The highest score that it is theoretically possible to achieve in a single turn in Scrabble is for the word "oxyphenbutazone". Even at the top levels of tournament Scrabble, this has never actually happened: it would require the game to have unfolded in exactly the right way up to that point, leaving exactly the right open spaces, and the right combination of letters in the bag. But if it did, it would span three triple-word scores, creating seven other new words on the board, for a total of at least 1,778, depending on which official word list you used. The closest anyone has come in real life was a now deceased Kurdish player, Dr Karl Khoshnaw, who got 392 points for "caziques" at a contest in Manchester in 1982. (Oxyphenbutazone, in case you're wondering, is a chemical compound used to treat arthritis; caziques were ancient Peruvian and Mexican princes. But if you had a Scrabble champion's mind-set, you wouldn't waste brain-space on what words mean: that's not the point.)

Hypothetically, there's a chance that higher-scoring words have been played in amateur games, around tables strewn with the remains of lunch on slow Sunday afternoons, and never publicised. But it's unlikely, and besides, we know what would happen: you'd play the word, then someone would dispute it, then you'd realise you'd never agreed which dictionary you were going to use, then you'd be able to find only a children's dictionary with a couple of thousand words in it, then someone would knock over a glass of wine, and the cat would jump on the table, and if the game continued at all it would be with an undertone of resentment and edginess; the emotional temperature of the entire day would have changed. Scrabble does these things to people.

The official position is that Scrabble is 60 years old this year - though that's slightly debatable and, believe me, Scrabble experts are the kind of people who like to debate it at length - so one hot afternoon this month, I took a subway train to Jackson Heights in Queens, New York, to try to find its birthplace. According to Mattel, which owns the rights in most countries, more than 150 million Scrabble sets have been sold, in 29 different languages, since it first went on the market; 30,000 games are started somewhere in the world each hour. I thought Scrabble's ground zero might be covered in worshipful graffiti, like the Abbey Road street sign or Jim Morrison's grave in Paris. But at the apartment building where Alfred Butts, an architect forced out of work by the Great Depression, had made the first board on his kitchen table, there was nothing. At the Methodist church hall a few blocks away, on 35th Avenue, where he'd tested different versions of the game on friends and neighbours, I'd been told I'd find a commemorative sign on which each letter of the word "avenue" had its Scrabble score displayed in the bottom right. But it was gone. Eventually, I found a tiny plaque on the side of the church annexe. It didn't feel like enough - but, as it turns out, Butts himself probably wouldn't have minded. He was a mild, undemanding man, and in any case, he was just glad Scrabble ever saw the light of day. Because it very nearly didn't.

"Here's the Parker Brothers letter," says Robert Butts, Alfred's great-nephew, carefully handing over a framed piece of yellowing letterhead dated October 17 1934. Robert is a lawyer in Poughkeepsie, two hours' train ride north of New York, and we are sitting in a conference room at his law office, drinking coffee from large mugs and examining Scrabble's holiest relics. "Dear Mr Butts," the letter begins, "Our New Games Committee has carefully considered the game which you so kindly sent in to us for examination" - Lexiko, a forerunner of Scrabble. "While the game no doubt contains considerable merit, we do not feel that it is adaptable to our line." It's easy to imagine this New Games Committee - fat men in suits, perhaps, sitting around a long table, smoking cigars, and completely failing to see what had landed in their laps; failing to see that within a few decades one in three American homes would own a Scrabble set, and that it would be commonplace, in Britain and elsewhere, for serious tournament players to spend two hours a day memorising words from an officially sanctioned 267,751-word list. To be fair, they could hardly have been expected to guess, from the vantage point of 1934, that a version would also be played by millions of people online using Scrabulous, part of the Facebook social networking site, in games spanning weeks or months and thousands of miles. (Mattel missed that one, too, as did Hasbro, the game's North American owner, which is why both firms are now suing the creators of Scrabulous.)

The Parker Brothers letter wasn't a one-off. Similar rejections came from the publisher Simon & Schuster and the major US games makers Selchow & Righter and Milton Bradley. "We do not feel that it is adaptable to our line," Parker Brothers wrote, when the truth, of course, was that they should have been adapting their line to Scrabble.

