Under President Recep Tayyip Erdogan, Turkey has updated this unique bargaining technique by contriving to aim one pistol at the West even as it presses another to its own temple. Over the past two years, Erdogan has willfully antagonized Turkey’s partners in the North Atlantic Treaty Organization by cozying up to their adversary, Russia. The consequence, entirely predictable, is Turkish isolation in Syria and Libya, where Ankara’s interests are in direct conflict with Moscow’s. Now that conflict is turning kinetic, with dozens of Turkish soldiers killed, quite possibly by Russian bombs, Erdogan’s response is to rail against the perfidious West — and threaten to open the path for millions of refugees to head for Europe. The “or else” part of the bargain is more European money for the housing of refugees in Turkey and, presumably, NATO assistance for Erdogan’s military aims in Syria. The case for the former is unarguable. Turkey already hosts more than  3.7 million refugees, and is bracing for a huge new influx from the fighting in Idlib. Although Europe provides substantial funding for the care of refugees in Turkey, it can and should do much more to share the burden. The hundreds of thousands fleeing Idlib are in an especially parlous state, enduring exposure to freezing conditions on top of everything else. But Erdogan does Turkey’s case great harm by wielding the threat of refugee flows to silence European criticism of his recklessness, such as his military offensive last fall against US-allied Kurdish groups in northeastern Syria. When European officials expressed legitimate concerns that the offensive was opening a new front in an already hopelessly complicated civil war, and harming international efforts to defeat ISIS, the president warned: “If you try to define our operation as an invasion, then our job becomes easy. We open the gates and send the 3.6 million refugees to you.” The case for military help in Syria is harder to make. Having disregarded Western advice against the offensive in northeastern Syria, and threatening an “Ottoman slap” if American troops got in the way, Erdogan now wants American-operated Patriot missile batteries to keep the Russian air force from pounding his soldiers and proxy militias. These are the same Patriots he turned down in favor of Russian made S-400 systems last year. The Trump administration’s response has been appropriately cautious: blandishments of support, without any military commitment. Erdogan has acknowledged that the Patriot batteries may not be forthcoming. At Ankara’s request, NATO has convened a meeting to discuss the situation under article 4 of the Treaty, where a member state can request consultations if it feels its territorial integrity, political independence or security is threatened. Since the first two categories plainly don’t apply, the Turks may argue that the outcome of the battle for Idlib has security consequences — and not only for Turkey. But it’s hard to imagine that other members of the alliance will plunge into the conflict. The West has been lamentably reluctant to impose any meaningful costs on Russia for its crimes in Syria. More likely, they will press for a diplomatic solution, and call on President Vladimir Putin to attend a March 5 summit on Idlib, along with Erdogan, German Chancellor Angela Merkel and French President Emmanuel Macron. For the moment, Moscow is disinclined. Russia has been careful to deny direct involvement in the killing of Turkish soldiers — claiming they were victims of shelling by Syrian forces — but it continues to support the efforts of Bashar al-Assad to drive the Turks and their proxies from Idlib. Erdogan has tried his usual negotiating tactic with Putin, warning that relations between Ankara and Moscow will be damaged over Idlib, even though such a break would leave Turkey utterly friendless, its economy in a hole. Turkish stocks have plunged with the escalation of tensions with Russia, and increased conflict will endanger a recent economic recovery. Putin knows Erdogan doesn’t dare pull either trigger. Bloomberg