Plenty of bettors spend sad Sunday afternoons grumbling that they could have done better in the office football pool if only they had bet * against * every team they had carefully decided to bet * on* .

It turns out they were right, and mathematics can prove it.

Professors at UC San Diego and Dartmouth College write in the current American Mathematical Monthly that punters who put money on both sides in a football pool--that is, bet on one set of teams while betting an equal amount on each team's opponent--have winning odds in their favor.

Mathematicians who calculated the odds call the approach the "evil twin" strategy because it is based on a suspicion that no matter how well people research point spreads and matchups, an evil twin making the opposite bets would do as well--or better.

Strictly speaking, the mathematicians--Peter Doyle of UC San Diego and Joseph DeStefano and J. Laurie Snell of Dartmouth College--suggest that the best strategy is not to bet * like * an evil twin, but to bet * with * one.

Snell and his colleagues said their system works best in football pools involving friendly, unsophisticated bettors. They introduce the system to students--and encourage them to find ways to defeat it--as a way to introduce them to the concept of probability.

The evil twin was born last fall when some professors and graduate students met at Emmy's, the Dartmouth mathematics department's informal lunchroom "tavern," to organize a football pool.

Pool bets, a common social activity in offices and saloons, are based on a list of football games. Each bettor usually bets a dollar, which is pooled with all other bets to provide prize money. Each bet allows bettors to pick a set of winners--one for each game. The person with the most correct predictions wins the pot; in the case of a tie, the pot is divided evenly.

Graduate student Joseph DeStefano wondered if the rules would let him make two bets--one the mirror image of the other--to see if he could better his chances of winning. The others agreed because it was as much a practical math experiment as an effort by DeStefano to change his luck.

At the heart of the evil twin betting strategy is the assumption that point spreads even out qualitative differences between teams.

"With the point spread, it's not unreasonable to assume the other people (in the pool) are guessing which teams will win," Snell said. "In that case, this gives you an advantage. It's not a large advantage, but enough to make it interesting."

Snell cautioned that this strategy is unlikely to work in sophisticated betting situations, such as the sports books at Nevada casinos, where managers continually recalculate the odds and point spreads to minimize the casino's risk.

In the simplest example of how the evil twin approach can be used in a simple pool bet, say that two people--let's call them Nancy and Tim--bet on a single game. Nancy employs the evil twin strategy, betting a buck on one team while letting a fictional evil twin bet another dollar on its opponents. Tim only puts a dollar on the team he thinks will win.

Regardless of the outcome, Nancy would see some return on her bets. If Tim's team wins, she would share the $3 pot with him; if Tim's team loses, she would get all $3.

Over time, Nancy's expected return on each $2 wager would be $2.25--or the average of $3 and $1.50. Tim, if he is a mediocre bettor who loses as often as he wins, can expect his return to average 75 cents per bet--when he's wrong he wins nothing and when he's right he gets $1.50.

Of course, no one in his or her right mind would bet against someone who took both sides in a single game. But multiple entries are common in pool bets.

As with any "sure thing," however, there is a caveat: Skill still plays a part.

In the example above, Tim would wipe out Nancy's advantage if he could pick winners two-thirds of the time. Conversely, Nancy would not need evil twin bets if she had winners more than 52% of the time; she would do better by simply betting normally.