate them.

By contrast, casual Scrabble, where you search your memory for cool words and put them down, is 90% different from “hardcore scrabble,” which is basically a math game where the accepted combinations happen to match English most of the time. Scrabble isn’t broken for the casual player, but anyone who plays it a lot can see that the letter values don’t sync up with the actual playability of the letter. X and J are each worth 8, but AX, EX, XI, OX, and XU are all acceptable two-letter words, whereas JO is the only acceptable J-word (interestingly these six have all been standard for years, but then ZA and QI snuck in with the 4th edition of the OSPD and gave all four of the megatiles a combo to look for). H and V are another example: H is very easy to use in a two-letter word, while V is impossible.

[Lest you think I overemphasize the value of the two-letter word, think of that one game you played against the asshole who insisted on clogging up the board with crappy fake words. "That's "WITH," also forming "WO," "ID," "TH," and "HM," with double letter going both ways, for 48 points. Oh, and your APHASIA counts for 16, good for you, but you should really have saved that S." That's me. I'm that asshole.]

Of course, the unbalanced “true value” of letters creates its own strategy. And I can’t do the math on this, but arguably having 10-20 “strong” tiles like the H, Y, W, M etc. lessens the overall variance and thus lowers the luck factor. If you just have the ten power tiles–J, Q, X, Z, 4 S’s, 2 blanks–and 90 average tiles, a simple 7-3 split in power tiles could give one player a significant advantage in a balanced game. Making 25-30 tiles “strong” makes a fair division more probable. And you can nerf the J Q X Z slightly, but then that gives even more power to the winner of the blank-n-S battle.

I am a nerd.

Urso January 16, 2013 at 6:22 pm

Great comment.

willitts January 16, 2013 at 10:18 pm

I’d rate it great if I understood it.

derek January 17, 2013 at 12:01 am

You are smart, but be warned that I would straight up beat you up for playing those fake words. Happily, I wouldn’t ever let you play those words, so I wouldn’t have to beat you up.

That’s the true WWF travesty; the computer is the arbiter, rather than the human.

Paul F January 17, 2013 at 10:43 am

Oh, God: V. What a horrible letter! Anyway, very good comment.

Brad January 17, 2013 at 12:49 pm

Our house rule is that you have to produce a definition on demand. It still advantages memorization, but at least it raises the bar a bit.

Sbard January 17, 2013 at 3:18 pm

Similarly see the difference between tournament level fighting game players who count hitbox pixels and execute counters with single-frame windows and those who aren’t. ( http://2.bp.blogspot.com/_2jOFQTFN4W8/TRSy4VSFixI/AAAAAAAAAEk/Ay1SxdCOJQc/s1600/1204223692289.jpg.jpeg ). Similarly, getting good at top-down shooters doesn’t require good reflexes and quick thinking so much as the ability to memorize attack patterns and enemy locations.

David Wright January 16, 2013 at 6:00 pm

+1. The Official Scrabble Dictionary has had an enormously negative impact on the game.

If you want to play a fun game for which a good vocabulary is a helpful skill, grab a paperback college dictionary and agree to use it as your reference dictionary.

If you want to engage in obscure machinations dominated by people who memorize and employ random strings of characters that bear only passing resemblence to words, grab Official Scrable Dictionary and head off to a tournament.

Steve January 16, 2013 at 6:22 pm

Rarely asked? Very surprising coming from an economist. The title should be “I don’t play Scrabble”. It doesn’t take playing a 2 letter word for over 60 points many times to begin questioning the values of the letters. Many games (and things in life in general) are broken by incorrectly setting values.

Max January 16, 2013 at 7:02 pm

Many of my scabble games are won by the player who draws 3 of the 4 big letters, J, X, Z, and Q.

Alan January 16, 2013 at 7:07 pm

I play Scrabble often and have done for nearly 50 years. I also have the complete, 20 volume Oxford dictionary, which we use as the arbiter, but not in the way you might think. If anyone puts down a word, they must, if challenged, provide the definition of the word.

It surprises me how many people use words like axon, dzo, quillon or adze who would not be able to name the physical article if they saw it.

As for the scoring … so what? All game rules are arbitrary.

