The latest line among politicians here is that when all the dust is settled Democrat Adlai E. Stevenson III will win the closest and most confused governor's race in Illinois history -- by one vote.

The margin will be 4 to 3. That is the edge Democrats hold over Republicans on the state's not-always-above-politics supreme court, where many believe the election ultimately will be decided.

That verdict is still half facetious and probably premature, but the election's aftermath saw precious little in the way of progress toward settling the matter between Stevenson and the man he may be on the verge of upsetting, two-term incumbent Gov. James R. Thompson.

It was instead a day for both sides to claim victory, and for the election numbers to keep changing.

At Stevenson headquarters here, they were answering the telephone "Governor-elect Stevenson" all day and projecting an ultimate winning margin of 3,000 to 5,000 votes.

But Thompson, in an unscheduled meeting with reporters at The Chicago Sun-Times building, countered that "I expect I will have won when all the votes are counted."

The governor had not stopped by the newspaper office intending to gossip with reporters. What he wanted was a ward-by-ward breakdown of the vote totals in the latest edition of the paper. When he got what he was looking for, he began poring over the paper with the determined gaze of an auditor.

At one point today, Thompson was being credited in some tabulations with having a lead of 171 votes out of more than 3.5 million cast. For budding mathameticians, that works out to a margin of five-thousandths of 1 percent.

That count did not include returns from 121 Cook County precincts -- 15 from the city, where ballot boxes that were supposed to have been delivered to the Board of Election Tuesday night did not straggle in until late today, and 106 suburban precincts, where the count was delayed by soggy ballots.

The "wet vote," as it has come to be known here, struck both Cook and neighboring Du Page counties, which were hit by two days of heavy rain and 100 percent humidity on Monday and Tuesday. The moisture had made the computer punch cards limp, and limp cards, election officials discovered to their chagrin, do not go through the scanning machines kept at each precinct to tally the votes.

Some resourceful precinct election judges had solved the problem Tuesday night by baking the vote, literally placing cards in an oven to dry them out. Others ran them under lights; still others found that a few hours without rain took care of the problem by itself.

But that was not the only problem. In the city, with its rich tradition of graveyard voting, there were 15 unaccounted-for ballot boxes Tuesday night from black precincts. City election officials insisted there was nothing unusual about this, that out of 2,910 precincts in the city there are always a handful of election judges who neglect to send their tally sheets and raw votes to the board on election night. They were being rounded up and tallied today.

But the problem may not even end with wet ballots and stray boxes. Thompson's press secretary, David Gilbert, today alleged "irregularities" in the Chicago vote totals and said that at least 11 ballot boxes had improper seals. He said a team of 25 lawyers and 30 volunteers was running down tips of vote tampering and illegal voter assistance throughout Chicago.

Thompson lost the city by an enormous 462,000 vote plurality, a much higher figure than had been expected. Democrats said there was nothing unusual about the turnout or 3-to-1 edge that city voters gave to Stevenson. It was the same strong response to Reaganomics that registered in large cities all over the country.

The governor's people were less sure, and so were independent election watchdogs.

"We feel that in the city of Chicago on Tuesday, there was probably massive illegal voter assistance," said Kristen L. Svare, director of Project LEAP, an election watchdog group. "We have reports from all over the city of election board judges telling voters to 'punch 10,' " -- the code word for voting a straight Democratic ticket. "It goes on every election day here."

Chicago, the city the pols love to say is "not ready for reform," has a long history of voter fraud. The most storied incident was in the 1960 presidential race, when legend has it that Mayor Richard J. Daley held back vote tallies in key machine-controlled precincts until he knew how much of a margin John F. Kennedy needed to offset the small plurality that Richard M. Nixon had built downstate. Once Daley knew what was needed, so the story goes, the votes appeared.

Svare said the most blatant voter fraud was cleaned up a decade ago, thanks to an investigation and a broad set of prosecutions spearheaded by a rising young U.S. attorney. His name: Jim Thompson.

Whether the allegations of fraud this time around can be proved is another matter, and it may take months. In Illinois, election returns are certified by the state on Nov. 22. After that, a candidate in a close race has the right to call for a recount, and failing to get satisfaction there, he or she can legally contest the election if a specific showing of fraud can be made. The challenge would be heard by the state Supreme Court.