Saudi-backed Yemeni forces have reversed the Houthis' September gains in a fast-moving attack, a clear win for Riyadh but one that may not hold.

• About 100,000 government troops, backed by over a thousand Saudi air strikes, retook the Bab al-Mandeb strait and nearby coastal towns in two days.
• The Houthis retreated in disarray rather than fight, losing hundreds of fighters and abandoning the port city of Mocha.
• The open desert along the coast favors whoever is attacking, so holding the ground is far harder than taking it — the same seesaw has already played out twice in a year.
• The Houthis are still winning in the mountain highlands, where they just cut the last road into the besieged city of Taiz, and they keep hitting Saudi oil sites and Riyadh's airport with missiles and drones.
• Turkey and Pakistan have now formally pledged troops to defend Saudi Arabia, with tens of thousands of Pakistani soldiers already on Saudi soil.

Outlook: Government forces will likely push north or east to widen their buffer, but overreaching into Houthi mountain territory risks handing the coast straight back.