Those who play the game liken it to chess, Monopoly, a jigsaw puzzle and musical chairs - except that this game uproots thousands of real people and moves them across a vast landscape using millions of real dollars.

It is the federal office shuffle, in which government officials and agencies compete for office space to keep up with the kaleidoscopic patterns of political and economic pressures, expanding and shrinking programs and bureaucracies aborning.

Congress is scheduled to take a turn in the game this week, by authorizing the new Department of Energy to spend $17 million on a controversial transfer of 10,000 employees into or out of the Forrestal Building, at 10th Street and Independence Avenue SW, astride the entrance of L'Enfant Plaza.

President Carter ordered the reshuffling - an unusually complicated one - last summer to provide a headquarters for his new energy department, which combines agencies currently scattered in 20 different locations around Washington. The almost 5,000 Defense department employees who currently work at Forrestal are to be moved out to various other locations. Some are swapping buildings with Energy workers.

The Forrestal building is in a prime location between the Capitol and the White House, overlooking the Mall and the museums of the Smithsonian, near downtown shops and restaurants - "high-visibility" showcase for a new agency, said one official. Known to some as the "Little Pentagon," because it was built for the Defense department, the Forrestal Building is about seven years old.

The President's order brought onto the big game board various comittees and task forces from the departments of Defense (and the individual services), Energy, and the General Services Administration - GSA is the federal landlord - to wrangle over a jumble of interdependent financial and logistical questions.

According to John Galuardi of GSA, "The thing that's really bad about (this move) is that it's more piece-meal, like a jigsaw with a lot of pieces . . . With other moves in the past, there was always something you could see on the horizon that solved the problem."

A veteran of almost 20 years at GSA, Galuardi is administrator of the office in charge of the Forrestal move.

The planners have proposed sending Defense employees to five or six different sites in Washington, Maryland or Virginia and reportedly are considering other locations from Pennsylvania and Alabama to California.

Most of 1,200 of the workers are expected to get shuffled off to the unpopular but available offices at Buzzard Point in Southwest Washington - a site that employees of several other agencies have fought to avoid because of its isolation and industrial surroundings.

The planners figure that just moving the telephones and switchboards alone will cost $900,000 - or $90 per telephone. The Defense phone system is different from that to be used by Energy, officials explained, so they have to be changed. The bulk of the $17 million is for remodeling.

The planners still are trying to decide whether to move out a specially designedcomputerfacility built into the lower level of Forrestal. (Among other things the computers make out pay checks for about 24,000 civilian employees in the area.) GSA estimates that moving the computers could cost $4.5 million - and that would be in addition to the $17 million estimate.

Some critics of the move, in Congress as well as in the Defense Department, believe Energy Secretary James Schlesinger has understated the cost of the move and probably will have to come back for more money. (GSA had estimated the cost at $22 million.) They grumble that Schlesinger and the Carter administration are trying to push the relocation through too fast, with inadequate study of costs and alternatives.

Carter's original June 3 memo had asked that all 5,000 Defense employees be moved out by last Oct. 1. GSA's current timetable has the last Defense employee out by late 1979 and the Energy department all moved in by spring of 1980.

Employees at Forrestal have complained bitterly about the administration's handling of the matter. Though they are used to being moved around by their Defense department bosses, they say, in this case the government has created unnecessary anxieties about their having to uproot their families without proper warning, and turned on a drizzle of rumors about where they will be sent.

According to Forrestal worker Hannah Zeidlik, one small agency at Forrestal has heard 50 different rumors about where it will be moved, ranging "from a few blocks from its present location to areas nearly 1,000 miles from Washington."

Schlesinger's side maintains that the move is the only practical solution to the problem. The energy secretary told a House appropriations committee that the cost of building a new building would "probably be $200 million."

As it is, Forrestal will house only about 60 per cent of Energy's 8,000 Washington-area employees. Having even this many of them together, Schlesinger argued, would provide "the quick rapid coordination of the sort that we were keenly aware last winter that we lacked."

The way the department is spread out now, said Energy staffer Frank Pagnotta, "it's like having your kitchen in somebody else's house. It's hard to cook a meal."

The Energy department is not the only one with that problem. The government tries to group its offices according to their mission, Galuardi said.Treasury has been pulled together in the last few years, for instance, and Labor moved into a new $93 million building three years ago.

"But there are still a lot of activities not totally consolidated . . ." Farflung elements of the Commerce department, as well as the National Science Foundation ad the Federal Trade Commission are among those he said are pusing for more togetherness.

In such territorial competition, clout with the White House has often determined who wins the new building or the hardiest location. "A recently-formed agency in which there is intense (White House) interest gets fairly high priority," Galuardi said. "It happened in other administrations with the Departmetn of Transportation, with Housing and Urban Development. Now energy is important to this administration."

Still, he added, it's not like the old days "when the President could just say 'do this' and everybody got up and changed seats."

Schlesinger had hoped to get on with the move without going through Congressional hearings, since he was "reprogramming" the $17 million from money he already had in various programs, according to Congressional aides, and not requesting new funds. But , explained one, "we felt that because of the magnitude of the dollars involved, they should come on in and have a hearing on this."

Energy officials had also hoped to hang onto the spiffy building at 20 Massachusetts Ave. which was custom built just a couple of years ago, which color-coordinated wallpaper and drapes, for the Energy Research and Development Agency (ERDA), according to insiders. But the House committee maneuvered back scenes to acquire that building for the Army Corps of Engineers, the largest single agency now occupying Forrestal (over 1,200 people).

"The Corps carries a lot of weight, and somebody had to look out for them," said a Congressional aide. "That was part of the deal that was cut."

Schlesinger also gave the committee assurances that, contrary to persistent rumors, he does not intend to build himself a lavish executive suite in the Forrestal, with a bedroom, dining room and kitchen. He said, "I am perfectly happy to inherit what is (at Forrestal)" and added that any improvements made to the building would be "conservative."

Meanwhile, for many of the Defense employees at Forrestal, the hardest part of the government shuffle game seems to be the waiting on the sidelines.

"We're 'good soldiers,' and we'll go where we're told," said an Army manager. "The worst part is just not knowing . . ."