Chanda Chisala has written a series of articles for this website, dealing with the strong performance of many Nigerians and other black Africans in competitive Scrabble. He argues that this fact invalidates the poor results of African populations in IQ tests, his key point being that you have to be very smart to excel at this game.

The series provoked a flood of commentary and dispute. Most of it was civil, but Chisala and his critics often seemed to be talking past each other. A big part of the problem, from my perspective, was that they didn’t really know what they were talking about.

I am not writing either to support or to assail Chisala’s position. I am no expert in intelligence testing; I could do no more than rehash the arguments of others. I am, however, an expert in Scrabble itself. Over several years of tournament play earlier in this century, I more than held my own against the best players in North America. My purpose here, then, is to shed light on a subject that seems very obscure to those who pontificate about it.

On becoming a database

The most salient aspect of Scrabble proficiency is, of course, knowing the words. Chisala seems to believe that this amounts to memorizing the dictionary, and none of his critics have contradicted him on the point. This perception is incomplete and quite misleading, so I need to correct it before I can convey to you enough true understanding of the game for you to discuss it intelligently.

Skilled Scrabble players don’t study words. We study alphagrams, and learn to associate them with the words they form. I personally have never used a Scrabble dictionary or wordlist for any purpose other than checking a word for validity when judging a challenged play.

An alphagram is a set of n letters, possibly including duplicates. Typically the letters are ordered alphabetically for reference and study, although some players prefer to separate vowels from consonants. Most alphagrams have no permutations which form valid words; these are generally not worth studying. Most of the rest have only a single valid permutation, but some form sets of two or more anagrams. For example, the seven-letter alphagram AEINRST forms many valid words (the exact number depends on the dictionary chosen), among them common English words such as NASTIER and RETAINS, as well as obscurities such as ANESTRI.

The most efficient way for a human to absorb the huge number of alphagrams needed for competitive Scrabble is to study flashcards. One side of the card contains the alphagram, and the other contains all of its valid permutations. Some players have complete sets of physical cards, which can be quite bulky, but more often a suitable computer program is used for study.

Many Scrabble players, even some good ones, consider “anagramming,” the process of finding valid words in an alphagram, to be a serious mental challenge, perhaps the core of the game itself. When studying, they’ll stare at an alphagram, possibly rearranging the letters, until they either find the word(s) or give up in frustration and flip the card over to the answer. Under timed game conditions, they try the same thing, but without the benefit of their flashcards. Obviously, this is far from optimal. When I was competing I took a radically different approach. In my study regimen, I always strove for instantaneous recognition of valid words. For example, AAFIRUY might come up in the deck I was studying. If I didn’t see RUFIYAA within a second or two, that card would be repeated the next day, and the day after, and so on, as many times as needed until the mental mapping from alphagram to word became second nature.

The reasons for this practice become clear when you know that the strategic aspects of play – deciding which word to play, where to put it, when to forego points in favor of a better “leave” of synergistic tiles, etc. – constitute the main difference in results between players who know most or all of the words. Each player is allotted only 25 minutes on the game timer. The more time he spends “anagramming,” looking for words that may or may not be there, the less time he has for the decisions that really matter. As a result of my study method, I could confidently rule out any letter combination if I didn’t see a word in it quickly, as well easily challenge my opponents’ invalid plays. I don’t believe I had much greater strategic understanding than most of my opponents in the top divisions of tournaments, but my results were better due to having more time available to apply that understanding.

The tenuous connection of all this to actual language

As for the question of whether verbal acuity is necessary, helpful, or even detrimental to Scrabble excellence, I can offer the following. My vocabulary is uncommonly extensive for a survivor of American public schools, yet there are a huge number of “Scrabble words” that I know, but whose meanings in English elude me. It is indeed possible, as Chisala has pointed out in his discussion of French Scrabble, to excel in this game without any proficiency in the underlying language. But that proficiency can’t hurt Scrabble performance, despite some players’ superstitions, and in some minor aspects it may help.

