They were turned down, but the request added urgency to the question: Would Israel take the risk of a strike? And if so, what would follow?

Now that parlor game question has turned into more formal war games simulations. The government’s own simulations are classified, but the Saban Center for Middle East Policy at the Brookings Institution created its own in December. The results were provocative enough that a summary of them has circulated among top American government and military officials and in many foreign capitals.

For the sake of verisimilitude, former top American policymakers and intelligence officials — some well known — were added to the mix. They played the president and his top advisers; the Israeli prime minister and cabinet; and Iranian leaders. They were granted anonymity to be able to play their roles freely, without fear of blowback. (This reporter was invited as an observer.) A report by Kenneth M. Pollack, who directed the daylong simulation, can be found at the Saban Center’s Web site.

A caution: Simulations compress time and often oversimplify events. Often they underestimate the risk of error — for example, that by using faulty intelligence leaders can misinterpret a random act as part of a pattern of aggression. In this case, the actions of the American and Israeli teams seemed fairly plausible; the players knew the bureaucracy and politics of both countries well. Predicting Iran’s moves was another matter, since little is known about its decision-making process. —DAVID E. SANGER

1. ISRAEL ATTACKS

Without telling the U.S. in advance, Israel strikes at six of Iran's most critical nuclear facilities, using a refueling base hastily set up in the Saudi Arabian desert without Saudi knowledge. (It is unclear to the Iranians if the Saudis were active participants or not.)

Already-tense relations between the White House and Israel worsen rapidly, but the lack of advance notice allows Washington to say truthfully that it had not condoned the attack.

2. U.S. STEPS IN

In a series of angry exchanges, the U.S. demands that Israel cease its attacks, though some in Washington view the moment as an opportunity to further weaken the Iranian government, particularly the Islamic Revolutionary Guard Corps.

Telling Israel it has made a mess, Washington essentially instructs the country to sit in a corner while the United States tries to clean things up.

3. U.S. SENDS WEAPONS

Even while calling for restraint on all sides, the U.S. deploys more Patriot antimissile batteries and Aegis cruisers around the region, as a warning to Iran not to retaliate. Even so, some White House advisers warn against being sucked into the conflict, believing that Israel's real strategy is to lure America into finishing the job with additional attacks on the damaged Iranian facilities.

4. IRAN STRIKES BACK

Despite warnings, Iran fires missiles at Israel, including its nuclear weapons complex at Dimona, but damage and casualties are minimal. Meanwhile, two of Iran's proxies, Hezbollah and Hamas, launch attacks in Israel and fire rockets into the country.

Believing it already has achieved its main goal of setting back the nuclear program by years, Israel barely responds.

5. IRAN SEES OPPORTUNITIES

Iran, while wounded, sees long-term opportunities to unify its people - and to roll over its opposition parties - on nationalistic grounds. Its strategy is to mount low-level attacks on Israel while portraying the United States as a paper tiger - unable to control its ally and unwilling to respond to Iran.

Convinced that the Saudis had colluded with the Israelis, and emboldened by the measured initial American position, Iran fires missiles at the Saudi oil export processing center at Abqaiq, and tries to incite Shiite Muslims in eastern Saudi Arabia to attack the Saudi regime.

Iran also conducts terror attacks against European targets, in hopes that governments there will turn on Israel and the United States.

6. IRAN AVOIDS U.S. TARGETS

After a meeting of its divided leadership, Iran decides against directly attacking any American targets - to avoid an all-out American response.

7. STRIFE IN ISRAEL

Though Iran's retaliation against Israel causes only modest damage, critics in the Israeli media say the country's leaders, by failing to respond to every attack, have weakened the credibility of the nation's deterrence. Hezbollah fires up to 100 rockets a day into northern Israel, with some aimed at Haifa and Tel Aviv.

The Israeli economy comes to a virtual halt, and Israeli officials, urging American intervention, complain that one-third of the country's population is living in shelters. Hundreds of thousands flee Haifa and Tel Aviv.

8. ISRAEL FIRES BACK

Israel finally wins American acquiescence to retaliate against Hezbollah. It orders a 48-hour campaign by air and special forces against Lebanon and begins to prepare a much larger air and ground operation.

9. IRAN PLAYS THE OIL CARD

Knowing that its ultimate weapon is its ability to send oil prices sky high, Iran decides to attack Dhahran, Saudi Arabia, an oil industry center, with conventional missiles and begins mining the Strait of Hormuz.

A Panamanian-registered, Americanowned tanker and an American minesweeper are severely damaged. The price of oil spikes, though temporarily.

10. U.S. BOOSTS FORCES

Unable to sit on the sidelines while oil supplies and American forces are threatened, Washington begins a massive military reinforcement of the Gulf region.

11. REVERBERATIONS

The game ends eight days after the initial Israeli strike. But it is clear the United States was leaning toward destroying all Iranian air, ground and sea targets in and around the Strait of Hormuz, and that Iran's forces were about to suffer a significant defeat. Debate breaks out over how much of Iran's nuclear program was truly crippled, and whether the country had secret backup facilities that could be running in just a year or two.

A REPORTER'S OBSERVATIONS

1. By attacking without Washington's advance knowledge, Israel had the benefits of surprise and momentum - not only over the Iranians, but over its American allies - and for the first day or two, ran circles around White House crisis managers.

2. The battle quickly sucked in the whole region - and Washington. Arab leaders who might have quietly applauded an attack against Iran had to worry about the reaction in their streets. The war shifted to defending Saudi oil facilities, and Iran's use of proxies meant that other regional players quickly became involved.

3. You can bomb facilities, but you can't bomb knowledge. Iran had not only scattered its facilities, but had also scattered its scientific and engineering leadership, in hopes of rebuilding after an attack.

4. No one won, and the United States and Israel measured success differently. In Washington, officials believed setting the Iranian program back only a few years was not worth the huge cost. In Israel, even a few years delay seemed worth the cost, and the Israelis argued that it could further undercut a fragile regime and perhaps speed its demise. Most of the Americans thought that was a pipe dream. —D.E.S.