In the end, Israel and Hamas both know that there will be a cease-fire in Gaza. Its timing and terms will be "negotiated" in bombs and bloodshed in the days ahead; it will be mediated by a third party or a combination of third parties; and it will be shaped by a complex regional power game involving an array of competing Israeli politicians, the rival Palestinian leaderships of Hamas and President Mahmoud Abbas, Egypt, Syria and even more distant players such as Turkey, Iran and, of course, the United States. The victims of this "negotiation", needless to say, will be scores of ordinary Palestinians, and a handful of Israelis. And at its end, the fundamentals of the Gaza standoff will remain largely unchanged.

While some Israeli political leaders have spun this episode as a decisive showdown, Israel knows that its military offensive is unlikely to end Hamas' political control of Gaza or even to eliminate the movement's capacity to fire rockets into Israel. Israel's objective is to force Hamas to stop all attacks on Israel from Gaza. Or, to put it another way, to restore the ceasefire Hamas abandoned on December 19, on terms more acceptable to Israel. Polls taken on the first day of the bombing showed that while 81% of Israelis supported the military campaign, only 6% believed it would finally end Hamas rocket fire. (See pictures of Israel's deadly assault on Gaza.)

Despite the heavy casualties inflicted by days of bombing, Israel believes it has not seriously impaired Hamas' ability to fire rockets at Israel. But by targeting the basic infrastructure of Hamas governance in Gaza — everything from police posts, government building and a university to the private homes of Hamas leaders — Israel is trying to set a crippling price for continued rocket fire.

Still, Israel's next step remains unclear: Its armored units poised to drive into Gaza have not yet been ordered to advance, and the Israeli offensive remains confined to air strikes. U.S. Defense officials have told TIME that the chances of a successful ground assault would have been higher if it had been launched earlier in the bombing campaign, and not several days into it. But Israel is well aware that a ground assault is precisely what Hamas wants. There is little the militants can do against Israeli air power, but they believe they can bloody Israel's armored columns and, in what they hope will be a reprise of Hizballah's success in Lebanon in 2006, inflict sufficient damage on the Israeli forces to be able to claim a symbolic victory. For the Israeli public, an outcome that leaves Hamas rule intact in Gaza may be easier to swallow if Israel has not suffered the significant casualties that could result from a ground war.

Still, many Israelis believe their "deterrent power", weakened in Lebanon two years ago, will only be reestablished if ground troops go in to destroy more of Hamas' infrastructure. Right now, it's not clear whether it is political calculations or simply the weather — which restricts the ability of the Israel Defense Forces to fly ground-support missions — from sending in its armored columns. Reports in the Israeli media on Tuesday that Israel may hold off on bombing for 48 hours in search of a truce were quickly denied.

Hamas, through its Damascus-based leader Khaled Meshal, has indicated acceptance of Israel's basic requirement for a truce, that is, an end to rocket fire — but only if the truce, apart from ending Israeli military strikes, also opens the border crossings that would allow normalization of economic life in Gaza. Hamas insists that it ended the ceasefire precisely because the truce had failed to lift the economic siege of Gaza.

Hamas' demand on the border crossings, though, is directed as much at Egypt as it is at Israel. Hamas' primary objective, in fact, is to open the border gate between Egypt and Gaza at Rafah, which was closed by Cairo at the request of Palestinian Authority President Mahmoud Abbas when his forces were driven out of Gaza by Hamas 18 months ago. Rafah, as the Palestinians' only entry point to the outside world not controlled by Israel, represents the closest thing to a symbol of Palestinian sovereignty, which is precisely why Hamas is so keen to control it — and Abbas is so reluctant to allow that.

Egypt, of course, shares Abbas' hostility towards Hamas, originally a creation of the banned but widely popular Egyptian Muslim Brotherhood. Earlier this year, Hamas created a crisis for the Egyptian regime by blowing a hole in the wall at Rafah, allowing Palestinians to pour into Egypt to buy up basic supplies. Embarrassed and under domestic and Arab pressure, President Hosni Mubarak left the breach open for the best part of a week, before sealing it, and renewing Egypt's insistence that it would only open the border crossing to Abbas' men. Now, in the midst of a new political firestorm created by the impression of Egyptian complicity in Israel's onslaught, pressure on Cairo is once again mounting. Still, Mubarak reiterated on Tuesday that Rafah would only be opened when the Palestinian Authority is in charge of Gaza.

Egypt's own escalating conflict with Hamas makes Cairo an unlikely mediator this time around. Instead, Egypt has been seeking help from other regional players, particularly Turkey — which has good relations with Syria, the regional player with the most influence over Hamas. In the power struggle that pits Egypt and the Palestinian Authority against Hamas and its regional backers, the Islamists may be betting that the backlash sparked by the Israeli raids will weaken the resolve of Cairo and Ramallah to keep Hamas' hands off Rafah. But Cairo and Ramallah may be hoping that the punishment inflicted on Gaza by Israel will prompt Palestinians to turn on Hamas. So far, the smart money says that Abbas is paying the higher political price. By contrast, Israel's current leaders may have slightly improved their chances of reeling in the lead of the more hawkish former Prime Minister Benjamin Netanyahu in the February election — although that could change if the operation ends badly from an Israeli point of view.

So, for all the blood shed in the past four days in the hope of changing Gaza's political equation, when the dust settles and the bodies are buried, the wider regional equation of which Gaza forms part is unlikely to change fundamentally — at least not in the favor of those who would prefer to see Hamas eliminated.