Meanings don’t matter much, but knowing parts of speech can be useful, as well as having some idea of a word’s etymology and, in the case of a foreign-derived word, its language of origin. All nouns can be pluralized, sometimes producing Scrabble-valid absurdities such as DEADS (as in “the dead of night”). Knowing that a word is a noun or verb, even if you don’t know its meaning, can help you remember whether a “hook” of -S, or additionally -D for a verb, to the word’s end is allowed. These are not hard and fast rules, but useful mnemonic aids, and memorizing the exceptions is less arduous than learning the hooks to each word individually. Verbs can be conjugated in the usual ways, and adjectives usually have comparative and superlative forms, helping to determine the validity of longer words that you may not have studied yet, or to extend a word already on the board.

Most of the short words ending in -AE come from Scots, and are either prepositions or verbs that take forms irregular in English. Reading Robert Burns can actually improve your Scrabble. Words ending in -EAU are of French origin and can be pluralized with an -X, but remembering which ones can instead take an -S is tricky. Many Italian-origin words take the unusual front S- hook. Physical units having to do with electricity can be prefixed with an AB-. Hebrew words ending in -OT are already plural and don’t take the final -S, but do take an -H. The same is true of -IM words, but without the -H. As for German and Latin … don’t get me started.

In sum, I must say that my strong command of English, along with scattered bits of knowledge of other languages, did benefit my Scrabble play, but the effect was mild, manifesting itself chiefly in ready mnemonic devices. A minimally literate coder-type with strong memory and logical skills could still do very well in this game without being hampered by his lack of verbal fluency.

Math? What math?

A claim often made by Chisala and the authors he cites is that Scrabble is “a math game, not a word game.” But the evidence for this claim is basically circumstantial, amounting to the observation that many excellent Scrabble players are also experts in math or related fields. Let’s look at the mathematics actually used in the game, so you can judge for yourself.

The math involved in the everyday play of Scrabble is simple arithmetic, consisting of addition and multiplication operations on small whole numbers. No single tile has a point value higher than 10, and the multiplier squares on the board introduce factors of 2 and 3. A player lucky enough to cover two triple-word squares in a single turn will need to be able to multiply by 9. Add together the scores of each word you make in a play, plus a 50-point bonus for a “bingo” if you use all seven of your tiles. Keep a running total for each player by adding the score of the current play to his cumulative game score, which will be a three-digit number after a few turns of play.

That’s it. Most kids learn this stuff before they’re tall enough to ride the rollercoaster. This sort of arithmetic was routinely mastered by not-very-bright store clerks in the days before computerized cash registers, though their descendants now atrophy their own brains with smartphones.

There are situations where somewhat higher-level math is useful, though it can’t be applied effectively during the game itself. I’ll give a simple example. Suppose we have a choice between two plays fairly close in value. But the stronger play slots an “A” next to a triple-letter square, which will offer our opponent a high-scoring counterplay if he has the single “Z.” Knowing the probability of this is worthwhile. With a basic understanding of combinatorics, the calculation is conceptually simple, but far too unwieldy to carry out mentally if there are many tiles left in the bag. In practice, an experienced player will have heuristics for handling such situations. Because I had spent a few hours with a spreadsheet generating numerical answers for many scenarios of this type, mine may well have been better than those that my rivals had developed through experience and guesswork. But there was nothing really clever in what I did, and I don’t believe it gave me a great advantage. After my opponents had spent a few years practicing and honing their strategic heuristics with the then-new Scrabble AI “Quackle,” that advantage may have vanished entirely.

The spatial factor: why Jews aren’t actually the best

Chisala’s assertion of Jewish dominance in Scrabble does not withstand scrutiny. While it is true that a disproportionately large fraction of excellent Scrabble players are Jewish, the very best of the best are not, and they’re not black African either. They are Gentiles of Eurasian descent, and I have a simple explanation.

