The lottery jackpot could go as high as pounds 35m next week, Camelot admitted yesterday.
Last Saturday the pounds 8m jackpot rolled over because no one matched the six winning numbers. If the same happens this weekend the estimated pounds 20m jackpot will roll over again and could reach pounds 35m.
In the unlikely event of the jackpot going unclaimed a third time it could be rolled a final time to reach more than pounds 50m.
"We think it's going to be very exciting. A pounds 35m top prize would be the biggest ever offered in Britain," a spokeswoman said.
According to Richard Lloyd, a computer scientist at Liverpool University who has been studying the pattern of lottery wins, a double roll-over is overdue.
"A double roll-over should happen every 16 weeks so it's unusual that there hasn't been one already," he said yesterday.
"A single roll-over usually adds pounds 11m or pounds 12m to the jackpot of around pounds 8m because so many more tickets are bought. A double roll-over should add at least pounds 15m more, giving a minimum of pounds 35m to be won."
A treble roll-over should happen every 64 weeks or so, according to Mr Lloyd, so the odds are it will happen by the end of the year.
Last weekend Pam Hiatt, a pregnant student, won pounds 56m on the Idaho state lottery in the United States, which had rolled over seven times. However, that would be impossible in Britain because the jackpot can only roll over three times.
Even a double roll-over is certain to raise concern. Chris Smith, the shadow heritage minister, has said he would like a ceiling of pounds 5m on the jackpot. Camelot argues that sales fall when jackpots are lower, rising dramatically on roll-over weeks.