Scrabble involves a lot of luck. People who think of themselves as intelligent say they prefer games of skill to games of chance, but in fact too little chance can ruin a game. Chess is a game of pure skill, and there are few things more futile and depressing than playing chess against someone much better than you: at any given point, your opponent can know all your possible next moves, and unless he or she slips up, the better player will stroll to victory. Connect Four is a game of pure skill, too, but the problem is the opposite one: with a bit of forward thinking, it's possible to force every game into a stalemate - so, unless you're drunk, or four years old, or both, you need never lose. Scrabble's crucial ingredient is that you can't know which tiles are on your opponent's rack, or which you'll draw next, so, with a bit of artful strategy, you stand a good chance of beating someone whose vocabulary is bigger than yours. At tournament level, the temptation to eliminate some of this luck by "brailling" - feeling the tiles in the bag, to pick the ones you want - is so strong that players use special tiles, made with a process called double-injection moulding that leaves the surface absolutely flat.

Scrabble's perfect equilibrium between chance and skill wasn't an accident; Alfred Butts meticulously studied the matter. He had plenty of time to do so: born in Poughkeepsie in 1899, he trained as an architect and took a job in Manhattan, but by 1931, aged 32, he fell victim to the economic chaos engulfing the country. Years later, asked what he did after losing his job, he was self-deprecating. "Well, I wasn't doing anything," he said. "That was the trouble."

He tried his hand at art, drawing New York scenes, but they didn't bring in serious cash. "So I thought I'd invent a game." He had a role model: by 1931, Charles Darrow, a Philadelphia heating salesman who'd lost his job in the Wall Street Crash, was on his way to becoming a millionaire thanks to Monopoly, which he claimed to have created. (It later emerged he was probably bending the truth.) "I think Alfred was hoping he could do something similar," Robert Butts says. "Invent a game and make some money."

So Alfred did his research, producing a typewritten document entitled Study Of Games. There were, he determined, three kinds of parlour games: "move games", such as chess; "number games", such as bingo; and word games. In the first two categories there were hundreds of successful examples, and some brilliant cross-fertilisations: backgammon, for example, is a move game combined with a number game, blending chance and skill. "It is curious," Butts wrote, "that while two of the three bases of table games have yielded such interesting developments, the third has produced nothing better than Anagrams," in which players tried to make words from tiles with letters on them. As Stefan Fatsis points out in Word Freak, his book about competitive Scrabble in the US, Butts' meticulous analysis was entirely in character: he also had a postcard collection he indexed using a complex classification system, so that pictures of balloons were coded 4E2, pictures of amphitheatres 3E4 and so, confusingly, on.

Thus was born the first of Butts' rejected games, Lexiko, in 1933. It didn't have a board, only tiles, and a daunting goal: to form nine- or 10-letter words. What makes it the ancestor of Scrabble was its major breakthrough: the letter distributions. As a child, Butts had read Edgar Allan Poe's The Gold-Bug, in which a pirate's coded treasure map is deciphered by matching mysterious symbols with letters based on how often they appear in the language: "e" is incredibly common; "b" and "h" less so; "q" and "z" are rarest of all. Lexiko needed a distribution of letters that matched their frequency in real English words, Butts realised, or there would be too much luck involved, and games would grind to a halt in a muddle of unusable consonants. He worked out the required frequencies manually, tallying the occurrence of letters on newspaper pages. Another of his great-nephew's yellowing relics is a page from the New York Herald Tribune of October 3 1933, marked up in black ink in Alfred's neat hand.

Butts sold a few sets for $1.50 each, but the big manufacturers didn't bite. Soon after, he added the board. He tried calling the game Alph, and It, before settling on Criss-Cross Words. He added blank tiles, and premium-score squares; he moved the starting point from the edge of the board to the centre. The guinea pig for his tweaks was his wife, Nina, who had been one of his schoolteachers in Poughkeepsie. (How much older Nina was than Alfred was "the most closely guarded family secret", according to Robert Butts. She was better than him at Criss-Cross Words: the legend was she'd once played "quixotic" across two triple-word scores, winning around 280 points on a single turn.) Butts organised Criss-Cross Words social events at the church hall in Queens, where locals tested new versions of the game. But still no manufacturer wanted to buy it. His application for a patent was turned down. By mid-1934, Butts had sold 84 handmade sets, at a total loss of about $20.