Scrabble players call it “board vision,” and Jews tend not to be very good at it. The most difficult Scrabble plays are bingos of nine or more letters, so that they must be played through at least two tiles on the board. Seven-letter bingos can be identified just from the tiles on one’s own rack, while eights intersect a single tile on the board. A dedicated studier of alphagrams will find the great majority of these. Nines introduce an enormous leap in difficulty. Even a player who has studied nine-letter alphagrams and knows the words thoroughly will miss them more often than not. Though not rare, they are rather uncommon, and actively looking for them will usually burn up too much clock time to be worth the effort. They mostly just have to be seen, by talent or serendipity. Computers, of course, never miss them. This can be very humbling.

This talent must be closely related to the so-called “visuospatial intelligence” that Chisala mentions on a few occasions, in which the brighter-than-average Ashkenazi Jewish population tests at a level significantly below the European average, which in turn falls short of East Asian performance. This may just be semantic nitpicking on my part, but I wouldn’t call it a form of intelligence. In a Scrabble setting, at least, it’s more a form of awareness.

Nigel Richards, the most accomplished Scrabble player ever, has more of this awareness than any other human I know of, if the recorded games I’ve seen are representative of his typical play. The one man who may possibly be better at Scrabble than Richards, by virtue of having a winning record against him over a significant number of games, is, ironically for Chisala’s theories, as black as a typical Bantu. But Ganesh Asirvatham’s name is Hindu and his appearance Dravidian, so presumably he is much closer genetically to the Anglo-Saxon Richards than to the Igbo and Yoruba champions of Nigeria.

Scrabble rewards a quick, alert mind and a capacious memory, along with the dedication necessary to maintain the player’s interest through hundreds, even thousands, of grueling hours of study before he can properly apply those talents to the game. A few dozen people at a given time, perhaps a low three-digit number in total over the history of the game, have made it that far. We tend to be bright, sometimes even brilliant. But intelligence, strictly speaking, is not what separates Nigel Richards from us. Nor is it memory, contrary to common assumption. The point of departure seems to be an uncanny spatial sense, one which allows its owner to easily see the exceptionally challenging plays that come up once every few games, plays which the dozens of merely excellent players will usually miss.

Endgames: thinking required

Serious players generally use a scoresheet printed with the distribution of letters in the game’s tile set, crossing out letters as they are played. Once the bag is empty, each player can quickly know exactly which tiles are on his opponent’s rack. The element of chance, very important in the earlier stages of the game, has vanished. Logic prevails.

With the great majority of tiles having already been played, the board tends to be “closed,” lacking open lines of fire for long words. Available plays are predominantly short words, which are both more familiar and easier to find for most players. A word-finding savant will see that his advantage has disappeared against an opponent with mediocre vocabulary and spatial skills, but a greater degree of what ordinary people, not privy to the jargon of a contentious subfield of psychology, might naively call intelligence.

Scrabble endgames, though comparable to chess endgames in the sense of being deterministic, cannot be learned by rote. The variety of board configurations is far too great. A common thread is often the presence of a hard-to-play tile on one player’s rack, and the other player’s efforts to “stick” him with it by blocking the squares where the few possible words containing that letter might be placed. Endgame skills can be improved with practice, but ultimately an optimal solution can only be found reliably through exhaustive search of a space too large for unaided humans to cover in a short time. Computers will always be much better at this.

Brain failure modes, and a surprising conclusion

I hope I’ve made it adequately clear that the dominant mental factors in Scrabble performance are long-term memory and recall speed, spatial awareness, and logic. The verbal and mathematical aspects of what the psychometric community defines as “intelligence” are relatively minor factors. Here I aim to show you just how minor.

I am a night owl by nature, seldom at my best before noon. Grogginess due to lack of sleep often hindered my Scrabble performance severely. Caffeine and appropriate food helped to counteract this, but not nearly enough. My Scrabble tournament results were mostly either superb or lousy, with little middle ground.