Steve January 16, 2013 at 9:55 pm

“All game rules are arbitrary”

That is true but usually games have an intentional ratio between the amount of skill and luck involved. There is a lot of luck involved in most games used for gambling. This allows even beginners to win sometimes. At the other extreme is chess where no luck at all is involved. The complaint about the value of letters in Scrabble is legitimate. The addition of multiple 2 letter words for the high value letters skews the game toward luck.

Willitts January 16, 2013 at 10:22 pm

Initial endowments matter, but luck evens out in multiple game play.

Hearts is interesting because of the ability to Shoot the Moon with a really bad hand. Poker has the bluff which can accomplish the same thing.

Steve January 16, 2013 at 10:44 pm

Don’t get me wrong I’m not saying skill is not important in those games just that they are designed to allow the unskilled to sometimes beat the skilled. That is why it is gambling. An unskilled person playing a skilled person in chess is not gambling it is just boring.

Willitts January 16, 2013 at 11:12 pm

The skill vs. gambling debate has raged over poker for years.

At first, I believed the argument that it was a game of skill because the same few people always seemed to win.

Then when internet poker arrived, no-names started winning and luck seemed to rule the day.

But it is becoming clear that players like Phil Hellmuth, even with his sponsorship into nearly every tournament, has a knack for getting into the money consistently. Some people do make a living playing cards which would not be possible in a game of pure chance unless they are the luckiest coin flippers on the planet.

Just because a game involves decision making under uncertainty with imperfect information doesn’t make it gambling. There are still optimal or near-optimal strategies.

True gambling is where no decision you make has a non-trivial effect of improving your chances to win. For example, lotteries. No choice of numbers will improve your chances of winning, however a bad choice of numbers could reduce your expected winnings by duplicating numbers that other players have chosen. Consequently, it is asinine to pick lottery numbers using birth dates which are highly concentrated between 1 and 31 and even more concentrated between 1 and 12. Your chances of winning are no better, but your chances of splitting the prize are greatly increased, thus lowering the expected value of your wager immensely. The worst lottery players pick systematically, e.g. 1, 2, 3, 4, 5, 6.

hgfalling January 16, 2013 at 8:36 pm

There’s a pretty high ratio of self-assuredness to knowledge about competitive Scrabble in the comments here.

Steve January 16, 2013 at 9:58 pm

It takes almost no knowledge of Scrabble to realize adding more words to the Scrabble dictionary changes the real value of the letters.

Willitts January 16, 2013 at 10:26 pm

Exactly. Game theory doesn’t change with the game. If we were just now inventing this game, we would likely be discussing scoring rubrics of relative difficulty in forming words from letters. It makes it easier to discuss improvements relative to an existing rubric.

Brian Donohue January 16, 2013 at 10:44 pm

Whoa! I never thought I’d type these words, but this has all the earmarks of an on-line Scrabble geek flame war.

All you Scrabble-enthusiast commenters upthread: you gonna take this shit?

Steve January 16, 2013 at 10:51 pm

We Scrabble’ers do not fool around :-)

Truthfully I was almost offended with the “questions rarely asked” thing. I think that does qualify for true geekdom.

Dan Weber January 17, 2013 at 12:46 pm

There’s a CSI episode where a guy gets killed during a tournament (the network’s no-name version of) Scrabble

They find the tiles “EXVIN” in the dead guy’s stomach. For some reason, they refuse to think it could be the word “VIXEN” and dismiss it.

JoeDog January 16, 2013 at 10:07 pm

Is our children learning?

Tom West January 17, 2013 at 11:08 am

http://scrabbleplayers.org/w/Valett is a technical rebuttal by one of the experts in the field.
I like John Chew’s point that making Scrabble tile points too mathematically valid (were it possible) would probably detract from the game itself.

Steve January 17, 2013 at 3:06 pm

That was a lot of writing to say that he likes the game better with more luck involved.

dana January 17, 2013 at 10:23 pm

I played NSA tourney and club scrabble for a while. i am the type who memorized all the four letter words and quite a few bingo stems and i just have to state here for the record that ZA and QI basically ruined scrabble, the only blocking tiles left are C and V. it could be worse, SOWPODS in the UK accepts CO and CH

Kenneth W. Regan January 20, 2013 at 3:40 pm

Agreed. A longterm friend and I play without ZA and QI.

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