KABUL, Afghanistan — For the past few months, possibly the most intriguing poker game in Kabul has been taking place in the sprawling pink sitting room of the man at the center of one of the most public corruption scandals in the world, the near collapse of Kabul Bank.

The players include people tied to President Hamid Karzai’s inner circle, many of whom have profited from the crony capitalism that has come to define Afghanistan’s economic order, and nearly brought down Kabul Bank. The game’s stakes “aren’t too big — a few thousand dollars up or down,” one of the participants said.

Betting thousands of dollars a night in a country where most families live off a few hundred dollars a year would seem like a bad play for Sherkhan Farnood, the founder and former chairman of Kabul Bank, the country’s biggest. His assets are supposed to be frozen, and he is still facing the threat of prosecution over a scandal that could end up costing the Afghan government — and, by extension, the Western countries that pay most of its expenses — almost $900 million.

Despite years of urging and oversight by U.S. advisers, Karzai’s government has yet to prosecute a high-level corruption case.

As Americans pull back from Afghanistan, Farnood’s case exemplifies how the United States is leaving behind a problem it underwrote over the past decade with tens of billions of dollars of aid and logistical support: a narrow business and political elite defined by its corruption, and despised by most Afghans.

The Americans and Afghans blame each other for the problem’s seeming intractability, contributing to the deterioration in relations that now threatens to scuttle talks on the shape of ties between the countries after the NATO combat mission ends in 2014. What is clear is that the pervasive graft has badly undercut the U.S. war strategy, which hinged on building the Karzai administration into a credible alternative to the Taliban.

“It’s a little late in the game to worry about anti-corruption measures because what in the world is the alternative going to be?” said Anthony Cordesman, a military analyst at the Center for Strategic and International Studies in Washington. “If you find people who aren’t corrupt it is largely because they haven’t had the opportunity.”