If Butts was frustrated, he didn't seem to have shown it. But clearly Criss-Cross Words wasn't about to become the next Monopoly. A few years later, the economy began to pick up. Butts's old architecture firm offered him his job back, and he said yes.

hat makes a board game a commercial success? It would be nice to believe it's the idea alone: that the fundamental genius of Scrabble, its synthesis of anagrams and crosswords, chance and skill, was always going to find stardom somehow. Perhaps. But it's difficult to deny that marketing and luck play a role, and it's at this point in the Scrabble story that savvy marketing first appears, in the shape of a man named James Brunot. Brunot was a bureaucrat: he'd spent the second world war as director of the President's War Relief Control Board, overseeing America's charitable efforts in war-ravaged Europe. But he longed to be an entrepreneur. He had owned one of the original sets of Criss-Cross Words, and seems genuinely to have loved the game, but it's impossible not to sense craftiness at work in the letter he sent Butts. "It seems apparent there is no marketable proprietary interest [in the game]," he wrote, in a bid to justify his offer to buy the rights in return for giving Butts a small royalty on each set sold. Butts agreed, and in 1948 Brunot lodged a copyright application for the game he had rechristened Scrabble. He later said he couldn't remember whose idea the new name was, or why he liked it - Fatsis suggests it was the aural link to the word "scramble" he was after. Brunot altered the board slightly, shifting a few of the premium-score boxes, and began to manufacture and sell the game we know today.

The game's lucky break, according to Scrabble lore, came four years later, when Jack Straus, president of Macy's department store in New York, played it on holiday. On his return, he tried to order a set from Macy's, but found they didn't stock it. They soon did, and a craze began: in 1951, Brunot sold only 4,853 sets, bringing Butts a paltry $135.43 in royalties, but by the end of 1952 he was selling 6,000 a week, Fatsis writes. "In intellectual circles, the game is played in French or Latin; in Hollywood, games of dirty-word Scrabble are in constant progress," Life magazine reported. "Buying a Scrabble set in New York today," the World-Telegram observed, "is akin to nabbing a prime rib roast at ceiling price during World War Two."

Brunot was submerged with orders: he corralled friends into helping him assemble Scrabble sets in a converted schoolhouse near his home, but finally gave up and licensed the game to Selchow & Righter, one of the companies that had originally rejected it. In 1972, they bought Brunot out - and in a contract headed "Final Scrabble Agreement", Fatsis relates, Butts agreed to give up his right to future royalties in return for a lump sum. He got $265,000; Brunot got $1.325m. "Alfred had no regrets about all that," Robert Butts says. "He was sort of pleasantly surprised by the whole thing. It wasn't his nature to have regrets. He was just thankful for all his good fortune, I think."

In total, Alfred Butts made just over $1m from Scrabble. (He had, of course, kept meticulous records.) It wasn't really very much. It wasn't private jet or multiple home money, or enough to give up architecture and move to the Caribbean. It was enough for him to leave Queens with Nina and buy a handsome white clapboard farmhouse in the countryside outside Poughkeepsie that had once belonged to his ancestors. Robert Butts still lives in it today.

Tournament Scrabble, in many ways, is a completely different game from the dinner-table version. In competitions, players keep tally sheets, counting the letters played so they can calculate the probability of what's on their opponent's rack. Timing is strict: normally, each player has 25 minutes in which to play all their words. Unlike most amateur players, they obsess about "bingos" - using all seven letters at once, for a 50-point bonus. They know that some obscure words such as "otarine", impressive though they look, really aren't much to boast about: "otarine" is actually the most likely seven-letter word to occur on a Scrabble rack, whereas "cobwebs" is far more of a coup. They compulsively study the relevant authorised word lists: Hasbro endorses one list for North America, Thailand and Israel, while Mattel endorses another for the rest of the world. Some players are crossword enthusiasts and lovers of words. "But the people at the top end are from IT, that sort of thing," says Allan Simmons, who has won two of Britain's three major championships several times. "We have people in their early 20s who have just said, 'I'm going to memorise all the words in the book.' They tend to be male. It's one of those single-focus things. They may not have any flair at the game, but they'll be good at the words."

