Such errors are unlikely to cost Russia military victory in a nominal sense. The Russian forces still boast overwhelming manpower and equipment advantages over their Ukrainian counterparts. But as great powers have learned so frequently in recent history, military victory is the easy part of a regime-change war. Ukraine’s resistance over the past week has not been sufficient to beat back the Russian invaders. But it has demonstrated what most analysts had assumed even before Putin’s invasion — that Russia cannot impose a puppet government on the Ukrainian people without embroiling itself in a ruinous occupation.

Beyond underestimating the Ukrainians’ will to fight, Putin has patently misjudged the West’s capacity to punish his aggression. The U.S. and E.U.’s sanctions amount to financial war on the Russian state, one that has wiped out ordinary Russians’ savings overnight. Not only has the West’s response devastated Russia economically, it has set back the very strategic objectives that Putin’s invasion was meant to advance. The NATO alliance has been reinvigorated, with Finland and Sweden both now contemplating applications for admission. Germany has committed $100 billion to its own rearmament. And nations throughout Europe are recalibrating their energy strategies so as to reduce their dependence on Russian fossil-fuel resources.

To look at these results and conclude that it would be wise and achievable to conquer every inch of Ukrainian territory, dissolve the nation’s military, and impose a puppet government is madness. There is no way forward that will leave Putin’s regime better off than it was before it blundered into war. The best way to cut his losses would be to seek some sort of negotiated settlement, perhaps a deal in which Russia annexes Ukraine’s separatist territories and then withdraws from the rest of the country, in exchange for the Zelenskyy government’s forswearing NATO and E.U. membership and the West’s lifting all sanctions.