The Parliament building here has been reduced to rubble. The five-story engineering department of the Islamic University is a pile of folded concrete. Police stations, mosques and hundreds of homes have been blown away.

But now that the battle is over — or has paused, after Hamas agreed Sunday to a one-week cease-fire with Israel — what has been accomplished is unclear. Have three weeks of overpowering war by Israel here weakened Hamas as Israel had hoped, or simply caused acute human suffering? Israel knew it could not destroy every rocket or kill every Hamas militant. Israel said its central aim was deterrence, to make Hamas lose the will to keep shooting at Israel’s cities. Did it succeed?

Israeli officials themselves said Sunday in briefings to the cabinet that even though Hamas institutions had been badly damaged, its militants might well keep shooting rockets just to prove otherwise. The chief of military intelligence, Amos Yadlin, asserted that even Hamas had to figure out how badly it had been harmed.

What is clear is that, despite vague Israeli hopes that Hamas could be completely removed, that has not happened. Much of the group’s manpower remains, mostly because it made a point of fighting at a distance — or not at all — whenever possible despite the fury of the Israeli advance and bombardment.

The caution is at least in part because Hamas wants to keep ruling in Gaza, not return to its previous role as a pure resistance movement. Therefore, Israeli officials say, an offensive that caused average people to suffer put pressure on Hamas in real and specific ways.

“Hamas is the dominant organization in Gaza,” a top military official said in a briefing last week that was given on condition of anonymity. “They are the regime and feel very connected to the people. They do not want to lose that connection to the people.”

The Israeli theory of what it tried to do here is summed up in a Hebrew phrase heard across Israel and throughout the military in the past weeks: “baal habayit hishtageya,” or “the boss has lost it.” It evokes the image of a madman who cannot be controlled.

“This phrase means that if our civilians are attacked by you, we are not going to respond in proportion but will use all means we have to cause you such damage that you will think twice in the future,” said Giora Eiland, a former national security adviser.

It is a calculated rage. The phrase comes from business and refers to a decision by a shop owner to cut prices so drastically that he appears crazy to the consumer even though he knows he has actually made a shrewd business decision.

The Palestinians in Gaza got the message on the first day when Israeli warplanes struck numerous targets simultaneously in the middle of a Saturday morning. Some 200 were killed instantly, shocking Hamas and indeed all of Gaza, especially because Israel’s antirocket attacks in previous years had been more measured.

When Hamas’s prime minister, Ismail Haniya, appeared on Hamas television from his hiding spot last Monday, he picked up on the Israeli archetype, referring in Arabic to the battle under way as “el harb el majnouna,” the mad or crazy war.

For most, of course, feeling abused like this has created deep rage at Israel.

“If you want to make peace with the Palestinians, they are tired of bombs, drones and planes,” said Mohammad Abu Muhaisin, a 35-year-old resident of the southern city of Rafah who is affiliated with Fatah, the rival to Hamas that rules in the West Bank and was ejected from Gaza in June 2007. “But a guy whose child has just been killed doesn’t want peace. He wants war.”

There are, however, limited indications that the people of Gaza felt such pain from this war that they will seek to rein in Hamas.

Halima Dardouna, 37, from the northern city of Jabaliya, whose house was destroyed by an Israeli shell, said both Fatah and Hamas were to blame because of their rivalry, “and we are the victims.”

She added, “I will never vote for Hamas. They are not able to protect the people, and if they are going to bring this on us, why should they be in power? If I thought they could liberate Jerusalem, I would be patient. But instead they bring this.”

For Israel, Hamas’s rule here is anathema. But the fact that the group controls all facets of Gazan society gave Israel a rationale for attacking a wide range of institutions.

As an example, Mr. Eiland, the former national security adviser, noted that Israel “can destroy the infrastructure of the regime, and that is much more painful than only hitting military targets.”

“The regime will be under pressure to stop the violence and will be careful not to repeat this experience again,” he said. “Due to the terrible devastation on the ground, there will be a lot of political pressure.”

Israel is counting on the idea that with the heavy damage to smuggler tunnels from Egypt and a mix of technology and policy to prevent further smuggling, Hamas will not again become the scourge it has been recently.

Still, the actual damage to Hamas appears to have been limited partly because it acted so cautiously. There is irony in this, that Israel, the state with the well-trained army, wildly pressed the attack, while Hamas, the Islamist militia that supposedly embraces death, shied from the fight.

The group was by all accounts able to preserve a substantial portion of its force. Hundreds of Hamas fighters were reported killed, but general estimates put the entire force well into the thousands. Israeli military officials said they saw very few fighters on the battlefield. They came out mostly in ones and twos and only a few attempted suicide bombings.

Those who know Hamas in Gaza say this was carefully calculated.

“In previous times, the fighters would confront and throw themselves at Israeli attacks,” said one man close to Hamas who declined to be identified further. “It was a kind of suicide. It was love of martyrdom. You go and confront the tanks and many were killed, 80 in a few days.”

“This time it was different,” he added. “They have more experience and they have training from Syria and Iran. They helped them rethink their strategy. They fired rockets in between the houses and covered the alleys with sheets so they could set the rockets up in five minutes without the planes seeing them. The moment they fired, they escaped, and they are very quick.”

A Hamas man interviewed on this question quoted a verse in the Koran that one should not throw himself into death in vain. “Hamas has not shown all its strength,” he said. “We have to maintain our strength. Israel did not want to fight face to face, so we stayed back. Israel said it felt like it was fighting ghosts.”

An Israeli military official involved in the operations said Hamas had three main goals: harming Israel, ruling in Gaza and extending its rule to the West Bank.

“He understands that he needs to get bloodshed and delegitimize us in the international arena,” the official said of Hamas. “So he cynically used people and hit us from within schools and mosques and inside civilian places. If our army wants to hit back, it has to hurt the civilian population.”

Still, he and others said, Hamas was a pretty impressive and disciplined force.

“I would say they are very professional, yes absolutely,” the operations officer said. “In each city they have a commander and brigades and battalions; they are very organized. They have mostly lost a lot of their simple fighters, but not their top men.”

Shlomo Brom, a researcher at the Institute for National Security Studies at Tel Aviv University and a retired brigadier general, said it was wrong to consider Hamas a group of irrational fanatics.

“I have always said that Hamas is a very rational political movement,” he said. “When they use suicide bombings, for example, it is done very consciously, based on calculations of the effectiveness of these means. You see, both sides understand the value of calculated madness. That is one reason I don’t see an early end to this ongoing war.”