Now, Professor Etzioni, who teaches computer science at the University of Washington, has directed his considerable intellect at the American ritual of shopping for bargains on Black Friday. After examining billions of prices of consumer electronics, he has decided to spend the busiest shopping day of the year scuba-diving in Bali.

Why? It is not until early December, Professor Etzioni’s research shows, that prices are likely to be the lowest for electronics, products that are among the biggest sellers on the Friday after Thanksgiving.

“The bottom line is, Black Friday is for the retailers to go from the red into the black,” he said. “It’s not really for people to get great deals on the most popular products.”

What the professor has determined with a complex computer algorithm for consumer electronics, others have found through less scientifically rigorous means for other products, including clothing and toys: despite all the ads that suggest otherwise, the lowest prices tend to come at other times of the year.

In the case of toys, stores actually offer the steepest discounts in the weeks immediately following Thanksgiving because they want to unload the inventory not swept up on Black Friday, said Dan de Grandpre, who has tracked deals for 15 years at Dealnews.com.

“Toys have a very short shelf life,” he said.

“On Dec. 26, they’re not really useful to retailers anymore, so they have to get rid of it and start slashing prices early in December.”

And it is a precise window of opportunity. In the week or so before Christmas, toy prices shoot back up, Mr. de Grandpre’s tracking shows, as last-minute shoppers come stampeding for Barbies and Lego sets and stores are less desperate “because they’ve been able to reduce their inventory.”

The added value Professor Etzioni brings to price discussions is the computer crunching of the trove of data provided by online prices — and specific recommendations about when to make a purchase.

Following the approach of Farecast, now part of Microsoft’s Bing search engine, the professor’s start-up company, Decide.com, studies current and historical prices, information about new models and rumors about new product introductions to figure out the best time to buy.

Type in the name of a product — a Soundcast SurroundCast speaker system, for instance. Decide.com will pull prices from around the Web, and tell you to buy or wait. In the SurroundCast case, it showed this week that prices were at $150 in early September and had now gone up to $160.

The verdict: wait. Decide.com said it was 96 percent confident that prices for the speaker system would drop within two weeks.

Introduced this summer, the Web site predicts prices for consumer electronics only, though Professor Etzioni says there are plans to expand to categories like cars and potentially even clothing in a couple of years. In the meantime, others are making educated guesses about when it is best to spend money on variety of products.

James C. Bieri, who heads a Detroit-based real estate firm that leases to retailers, has determined there are far better times than the Friday after Thanksgiving to make most apparel purchases. Many stores offer steep discounts on products other than clothing, he said, to get shoppers into their stores.

“They’re going to use apparel to get some of the margins back on the stuff they’re giving away,” he said. Better times to make apparel purchases include back-to-school and post-holiday clearance sales, and it is an area where coupons, friends-and-family discounts and the like are big money-savers.

Assuming fruitcake and candy canes still sound good after the holidays, sales of gourmet food and candy should be postponed until then, advised Brad Wilson, of BradsDeals.com, because prices drop drastically.

As for appliances, major retailers like Sears tend to discount those at the end of their fiscal quarters (Sears’s next quarter ends Jan. 31.) But Mr. de Grandpre said that this year, the deals in the weeks before Thanksgiving had been as good as he could remember, especially from retailers like Lowe’s and Home Depot, and brands like LG and Samsung.

Retailers do discount smaller appliances on the Friday after Thanksgiving. “You’ll see small kitchen electronics under $20, sometimes under $10 — blenders, toasters,” he said. “But it’s low-end, cheap Chinese knockoffs that are heavily discounted — often there’s a mail-in rebate hassle that goes with it — but it’s a very, very low price.”

That is true of most of the biggest deals on that Friday, he said. Because retailers want to impress shoppers with very low prices, the quality of the discounted items can be low.

For higher-end electronics, Mr. de Grandpre’s trends show, shoppers should wait until the week after Thanksgiving.

“Black Friday is about cheap stuff at cheap prices, and I mean cheap in every connotation of the word,” Mr. de Grandpre said. Manufacturers like Dell or HP will allow their cheap laptops to be discounted via retailers on that Friday, but they will reserve markdowns through their own sites for later.

“Their best promotions happen during Cyber Monday week,” he said, referring to the marketing name drummed up by online retailers for the Monday after Thanksgiving.

Did Decide.com agree with the laptop advice?

It did. A low-end Dell laptop had dropped to $249 at Amazon this week, and Decide said to buy it now. But for a more feature-heavy laptop, priced at $1,528 at Sears and $1,541 at PCNation, Decide said to wait, as it expected prices to stay flat or decline by up to $339 within two weeks.

On Friday, “there will be big sales, but are they big sale on the items you want?” Professor Etzioni said, over his remarkably clear cellphone connection from Bali. “Look at all the amazing volatility, and wait for the price drops.”

If some consumers insist on shopping on Friday, Professor Etzioni and Mr. de Grandpre have some suggestions. Movies, music and books are among the few categories that reach their lowest prices starting the week of Thanksgiving, Mr. de Grandpre said. And for online shoppers, the professor’s Decide.com could spot a good deal in a holiday special of smartphones for 1 cent from Amazon.

“Buy,” the Web site advised, “before prices rise.”

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