The open houses for the $1.895 million brick tudor were crowded, and for anyone competing in Chestnut Hill’s tight market, the scene was daunting. Expensively dressed couples were swarming, their inspectors in tow, their Teslas and BMWs parked outside.

It was oncologist Erik Knelson’s “dream house,’’ and he and his wife knew what needed to be done. They waived the inspection and mortgage contingency, he said, and agreed to the seller’s request to stay in the house for 2½ months after the closing — rent free.

And, in a brief but intense bidding session, they made the decision to go over the asking price — by hundreds of thousands of dollars.

“We thought it was a really nice offer,’’ Knelson said wistfully.

Alas, another offer — $805,000 over asking — was even nicer.

This is where we are right now in the Greater Boston housing market: In April, the median price for a single-family home in Greater Boston hit $845,000, an 11.2 percent rise compared with a year prior, according to the Greater Boston Association of Realtors.

On the one hand we’ve got people who are struggling to make rent on a place that’s safe and cheerful for their family, and close enough to work that they don’t need to spend hours commuting. Others are so flush that their “over asks’’ are more than the price of many entire homes.

In fact, so many homes are selling for not just over asking — but so ridiculously over asking (to use the industry term) — that sellers whose properties go for merely full price feel they’ve failed.

In Brookline, a woman whose home sold, in one weekend, for $1.029 million —its precise list price — felt shamed by a neighbor who sidled up to ask, “How much over-asking did you get?’’

“It’s like I’m a loser,’’ she said.

The over-asking statistics raise the real estate version of a philosophical question: If everything sells for over asking, what is asking? (More on this in a moment.)

In the first 4½ months of 2022, 71.2 percent of single-family homes in Greater Boston sold for over their list prices, according to figures compiled for The Boston Globe by the MLS Property Information Network Inc.

In comparison, over the same Jan. 1-May 15 period in 2017, only 38.4 percent of single-family houses in the area went above their list price, according to the organization.

How much over asking are we talking? On average, about 8 percent over asking price — or $80,000 on a $1 million property.

But some are going for so much more than asking price that they’ve become famous for it — gushed over in real estate circles and immortalized on social media.

“I’m rarely too stunned to speak,’’ Rachel Person, a real estate agent in Newburyport, says in a TikTok, “but this over list price in Wakefield has me questioning reality.’’

The Wakefield house, she sputters in theatrical disbelief, was listed for $1.99 million, “… wait … just wait for it, OK ... went for over $750,000 over asking. What? Like, what?’’

David Bates, a broker associate with William Raveis Real Estate in downtown Boston, took to YouTube in April to count down the top five “most wicked’’ recent over asks in Greater Boston.

The drama starts with a 10,600-square-foot Needham house that listed for $4.295 million and sold for $655,000 over that, and it builds to a 6-bedroom, 7½-bath estate in Newton that listed for $4.095 million and sold for $5 million.

“An almost unbelievable $905,000 over ask!’’ Bates says, as a photo of a luxury bathroom — cue the glossy, white free-standing tub — flashes on screen.

The obvious question about all of this — other than “what the heck is going on?’’ — is, well, actually that is the question. What the heck is going on?

For starters, inventory is low and buyer demand is high. As the Globe reported in May, the market is being lifted by an extremely tight supply. The number of single-family homes listed for sale so far this year is down 10 percent.

Interest rates have already started rising, and people are worried they will go even higher, which means waiting for a house on which there is not a bidding war might only make things worse. Better to pay an extra $100,000 now, the thinking goes, than to be locked into a mortgage with an even higher interest rate.

Many aspiring buyers are people who’ve been burned in previous bidding wars, and some have adopted a practical strategy: They’ve started looking at lower-priced homes specifically so they can afford to overbid, said Jared Wilk, vice president of the Greater Boston Association of Realtors, and principal of The Shulkin Wilk Group at Compass.

Asked how he advises buyers in this market — like, how do you figure out whether to bid $100,000 over asking or $400,000? — Wilk said he tells clients not to focus too much on the asking price since it doesn’t mean everything; some sellers are intentionally underpricing homes specifically to trigger bidding wars.

For that strategy, let’s meet Philip J. Vita, an agent with Compass in Winchester, who recently tweeted the following:

“The greatest gift we can give our sellers? Results like THIS! $321,000 OVER ASKING at this beautiful home situated on the Mt Hood Golf Course in #Melrose!’’

Reached by phone, Vita explained his strategy. “What I say to my sellers in this market is that you want to make the price ‘delicious’,’’ he said.

“That sounds crazy — it’s not food — but it is something that someone can’t resist. It’s too good to be true.’’

Asked if delicious, translated from realtor speak, means intentionally underpricing to hook people, and then hoping their emotions will take over in a bidding war, he responded in the affirmative: “If anything, yes,’’ he said.

“I also want to point out that another very major and important reason for imposing this strategy,’’ he explained in a follow-up e-mail, is to “get ‘cleaner’ offers. Meaning offers that don’t have home Inspection or financing contingencies.’’

Meanwhile, with a recent Money headline reporting “More than one third of people who bought homes during the pandemic say they overpaid,’’ perhaps the luckiest buyers are those like Knelson, whose whopper over-asking bids aren’t accepted.

“It would have been a stretch for us,’’ he said of his (unsuccessful) bid for the Chestnut Hill tudor. “Maybe it was a blessing.’’

Beth Teitell can be reached at beth.teitell@globe.com. Follow her on Twitter @bethteitell.