It began as a simple dancing competition, with seemingly simple rules. The celebrities danced, the judges judged, and the public voted. The bad dancers were voted off, the good ones remained, and at the end of it all, someone went home with the Strictly Come Dancing trophy.

But it was not to be. After three months of a competition that has been as packed with cockups as it has been with cha-cha-chas, the BBC revealed last night the voting mechanism by which the winner of tonight’s Strictly final will be crowned.

Those who have struggled through descriptions of the Federal Reserve’s economic policy on quantitative easing, or balked at the integrity of the Zimbabwean presidential elections, are sure to despair. Tonight’s winner will be decided by the combination of seven separate calculations.

The BBC was forced to discount the results of the public vote on the show’s semi-final last week after it became clear that a quirk of mathematics meant that Tom Chambers, the Holby City actor, could not be saved from the dance-off, where the two lowest-placed contestants get a last chance to progress.

The corporation put all three dancers into the final and promised that those public votes would be rolled over into tonight’s show. After nearly 2,000 public complaints, it also offered refunds to those who had called the premium rate numbers to vote for any contestant.

Encouraging viewers to call a premium-rate number to prevent Chambers entering the dance-off, when he could not do so, would have breached broadcasting regulations. The BBC, which was fined £95,000 on Thursday for faking phone-in competitions, could not run that risk.

After spending a week locked in talks with an independent adjudicator, yesterday evening the BBC announced the method by which the public will decide who – from Chambers, Lisa Snowdon, and Rachel Stevens – will be the new Strictly champion. It is not for the fainthearted. Those who were promised this week that their votes from last weekend would count towards the final may well be disappointed. The methods the BBC have come up with will mean that each vote from last week will count for only a third of a vote of those who ring in tonight.

The dancers in tonight’s first show, at 6.40pm, will be marked by the judges, whose points will be totted up with last week’s judges’ vote and last week’s public vote.

That score will then be scaled down to represent half of the decision as to who will be the first of the three celebrities to be kicked out tonight, with a fresh public vote representing the other half.

In the second show of the evening, at 9pm, the remaining two couples will dance for the final time, before the public choose between them in a straight fight for the most votes. The BBC said that the method had been independently adjudicated and represented the best available solution.

This series of Strictly has already been filled with controversy. John Sergeant, the former political journalist, quit the show last month after the audience continually voted for him to progress, despite his obvious lack of dancing skills.

The economy may be in meltdown, the City in a spin and the pound in a decline matched only by the growing length of the dole queues, but Her Majesty’s Secretary of State for Business has found time to attend the final. Lord Mandelson, who has long been a fan of the show, has accepted an invitation to watch the dance-off.

The twinkle-toed minister has made it known that he would love to appear on the programme, and is quoted at odds of 7/4 to star in the next series. “It would be nice to be asked,” he told a breakfast television show last month.

The corporation said that Lord Mandelson would remain firmly in his seat, but his private office was more evasive. “Will he be dancing on Saturday night?” said a spokesman. “You’ll have to wait and see.”

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