This leads to some curious situations. "I was at the World Youth Scrabble Championship and most of the people there were from Asia," says Annie Hawes, a 16-year-old from London who is a rising star in tournament Scrabble. "Singapore, Malaysia... Their vocabulary had been built up specifically in relation to Scrabble. They couldn't speak fluent English, but they were playing seven-letter words I'd never heard of in my life. It was amazing: I was being thrashed by people who could barely speak the language."

By the time competitive Scrabble began in the 70s - it was launched in Britain by Gyles Brandreth - Alfred Butts was little more than a footnote in encyclopedias of games. But then, in 1979, his wife died. Lonely, perhaps, Butts wrote a letter to Selchow & Righter. "He said, 'You may not know me, and I haven't met you folks, but I'm the inventor of one of your most popular games, Scrabble'," Robert Butts recalls, "'and I have a new game I'd like to show you.'" Selchow & Righter wasn't going to pass up a public-relations opportunity like that, so a deal was struck: the game would be marketed, and in return Butts would make some publicity appearances on behalf of Scrabble. Butts's new invention, a solitaire word puzzle inadvisably marketed as Alfred's Other Game, wasn't much of a hit. But the appearance of Scrabble's inventor at Scrabble competitions certainly was.

"I'm a terrible speller," Butts confessed to John Williams, director of the US National Scrabble Association, at one such contest. Butts was a genial man, Williams later recalled, but somewhat baffled by the seriousness with which the players took his parlour game. He carried with him an ordinary plastic shopping bag in which was one of the first hand-rendered prototype Scrabble boards. "Shouldn't this be in the Smithsonian or something?" Williams asked Butts. Butts seemed surprised. "You really think so?"

The PR people flew Butts on a Learjet to Vermont, to watch Scrabble tiles being made, and to Long Island, where the boards were manufactured. There, he saw four machines churning out Trivial Pursuit boards, but only one making Scrabble. "Trivial Pursuit is a fad," the company president reassured him. "When Trivial Pursuit is long gone, we'll still be turning out Scrabble."

Alfred Butts died in 1993, aged 93. Twelve years later, two brothers from Kolkata, Jayant and Ragat Agarwalla, launched Scrabulous online. It's hard to imagine Scrabble's modest inventor minding all that much. The same can't be said of Mattel and Hasbro, who earlier this year caused uproar among Scrabulous users by demanding that Facebook remove the game from its site. (The request has so far been ignored. Mattel declined to comment; Jayant Agarwalla did not respond to messages.) It seems inconceivable that the games companies would want to alienate such a vast number of Scrabble enthusiasts - some of whom have doubtless bought physical sets as a result of playing Scrabulous - so the logical solution would be for a deal to be reached.

In his final years, Butts was confined to a nursing home in upstate New York; a serious injury in a car accident in 1987 hastened his decline. Robert Butts became closely involved in his great-uncle's care, visiting weekly and making sure the bills got paid. "He was in the nursing home for the longest time before we even thought of playing Scrabble with him," Robert remembers. "He was becoming senile, and there was this creeping dementia, and we sort of assumed he couldn't play. But one day I brought in a Scrabble set. 'Let's play, Alfred!' He says, 'OK.' But his hands are shaking; he'd try to pick up a tile from the rack and knock the rack over. So next time I brought some window caulk - like putty - and stuck the rack on the table. That more or less worked.

"He had good days and he had bad days. Sometimes I'd come in and he wouldn't remember my name, but he could play. Some days, he'd lay down gibberish - a bunch of letters that wouldn't make a word at all. I'd say, 'Sorry, Alfred: I don't think that's a word. You can't play that.' And then there were other days. One day, I remember, he played the words 'ox' and 'xi', with the x on a triple-word score. People hang on to what's closest to them the longest. Alfred hung on to Scrabble pretty much up to the end."

"Ox" and "xi", with the x on a triple-word score: 54 points. It's not oxyphenbutazone, but it's pretty damned good.