I can arise early and due routine physical or mental work well enough, but with my mind foggy I don’t have the mental energy to hold a train of thought long enough for real problem-solving. My physical strength is impaired slightly, but balance and awareness of my surroundings suffer far more. I postpone intense physical exercise until later in the day; trying to clean a barbell in the morning is a recipe for a muscle strain or worse. The same tunnel vision that makes morning weightlifting dangerous for me has disastrous effects on my ability to “see” Scrabble words. Precisely the mental factors most valuable for Scrabble excellence – that is, logic and spatial – are hit hardest when I haven’t slept well.

On the other hand, my verbal and math abilities didn’t seem to suffer much. An entirely unrelated experience will help me to corroborate this quantitatively: the GRE General exam, which was, conveniently for self-examination of my mental lapses, broken down into verbal, math, and logic sections, each scored separately.

I took the General GRE in 2001. A few weeks before I was scheduled to take it, the testing company sent me an informational packet including a CD-ROM with a full practice exam, presumably intended to familiarize testees with the format. I completed this practice exam one afternoon, having recently bicycled a few miles over flat pavement and eaten a light meal. I scored 730 on the verbal section, and the maximum of 800 on each of the other two. The math section was all high school-level material, and I easily finished it with ample time to spare. The only difficulty I encountered in the verbal section stemmed from my ignorance of a few of the words used in the analogies. The logic section required a good deal of focused mental effort and scratch paper, but I finished in the allotted time with no mistakes.

The night before the exam, I was unable to sleep until 2 a.m., my mind churning over a difficult physics assignment rather than this standardized test that I didn’t really care about. After my alarm clock woke me at 5:30, I ate a quick breakfast and picked up a carless friend. Unaccustomed to classes or other requirements before noon, we hurried to arrive by 8 at the testing center in the nearest big city, about a 70 mile drive through the early stages of rush hour traffic. I took the GRE on less than 4 hours of sleep and a good deal of stress. While my verbal and math scores were exactly the same as they had been on the practice exam taken under nearly ideal conditions, I was unable to finish the logic section in time, scoring only 700, a drop from the 99^th percentile to somewhere in the eighties. I knew how to solve all the problems presented to me, but pushing my brain to perform the needed operations was like driving a car with an obstruction in the transmission’s valve body: it just wouldn’t get into higher gear.

I competed in Scrabble tournaments under similar conditions many times. Evidently, my verbal and math skills, those that are supposed to lead to Scrabble success, are unaffected by levels of fatigue that make me a public safety hazard with a steering wheel in my hands. But my tournament results correlated quite strongly with the hours I had slept the prior night. In fact, the disparity between the rested and fatigued versions of me was even greater than it appears. Scrabble tournaments with large fields use a “Swiss” pairing system that matches players with similar ranks in the tournament standings. On average, then, a winning player will face stronger opposition than a loser. Given the bimodality of my results, that meant that I was either beating winners or losing to losers. I’m a lifetime winner against the elite players of the Pacific region: Dave Wiegand, Carl Johnson, and Conrad Bassett-Bouchard; and a loser against a lot of scrubs who I won’t embarrass by mentioning their names here.

My mediocre, but not awful, performance on the GRE’s logic section while tired and stressed shows that even my logical abilities (what I would consider to be actual “intelligence”) don’t drop precipitously as long as I’m able to keep my eyes open. This suggests that explicit, deductive reasoning is only a secondary factor in Scrabble performance. My experience with the game bears that out: logic, properly speaking, plays a key role only in the endgame. Play during the game’s earlier phases, where random draws and incomplete information create a greater similarity to poker than to chess, relies mainly on heuristics developed through playing experience and computer simulation. I believe the current version of Quackle does have Bayesian inference capability, but can only use it effectively when the bag is nearly empty. You can’t expect even that from a human.

