When Lew Beyer ran a little roadhouse out in Manley Hot Springs, far into the frozen Alaskan bush, he left a pad and pencil on the bar so customers could figure their own bills.

More often than not, they cheerfully overcharged themselves. "People are incredible when you treat them that way," he said.

Today Beyer, somewhat against his better judgment, is in Fairbanks, serving a spell as state treasurer of a political party that wants to turn the whole government into a pad-and-pencil operation. Beyer is a Libertarian, and only a decade after his party's birth in the United States the Alaskan branch has become its most shining success.

In the 1980 presidential election, Libertarian presidental candidate Ed Clark captured 12 percent of the vote in Alaska, the party's best state by far. Here in Fairbanks, the last jumping-off point to the frontier, Clark won 19 percent and the Libertarians elected two representatives to the legislature.

Now one of those representatives, insurance agent Dick Randolph, 45, is barnstorming the lower 48 states to raise money for a full-fledged campaign for governor in 1982.

He and his fellow Libertarians, accustomed to the fringes of political power, are looking back in happy astonishment at a successful fight to abolish the state income tax and ahead to powerful new assignments in the legislature brought on by a political coup organized by several conservative lawmakers.

Their ongoing battle against federal and state land-use restrictions, although not nearly as successful, has brought thousands of new supporters for the party in a state full of frontier-lovers who bridle at government interference.

"You get a lot of independent types who come up here to escape one thing or another," said Alaska Gov. Jay Hammond, a Republican who reluctantly bowed to Libertarian-led pressure for an end to the state income tax.

Lt. Gov. Terry Miller, a Republican who hopes to succeed Hammond, said, "One could say the Libertarian Party is the best organized party in Alaska." He called Randolph "a fine man," and said the party deserves its own line on the state ballot, although Miller added that voters may not yet have considered the "natural consequences" of some Libertarian stands on the issues.

The Libertarians say they support the greatest possible personal freedom and the least possible government. This sends the party platform leaping back and forth between the usual divisions of liberal and conservative, opposing laws that restrict abortions or drug use but also opposing gun control and income taxes.

Like the customers in Beyer's roadhouse, Libertarians would prefer to decide for themselves what services they pay for. They favor helping the poor with charity, not welfare, and support voucher systems that would let people decide where to send their children to school.

The party has found fertile soil in the Alaskan wilderness. Of more than 260,000 Alaskan voters, 54 percent are registered nonpartisan, against 26 percent Democratic and 17 percent Republican. (Nonpartisans may vote in any primary they choose).

About 57 percent of the population lives in rural communities, where a passion for hunting and fishing and prospecting have produced intense resentment of federal and state efforts to regulate the last great American wilderness.

If a thread unites the rugged individuals who serve, often reluctantly, as Libertarian leaders, it is a tie to that wilderness. Beyer, 49, sold his Fairbanks business in 1964 and retreated for a decade to a log cabin in Manley Hot Springs.

"I gave up, said the world could not be saved and got out of there," he said.

Ken Fanning, 33, who followed Randolph to become the party's second state house representative last year, is a professional trapper and wilderness guide who gained a measure of recognition for lobbying in Washington against the Carter administration's Alaska Land Act of 1980.

The law restricts development and private use of 159 million acres of Alaskan territory, and led to a surge of new support for the Libertarians. Susan Bickman, 30, the state party chairman, joined the party about the time it appeared the lands bill would make it impossible for her and her husband, Jim, to work a gold claim they had developed in the Nutzotin mountains.

It is hard for an urban resident of the lower 48, accustomed to general support for the "war against pollution," to appreciate the resentment many Alaskans feel at the government's attempts to tell them what they cannot do with their wilderness.

"I think the lands issue really brought a lot of people to the party," Bickman said.

Fanning, a tall man with beard and glasses, is spending the winter working toward a long-delayed bachelor's degree at the University of Alaska, but he warns the party against entangling itself in long philosophical debates over difficult issues such as whether supporting abortion fits the Libertarian principle.

In the capital, Juneau, during his first session, Fanning grew so impatient with the political maneuvering and speechmaking that he announced that nothing of importance was getting done and he that would donate his per-diem for the last two months of the session to charity.

"To the extent that we keep offering a philosophical diversion for Ph.Ds and intellectuals, we're in trouble," Fanning said. The party's followers "see individualism in a very specific way, cutting wood tonight as opposed to waiting a week to cut wood" because of some government regulation.

Randolph's growing reputation as a legislator has also attracted many votes for the Libertarians. He forced a removal of the state income tax by organizing a petition drive that would have put the idea on the ballot. State legislators, determined not to pass up a chance to take credit for such a cut, then put aside their previous reluctance and passed it.

Randolph was elected narrowly as a Libertarian in 1978, but he was Fairbanks' top legislative vote-getter in 1980. He had served two terms earlier as a Republican, but resigned in disgust after he found a Republican-controlled legislature spending even more money than the liberal Democrats had.

In his gubernatorial campaign, Randolph said in a telephone interview from Milwaukee, he will concentrate on the lands issue, particularly "ways of divesting the state of the major part of its land resources and conveying them to the individual people."

Although Beyer says "there is no reason why we can't have five or six legislators and a governor" elected in 1982, he acknowledges that the party has a few weaknesses in the political game.

One of them is its propensity for long discussions, and another is its aversity to the kind of relentless organization that powers political campaigns.

Libertarians dislike organizations of any kind, even their own party. Bickman, who runs a bookkeeping service in Anchorage, was elected chairman within a year of joining the party, so desperate were the Libertarians for someone willing to act as an organizer.

It is uncertain how long the party can keep free spirits like Fanning, who, Beyer said, "would rather be out chasing a moose any day, the whole thing is torture to him."

"Unfortunately," Beyer said, "it's a party loaded with contemplative people. Libertarians sit around for years trying to decide if they are one."