A SCHOOLBOY ONCE wrote: "The trouble with Hamlet was that he was always letting his self-control get the better of him." Boris Pasternak did not disagree with that perceptive thought: "'Hamlet' has been called a tragedy of the will. This is correct."

This weekend two Washington "Hamlets" overlap. The Folger Theater Group is ending a six-week run of "Hamlet," and Arena Stage is in previews for a Wednesday opening of its version of William Shakespeare's play. Surely it is mark of this play's lasting fascination that in its 378th year no other local theater event his session can come up to the happenstance of a double "Hamlet." (Indeed, there was even a third version, a spoof by the New Playwrights' Theater, that just had a brief inning.)

The play and his characters are intriguing because the choices in bringing "Hamlet" to the stage are limitless. There can be so much of thing as the "definitive 'Hamlet'." In a score or so of "Hamlets" I've seen, and the scores I've read about, there has not been in all-out "best." Invariably, there have been particular qualities or attitudes to admire or despise in each.

To the "Hamlet" collector, nothing can approach the sense of anticipation one feels in setting out for a fresh production. It is like unwrapping, a gift. What will be the package contain? One never knows. As the ribbons and wrappings give way, one enjoys the sheer excitement of discovering what yet someone else perceives in the play.

Not that everyone loves "Hamlet." To Voltaire it seemed "like the production of a drunken savage." Critics denounce its infraction of the unities, it persistors have faulted construction, pilot and characters.

People get dismayed about seeing "another 'Hamlet'." Columnist Tom Donnelly used to groan at the announcement of any new production. "I can't see it again," he'd rage, while I argued that while he'd been fortunate enough to see it. Others had never yet had the opportunity. The Kennedy Center's Roger L. Stevens recently told me he never intended to see it again. My wife agreed. As an official guest of the West Germany government, she'd once spent a freezing Fourth of July seated next to the mayor of Hanover in an outdoor theater during an intermissionless production in a tongue she didn't understand. "I could not possibly leave, but I made up my mind: Never Again."

Because of Romanian director Liviu Clulei's superb production of "The Lower Depths" last season at Arena, I'm excited over what he will reveal in his version of "Hamlet" on the same stage. He has allowed that he has discovered that "Hamlet" is "a play about rooms . . . about rooms and closets and whispers."

Because Arena's seats are above the stage, we have been discovering the versatility of its stage floor. Instead of looking out, we watch from above. In this juxtaposition a whole range of fresh choice opens up. The stage design by Ming Cho Lee will be as important to Ciulei's "Hamlet" as Santo Loquasto's was to "The Lower Depths."

Jonathan Alper's Folger production also was governed by its physical features - a slightly thrust stage wrapped within only 210 seats - which automatically dictated his choices. The result was unlike any "Hamlet" I'd seen, so intimate that one thought of closet drama. But it was more than just a costumed reading, thanks to Michael Tolaydo's spirited fencing.

For all its philosophy, poetry and character shadings, the story line - will Hamlet avenge his father's murder? - remains the play's basic strength.

The first Hamlet was Richard Burbage, 85 at the time, and he was directed by author Shakespeare, who insisted on playing what he considered the vital, if small role of the Ghost.

Though short, Burbage is known to have been a very active Hamlet. As it often would be later, the initial performance was performed in the dress of the period. Beards were in style at the turn of the 17th century ("who call me villain . . . plucks of my beard?), and a surviving portrait of bearded Burbage can be seen at London's Dulwich College. When Tyrone Guthrie presented his modern dress "Hamlet" (Laetes wore a trenchcoat) in 1963, starring George Grizzard, he was only following Shakespeake's lead.

There's a direct line of descent from the author, because in his youth William Davenant, who later presented the play, had seen a Hamlet (Joseph Taylor) coached by Shakespeare. Pepys tells his diary of the Hamlet in Davenant's version: "Betterton did the part beyond imagination," and Colley Cibber described details of his performance as "a serious, penetrating aspect." As it would through time, the closet scene (Hamlet with his mother) inspired minute descriptions.

Dauntless David GarricK, who arrived in London at the age of 20 with his admiring schoolmaster, Samuel Johnson, took "an astonishing yet natural" approach to the role, which he acted for 34 years after his 1742 bow. Known for the fright he assumed at the appearance of the Ghost, Garrick also tinkered with the play, saving the lives of Ophelia, Laertes, Rosencrantz and Guildenstern.

Actors, directors and economics often have brought cuts to "Hamlet," lopping off Fortinbras (a Shavian sin!), Osric, Reynaldo, Voltamund, Rosencrantz and Guildenstern. Playwright Tom Stoppard, a Bristol drama critic a few years back, had the wit to avenge their frequent disappearances by writing a whole play "Rosencrantz and Guildenstern Are Dead."