I can’t imagine that memory lapses were a significant factor in the variability of my performance. Once words were on the board, I had no trouble recognizing them as valid, or challenging them if they weren’t, regardless of how much sleep I had gotten.

Eliminating all of the other possible key factors leaves only one plausible conclusion: of the mental aptitudes associated with any form of intelligence, the enigmatic “board vision,” the ability to visualize how letters fit together and potentially interact with those on the board, was by far the largest contributor to the gap between my Scrabble Jekyll and Hyde phases. With ample rest and low-glycemic food, my board vision, not quite at the Nigel Richards level but still excellent, made me a highly dominant player, but it quickly abandoned me when the fog of fatigue obscured my mind’s eye.

In conclusion, I can tell you with some confidence that visuospatial ability is the key to Scrabble excellence, and likely the main factor separating players at the very top.

Invoking the Jabberwock, and why I don’t play Scrabble nowadays

English-language Scrabble is not the same game worldwide. The North American and global versions use different dictionaries, the global being considerably larger, and have crucial rule differences that often yield major effects on strategy.

If a player believes his opponent has played an invalid word, he has the option to challenge the play in any variant of Scrabble. The play remains on the board if valid and is removed if not, and the loser of the challenge suffers a penalty. The challenge option only exists for the most recent play, and must be taken before the player who played it draws replacement tiles. By convention, the “phony” word is marked with an asterisk on the player’s scoresheet and in subsequent analysis.

The difference, and it is a large one, comes in the nature and magnitude of the penalty. Under global rules, the loser of the challenge loses five points, but under North American rules, he loses his turn. The latter is much harsher, since the average play scores more than twenty points. This creates a more strategically interesting game, since a player must have much more confidence in a play’s invalidity to challenge it. It also allows for intentional bluffing, which can be very effective if there is a large disparity in word knowledge between the players.

The option to deliberately play fake words creates a fascinating problem, intractable to artificial intelligence and unique to North American Scrabble among games of strategy. In poker, we can apply basic game-theoretic concepts to compute optimal bluffing ratios according to the ratio of the bet size to the pot size. It is a matter of balancing risk and reward. In Scrabble, the reward desired by the word-bluffer is the additional score, or more accurately the increased probability of winning, beyond that provided by his best valid, certain-to-remain-on-the-board play. Positions ripe for linguistic innovation, then, are those with no really good legal options. But how can we even begin to estimate the risk?

A general means of quantifying plausibility of Scrabble words may well be beyond mortal reach.

I can tell you, using the same principles of game theory that work so well in poker, how often a phony needs to succeed to make it a better choice then the best valid play. I can’t tell you so easily how you might estimate the chances of a particular player challenging a particular word. How well do you know him? Speaking of optimal ratios here just doesn’t make sense. The nature of the problem is fundamentally different. A poker bluff isn’t something conjured up out of the player’s imagination; it’s an actual poker hand, chosen from a finite, easily definable range of hands. Eight high is a bluff, but it’s as valid a part of the poker “lexicon” as a flush. A word-bluff, however, is in some sense incommensurate with the set of valid words it is meant to infiltrate. Playing BIOPHONICS* in Scrabble is not like betting in poker with Eight high; it’s more like betting while holding a Pokemon card and a bus ticket. Linguistic innovation is potentially infinite, and even in written language limited (to an absurdly large number) only by the constraint of permuting a finite character set.

I’ll leave this topic with a closing thought. I explained earlier in this essay that Scrabble performance is not very dependent on either verbal or mathematical proficiency. Yet here I am describing an aspect of the game that, uniquely and delightfully, allows for tremendous verbal creativity within a mathematical framework. It has practically been eradicated from the game’s more widespread and prestigious global variant, while more and more North American players abandon their traditional game for that variant. With a larger, harder to assimilate lexicon, the global game should offer the player more, not less, incentive to try to expand the English language into the realm of the incalculable.