The House and Senate Armed Services committees, locked in a political numbers game that could shape the future of the nation's military, this week will attempt to unsnarl the biggest defense tangle since President Reagan began his trillion-dollar rearmament program.

Both chambers are struggling with major defense policy decisions against a backdrop of demands for reduced deficits, sharp assaults on the president's prized strategic weapons program and complex budget juggling that even most legislators cannot follow.

Teetering in the balance are dozens of other issues, including pay raises for military personnel, major purchases of ships and aircraft and development of numerous advanced technology weapons programs.

And overshadowing the controversy is the question of whether the Republican-controlled Senate, bogged down in many other debates, will have time to pass its defense spending bill before the year is out.

The defense fight is so tangled that no one is willing to predict how it will be resolved. "Anybody who tells you they know what's going to happen, doesn't know what they're talking about," one congressional staffer said.

"All of the differences have to be reconciled somehow," said Gordon Adams, director of the Defense Budget Project for the think-tank Center on Budget and Policy Priorities. He also noted, "But what I say today might be wrong tomorrow."

Most of the debate is set against the framework of a political numbers game.

Reagan asked Congress for $320 billion in defense spending authority for fiscal year 1987. The House Armed Services Committee has said it will give the president $285 billion while the Senate panel voted $301 billion.

Since the committees voted, Congress has imposed a $292 billion ceiling on defense spending authority. In past years, the major debate would have revolved around the Senate panel's efforts to shave its bill to meet the congressional cap.

This year, however, in the face of the Gramm-Rudman-Hollings balanced-budget act, the debate has one more wrinkle: another set of numbers the panel must reconcile. Those numbers involve budget outlays, which is the amount of money the Pentagon will spend in the next fiscal year.

Budget authority, or the amount the administration has permission to spend, is a policy number that indicates how much the defense program can grow. The out-year figure is an economic number that bears on the deficit. The amount actually spent is invariably lower than the full amount authorized because many programs are approved in one year's budget and are paid for over a series of years.

Both committees now must place greater emphasis on how much they want the Pentagon to spend in 1987. That is expected to be the focus of debate when the Senate panel meets Tuesday and the House committee meets Wednesday to try to finish their bills.

Committee budget analysts say they are so preoccupied with resolving those conflicts in their bills that they have yet to begin counterattacking legislation in the other chamber.

"We're not worried about the Senate," one House source said. "We're worried about ourselves."

The task facing the two panels is colored by years of huge increases in defense budgets. The demand for greater austerity in defense spending is prompting debates about weapons systems and uses of military technology that will be argued in coming years.

One of the bitterest fights surrounds the president's most-cherished military program, the Strategic Defense Initiative (SDI) program, the space-based missile defense system. The Senate cut $1.4 billion of the $5.4 billion requested by the White House, while the House reduced the funding by $1.7 billion.

The accounting tangle will play a major role in the many differences between the two panels if the bills reach a conference committee. Currently, the Senate bill is more weighted toward hardware buildups and future research and development, while the House makes major cuts in both areas.

The Senate panel has voted to give military personnel a 4 percent pay raise; the House has decided against pay increases. The Senate committee tentatively approved the administration request for a Trident submarine; the House refused.

The Senate provided the $1.42 billion requested for 21 new MX missiles; the House stripped $300 million and nine missiles from the request. The Senate approved the full request of 260 AMRAAM air-to-air missiles; the House cut the request to 135 missiles. The Senate, however, cut the proposed Midgetman missile program in half, while the House granted the full $1.4 billion requested for the small, single-warhead ICBM.

The Senate approved funding for the controversial ASAT antisatellite weapon, while the House cut the $278 million proposal for research in half and eliminated $28.5 billion to begin procurement.

The House slashed almost one-fourth of the Navy's budget for shipbuilding; the Senate left the program intact. The House cut procurement funds by 17 percent -- $14.7 billon -- while the Senate trimmed only small amounts off the $84.7 billion procurement request.

The House slashed $7.9 billion from the administration's $41.9 billion request for research, development and testing programs. The Senate, which uses a different budget format that cannot be compared precisely on this issue, cut about $2.1 billion.