* Arab Spring puts Hamas on broader Islamist path
* Rocketing Israel does not clash with bid for acceptance
* Hamas aims to lead Palestinian national movement
GAZA STRIP, Oct 26 (Reuters) - One of 70-odd rockets fired from Gaza into Israel this week hit a chicken coop, critically wounding two Thai migrant workers, innocent bystanders in a deadly game of brinkmanship.
If it had killed children on the Israeli farm they work for, Israel and Gaza would probably be at war right now.
Gaza's Islamist rulers, Hamas, know what a fine line they tread when they fire rockets at Israel: maybe they'll explode in a field and draw a few targeted air strikes; or maybe they'll hit a kindergarten and Israel will bombard the Gaza Strip, as it did in their lopsided three-week war at the turn of 2008-2009.
Over 1,300 Palestinian lives were lost and 13 Israelis died.
Since then, there has been a sporadic low-intensity conflict with its own codes and rules, looking almost choreographed at times in the predictability of strike, counter-strike, escalation, de-escalation and truce.
What was less predictable about the latest flare-up was that Hamas, which has been trying to curb attacks, would launch one of the biggest rocket barrages of the year just one day after the Emir of Qatar paid a landmark visit, happily celebrated in Gaza as the end of nearly six years of isolation.
The pro-Western Qatari leader, no gun-kissing militant, was the first head of state to visit Hamas since they seized power in the crowded enclave in 2007. He also donated a cool $400 million in reconstruction aid to help its 1.7 million people.
This might have prompted a reflective pause in the impoverished enclave running a skinny 40 km (25 miles) down the Mediterranean shore between Israel and Egypt.
Instead, a rain of Hamas rockets sent Israelis in southern towns and farms running for shelter. Hamas posted video of multiple rocket launchers firing at the ``vampire, criminal'' Zionist enemy they vow to drive out of the region.
``It was a calculated escalation,'' said Khalil Abu Shammala of the Ad Ameer human rights group. ``The rockets used were short range, though Hamas and other groups have rockets with ranges of 20 km and more. But they did not use them and that is evidence the escalation was calculated and limited.''
``As a resistance movement, Hamas feels embarrassed in front of its own members, so it attempts through these limited responses to prove it remains on the battlefield,'' he said.
This is only a tactical necessity, he said. ``Hamas strategy today is to win the recognition of the international community and to present itself as viable political entity.''
Analysts think Qatar, building up a leader's role in the Sunni Muslim world and influence beyond the Gulf, hopes to tame Hamas, get it to reconcile with the Fatah movement of Western-backed Palestinian President Mahmoud Abbas, and perhaps advance the cause of Middle East peace.
This is a tall order: Abbas recognises Israel, Hamas does not; the major powers do not talk to Hamas; Abbas has not talked peace with Israel for two years. Small wonder that Middle East peace got scant mention in the third Obama-Romney presidential campaign debate. The ``peace process'' is dead on its feet.
But the gas-rich Gulf monarchy has deep pockets, and Hamas says it has time and stamina for a long game. The energy and confidence it displays contrasts with an air of fatigue in the camp of Abbas, after years of fruitless peace talks with Israel.
``Hamas is in its golden era as the other side is faltering,'' said West Bank analyst Basim Al-Zubaidi.
Gaza consultant Omar Shaban says the Gaza Strip may be poor but the West Bank's aid-inflated ``cappuccino economy'' is a hollow sham rotting Abbas' Fatah movement from the inside.
``Deterioration happens gradually. You don't see it. But Abbas is in bad shape while Hamas is in a good position.''
Shaban said Wednesday's rocket barrage did not ``violate the rules of the game'' -- a phrase Israeli strategists also employ.
``I believe restraint was part of the Qatari deal,'' he said.
Analysts say Hamas aims to replace the creaking Palestine Liberation Organisation, headed by Abbas, and give a new face to the Palestinian movement: sober, incorruptible, Islamic, moderate; backed by Egypt and Qatar, and able to advance the Palestinian cause better than an exhausted Old Guard.
It wants to rid itself of the ``terrorist'' label which bars it from international conference halls. But it is also looking nervously over its shoulder at smaller militant groups primed to charge it with cowardice and betrayal if it stops shooting.
The movement, says Shaban, is creeping towards the diplomatic provisions of the Middle East Quartet -- the United States, the European Union, Russia and the United Nations -- which demand renunciation of violence and acceptance of Israel.
``Hamas won't go from a Big No to a Big Yes,'' he said. ``They are moving subtly. They do not want a state (just) in Gaza. They want to be perceived as a modern, sophisticated civil authority.''
ADJUSTING TO WIDER AIMS
Hamas' Sunni Muslim leaders quit their headquarters in exile in Syria this year to end embarrassing ties to President Bashar al-Assad, as his forces battle and kill Syrian Sunni Muslims. Its leadership is in flux but analysts believe the Gaza faction led by 'prime minister' Ismail Haniyeh will trump the exiles.
Whether Haniyeh has loosened ties to Shi'ite Muslim backer Iran, Assad's main ally, is unknown. Israel says Tehran, displeased with Hamas for abandoning Damascus, now funnels more of its money and arms to Hamas' rival Islamic Jihad.
Haniyeh denies Hamas aims to declare a state in Gaza alone, saying it is the springboard to Palestinian statehood. ``Gaza is the shortest road to Palestine. Gaza is the first step to liberate all of Palestine,'' he said in a speech on Friday.
George Jaqman, a political analyst in the West Bank, said Hamas had taken a step towards international acceptance by advancing the idea of a long-term truce with Israel, with a Palestinian state on the 1967 Middle East war borders.
But Israel mistrusts such an idea. And there is no sign from Hamas of willingness to recognise Israel.
Egypt's ruling Muslim Brotherhood led by President Mohamed Mursi, however, does recognise Israel and has promised to uphold their 1979 peace treaty. The Brotherhood, as spiritual father to Hamas, has great influence with the Palestinian group.
Mursi intervened on Wednesday to arrange a tacit ceasefire.
``The Muslim Brothers may work as an important force to tame Hamas rhetoric in relation to conflict with Israel,'' said West Bank analyst Zubaidi. ``I think two years from now we may see an Egyptian initiative whereby Hamas would be willing to discuss peace or truce or an understanding with Israel.''
By waiting patiently until the balance of power turns in their favour, Hamas can focus on its social, cultural, and religious agenda and keep up the spirit of armed resistance without going to war.
Asked if Hamas wants to replace the PLO, Hamas official Mustafa Assawaf said: ``The coming stage is that of Hamas, especially amid the changes in the Arab region. Every stage has a leadership. Decades ago that leadership was owned by the PLO and I think the current stage should be led by Hamas.''
``Hamas is not in a hurry,'' he said. ``It relies on time and time looks to be on the side of Hamas.''
(Additional reporting by Crispian Balmer and Ali Sawafta; writing by Douglas Hamilton; editing by Philippa Fletcher)