By the 19th century's end, vocal recordings were possible. These wax cylinders captured only a wisp of styles. One is surprised by the high pitch of the celebrated Henry Irving's Richard III. On an 1890 cylinder Edwin Booth's 57-year-old voice shows a deeper pitch than Irving's though can one trust the rudimentary recording technique? Anyway, the late 19th century productions were long on scenery and production pomp - and visual spectacle.

Of the early recordings, the one which has satisfied me the most is John Barrymore's "O", What a Rouge and Peasant Slave," recorded in 1928, five years after his first stage Hamlet. His had a gloriously deep voice - before his collapse into self-caricature - and listening to it does conjure the production so admired by his comtemporaries. His accent was a desirable "mid-Atlantic" English. He relished the words and poetry but sharpened the word's meanings - and all with the most remarkable, sustained breath control. The Barrymore's Hamlet is legendary, including the assertion by his Player Queen, Olney's one-time manager, Richard Skinner, that during Barrymore's Hamlet at our National Theater, President Coolidge fell fast asleep.

Age hasn't mattered much when it comes to tackling the part. The youngest on record seems to be William Henry [TEXT ILLEGIBLE]"The Young [WORD ILLEGIBLE] ." Sarali Bernhardt was in her 50s when she first acted Hamlet, and Judith Anderson insisted on realizing her ambition to play him when she was 73. Max Beerbohm's description of Bernhardt's audience fitted my own for Dame Judith: "One laugh in that dangerous atmosphere and the whole structure of polite solemnity would have toppled down, burying beneath its ruins the national reputation for good manners."

John Gielgud was 26 for the first of his several Hamlets. His New York version in 1936, with Lillian Gish as his evanescent Ophelia, remained for years my "definitive" Hamlet, and when I last saw him play it 10 years later in the Cairo Opera House, before a mix of troops and Arabs, it remained compelling, especially his vocal beauty. Fortunately, Gielgud's Hamlet is preserved on several subsequent and differentl recordings.

The most adventurous Hamlet of this country surely has been Maurice Evans, whose full-length version, staged by Margaret Webster, was a New York revelation in 1938. Six years later as a U.S. Army major, Evans devised his shortened "GI Hamlet," which exposed the play to those who'd been afraid of it as high art.

Later Evans did it on national TV, and when I took a dim view of its cuts, my editor grumbled that I'd missed the thrill that on that evening more people had been exposed to the play than the total of all who previously had seen it.

There is the Catch-22 of all "Hamlets." Our perceptions need not necessarily mesh with the perpetrators or audiences. Nicol Williamson's mod peasant of a few years back displeased me almost as much as the self-indulgent one Jonathan Miller staged for Britain's Oxbridge a few winters ago at the Trapier at St. Albans School here. Nor was I amused by Joseph Papp's 90-minute public school version of '68, though Stoppard's Dogg's Troupe Hamlet, a sophisticated 15 minutes, is a hilarious summation. With Gielgud as director, Richard Burton's version as a dress rehearsal boasted Burton's melodic mystery, but in an erratic supporting cast there was only one mark of genius, Hume Cronyn's other-side-of-the-track Polonius.

My strangest "Hamlet" was at Denmark's actual Elsinor Castle. Originally mounted by the Barter Theater of Virginia with Cronyn in the title part, it was taken over by ANTA following a Danish government request for an American "Hamlet" at Elsinor. John Garfield got cold feet at the last minute and director Robert Breen bravely stepped in, but I had to agree with the Copenhagen critic who, probably from the red handkerchief Walter Abel sported as Claudius, got the image of Railroadin' in the Old American West.

A year later Scandinavia saw a Howard University production, applauding the young Earle Hymon and his student Ophelia, who grew up to become Patricia Robert Harris, now secretary of Housing and Urban Development.

The most commanding film version captured the sea atmosphere of Elsinor, directed by the U.S.S.R.'s Kozintsev, who used an old Baltic castle for his setting. For BBC-TV Christopher Plummer had the same advantage of sea spray and an uncommon king, Robert Shaw, who remains my most perfect, sensual choice for Claudius.

So go the Hamlet choices. Was he self-controlled or indecisive? Was he mad or too sane? Did he have a thing about his Mom? How much did Gertrude know and when did she know it? Why was Hamlet so beastly to Ophelia? Did student days at Wittenburg mean he was a philosopher? How did he suffer Rosencrantz and Guildenstern as friends? This time, while Claudius is at his prayers, will Hamlet kill the king?

You never know. You always think he just might. It's the greatest mystery play of them all.