The end of lunch at the Association of Black Social Workers Senior Center on the Upper West Side usually spells B-I-N-G-O. On a recent Wednesday, a dozen seniors gathered around tables, finished off their macaroni salad and talked about a special O-15 — October 15, when annual enrollment for Medicare begins.

As they do every year, seniors nationwide who are insured by Medicare have to decide between now and December 7 whether to stick with the plan they have or to switch. Most participate in the government-run program. But about one in four enroll in Medicare Advantage — a public/private hybrid insurance plan that has been the subject of heated and sometimes distorted debate in this fall’s presidential campaign.

In New York, Medicare Advantage is even more popular, particularly in New York City, where more than one-third of eligible seniors in Brooklyn, Queens and the Bronx are signed up.

Catherine Horran, 85, is one of some 900,000 New York State seniors now enrolled in Medicare Advantage. She decided to try it when she retired, because it meant she could stick with her old insurance company, Health Insurance Plan of Greater New York — a subsidiary of the city’s second largest Medicare Advantage insurance provider, EmblemHealth Inc. She has been a happy Medicare Advantage customer ever since.

Who can blame her? Medicare Advantage patients, for a small premium payment, receive additional coverage – for eye care, podiatry, hearing exams, nutrition services and much more.

“I don’t want to change,” said Horran. “Well, not until we know who the next president is.”

The future of Medicare Advantage is in flux, depending on who wins the White House. The program is expensive, costing the federal government nearly $300 billion over original Medicare in the past quarter century, according to a new report by Physicians for a National Health Program, a consumer advocacy group.

To keep private insurers interested and the out-of-pocket costs for seniors lower, the federal government has reimbursed the plans at a higher rate than original Medicare. Last year, the congressional Medicare Payment Advisory Council calculated Medicare Advantage payments to providers are 7 percent higher than those under original Medicare.

The Affordable Care Act, advanced by the Obama administration, moves to cut the cost of Medicare Advantage by reining in the federal government’s reimbursements to the plans. Meanwhile, Republican candidate Mitt Romney says he would like to use Medicare Advantage as a starting point for a market-based Medicare system.

In recent weeks, the campaign trail has been littered with ominous predictions from both candidates that their opponent’s plan for Medicare, and particularly the private insurance plan offerings — Medicare Advantage — will destroy the program as seniors have come to know and largely love it.

During the first presidential debate, former Massachusetts governor Mitt Romney accused President Barack Obama of stealing the program right out from under those who benefit — even though the full scope of the cuts haven’t taken place yet. “I can’t understand how you can cut Medicare $716 billion for current recipients.”

Obama returned fire by charging that his opponent would voucherize the program, leading to its eventual collapse. And in the meantime, he insisted, the amount of profit that private companies make off the program had to be reduced.

“You’ve got higher administrative costs, plus profit on top of that, and if you are going to save any money through what Governor Romney’s proposing, what has to happen is that the money has to come from somewhere,” said President Obama.

The Congressional Budget Office recently projected that the Centers for Medicare and Medicaid Services would reduce direct payments to private Medicare Advantage plans by $156 billion by 2022 and another $152 billion indirectly through other cuts to Medicare payments. Under the Affordable Care Act, all of the $716 billion would be reaped through lowered reimbursements to providers and other cost savings.

While the campaigns stake their sharply different positions, sales forces are getting to work to entice New York’s seniors to sign up for one of 47 Medicare Advantage programs on the market. At UnitedHealth, whose AARP MedicareComplete is a major Medicare Advantage player in the city and state, Medicare Advantage is the parent company’s biggest growth business, with enrollment jumping 18 percent in just the past year according to disclosures to investors.

So far, despite alarms from critics of the Affordable Care Act, plans and patients report few cutbacks in their services. This is in part because the reductions to medical providers’ payments are in their initial stages. But it also is likely due to a huge bonus-payment initiative that is funneling billions of federal dollars right back into the private insurers’ hands.

The Affordable Care Act authorized a bonus payment to high-quality plans as a pay-for-performance measure tying extra money to quality patient outcomes and satisfaction. Any plan that rated between a 4 and 5 in the agency’s star rating system would get rewarded. But late in 2010, the Centers for Medicare and Medicaid Services authorized a near doubling of bonus repayments, expanding most of the $8 billion in rewards to plans that scored between 3 and 4.

James Cosgrove, health care team director for the U.S. Government Accountability Office, said that the program will offset about three quarters of the cuts to Medicare Advantage plans in 2012 and about a third of the cuts over the program’s three-year lifetime.

CMS has defended the program, saying that the extra federal funds have led to much improved star ratings nationally.

“In 2013, people with Medicare will have access to a wide range of plan choices, including more four and five star plans than ever before,” said Secretary Kathleen Sebelius in a press release last week. The Centers for Medicare and Medicaid Services showed an almost 20 percent increase in the number of plans with 4 or 5 stars nationally from last year to this year. In New York City, only two plans received 4-star ratings, and none received 5.

But critics contend that the program is ultimately a political move on a contentious issue during an election year.

“CMS has sent an unprecedented, and perhaps unlawful, $8.3 billion to MA plans, filling in over 70 percent of the cuts in 2012 alone — quite plainly because the agency wants to mitigate the impact of the cuts required by the 2010 law,” said James Capretta, a visiting fellow at the conservative Heritage Foundation, in testimony before the House Ways and Means committee in September.

“There is no other way to explain what they are doing. Certainly there is no public policy rationale for the payments.”

The bonuses have helped ease the transition for the insurance companies, which are being careful not to cut their services or raise premiums lest they lose Medicare Advantage customers.

“One of the things that we had heard health plan lobby say was, ‘Look, if you change the way you’re paying plans, you run the risk of cutting benefits or large rate increases,’” said Doug Goggin-Callahan, director of education and New York State policy of the Medicare Rights Center. The center published a report earlier this year on the state of Medicare Advantage, which found that despite the bluster, New York plans have not cut back on their benefits.

“There really wasn’t much change.”

And in the meantime, private insurers will continue to find ways to keep enrolling more seniors.

“Regulations are going to continue to evolve regardless of who wins the election, or who’s the governor,” said Bill Lamoreaux, Senior Vice President of government programs at EmblemHealth. Emblem operates half a dozen plans in the city, all rated 3 or 3.5 stars. “Our number-one objective here at Emblem is to find a way to continually enroll people in services in New York.”