The Cuomo administration’s Medicaid-reform strategy is riskier than most New Yorkers realize in good part because it doesn’t reform the Empire State’s longstanding practice of seeking to grab every federal Medicaid dollar it can get.

Lord knows, the state’s program needs reform. Medicaid now covers nearly one in three New Yorkers, at a cost of $53 billion a year. We not only provide more services and have more generous eligibility levels than most states, we’re far more relaxed about seeing if applicants truly qualify for taxpayer help.

And the rolls keep growing — up 73 percent from April 2000 to April 2010, rising 13 percent in the last of those years alone.

Compassion has trumped even the most basic anti-fraud measures: Applicants no longer need any face-to-face interview to become eligible. Up-front screening for potential error or fraud is modest at best. Even the screening of service-providers for patterns of likely fraud has become less aggressive.

Gov. Cuomo’s new cap on Medicaid state-spending growth of 4 percent is a step in the right direction. And, to its credit, the governor’s Medicaid Redesign Team sensibly wants to contain costs via an aggressive managed-care approach for all long-term care, mental-health and substance-abuse patients — three populations who drive more than 70 percent of all Medicaid costs.

It’s an overdue approach — but not without risk. The scope of change is ambitious, and the feds must sign off.

The reforms are expected to save the federal government $18 billion; the Cuomo administration will soon ask the Obama administration to grant the state a waiver that would allow us to keep $10 billion of that savings to underwrite reform.

The managed-care plan hinges on a major expansion of New York’s “health homes” pilot program and similar approaches, where a single care coordinator directs patients into primary-care rather than emergency settings, as well as on the broad sharing of electronic-patient information to allow providers to successfully coordinate care in a team approach.

Extra federal funding is available for both efforts, but only temporarily. New York has already gotten the green flag for expanding “health homes,” with two years of greater funds from Washington for each patient enrolled.

But, again, $10 billion of the anticipated funds depend on getting that waiver — which the Obama administration might not grant. Health Secretary Kathleen Sebelius just rejected a major waiver request from California Gov. Jerry Brown.

A bigger worry: New York is also counting on more federal funding, under the ObamaCare law, for upping Medicaid enrollment. The law offers enriched Medicaid funding in 2014 to states, like New York, that maintain current eligibility and benefits until then. It also promises significant funds down the line to states, like New York, that already provide generous Medicaid coverage to the populations all states will have to cover in 2014 under the Obama law.

The Empire State will fare very well — if ObamaCare kicks in, those match rates kick in. But the Supreme Court may overturn all or some of the law, putting New York’s bold plan for federal reinvestment at risk. Even if it doesn’t, this November’s elections could further undermine support in Washington for the original ObamaCare vision.

If the law goes, so too does the promise of enriched federal dollars. This could prove the knockout punch to most of New York’s aggressive approach and planned savings. Where does that leave Gov. Cuomo’s Medicaid reforms? Up in the air — much like the anticipated revenues from casino gambling.