Jim Hoagland is a contributing editor to The Post. His e-mail address is jimhoagland@washpost.com.

The thrill of witnessing angry Ukrainians chase a larcenous tyrant from his palace had brightened this leaden winter before yielding to war clouds gathering over Crimea. But the Kiev moment of liberation — long may it endure — represents a final shovel of earth on the grave of a client-state system the superpowers built for the Cold War.

Ukraine’s revolt greatly accelerates the transformation of international relations begun by the fall of the Berlin Wall. No alliance or strategic friendship is immune to sudden and dramatic reversals as nations recalculate their interests and decide who can — and cannot — help achieve those interests.

Vladimir Putin’s offer of a $15 billion payoff did not persuade Ukrainians to stay mired in the corruption and official lawlessness of the Moscow system. Not even the Russian president has enough rubles to buy off revolution on his doorstep. He will now test whether old-fashioned aggression can still turn the tide.

In their five decades of open ideological competition, Washington and Moscow could justify the costs, financial and human, of propping up thieves and dictators who would vote for “us” and against “them” at the United Nations and otherwise tip the scales in the zero-sum power game of the Cold War.

Today, what does Putin gain if a blood-stained Syrian regime prevails with his help? A broken state led by an internationally discredited ruler hated by the great majority of its citizens. That’s a heavier burden than the United States and Europe take on by “winning” in Ukraine — a financial basket case that needs billions in immediate aid.

In the modern global economy, ­cost-benefit ratios must be considered even by strategists and generals. Money joins fear in cementing new international friendships and alliances — or in making them unworkable.

That is already apparent in the Middle East. Saudi Arabia has willingly replaced the United States as top paymaster for Egypt’s ruling military caste. And Gen. Abdel Fatah al-Sissi, Egypt’s president-in-waiting and a man seemingly immune to irony, recently went to Moscow to rattle the cup. It was as if Anwar Sadat had never expelled 20,000 Soviet military advisers in 1972 to clear the way for a brilliantly successful Egyptian switch to U.S. financial and military aid.

Reversals of alliance, rare in the Cold War’s framework of mutually assured destruction, were far more frequent in the days when balance-of-power strategy ruled the globe. In Europe, alliances often were made to be broken at the right moment. Abrupt shifts by key nations, made for reasons of advantage or survival, could result in decisive victory.

Alert world leaders are reacting to the great fluidity of power relationships today — a situation former secretary of state George P. Shultz calls “a world awash in change.” They eye allies nervously and flash hidden smiles at former foes.

Chinese President Xi Jinping tried to engage President Obama in a dialogue about new power relationships when they met in California last year, but Obama showed no interest. Xi is expected to return to the theme of new Chinese-U.S. global cooperation with Obama in a nuclear security conference that both plan to attend in Holland in late March.

Japanese fears that the United States can be tempted by Xi’s overtures help drive outside-the-box thinking in Tokyo, ranging from informal Japanese efforts to find new common ground with Russia on international issues to increasing defense spending and developing greater self-reliance in security.

But the most immediate and neuralgic pivot point for U.S. allies is Iran. For differing reasons, countries as diverse as Israel, Saudi Arabia and France worry that successful nuclear negotiations could lead to a new Iranian-U.S. “axis” that would return Iran to its former position as a privileged U.S. partner. And Saudi Arabia poked a thumb in Uncle Sam’s eye by giving Lebanon $3 billion to buy French armaments.

Such concerns may seem strange, or at least gravely premature, in current circumstances. But nations are folding unpredictability into their strategic calculations as never before and reacting now to expectations of upheaval to come.

Obama critics assert that this is largely his doing — that his willing acceptance of U.S. retrenchment abroad has opened strategic vacuums into which hostile powers rush and out of which friends tumble. There is some truth in that view.

Yet the real problem with the Obama White House is not that it is causing such monumental changes but that it is failing to adapt to them — failing to think through the consequences of “a world awash in change” and devise strategies to turn this change to U.S. advantage. It has allowed the United States to become a stumbling, status-quo power in a time of global upheaval.