A typical American turning 65 this year is in line to receive about $500,000 in lifetime Social Security and Medicare benefits. That’s more than $1 million for older couples. But many still won’t have enough money to pay for out-of-pocket medical care and long-term supports and services.

While the wealthiest seniors will have the resources to pay these hefty out-of-pocket costs, most older adults won’t come close. As with the overall population, there is an enormous gap between the incomes and assets of the best off and everyone else.

In 2014, half of those 65 and older had financial assets of less than $76,000. Half had housing assets of $81,000 or less. Half had annual incomes below $26,150, according to new research by the Kaiser Family Foundation and my colleagues at the Urban Institute.

Consider that an average couple needs to put away about $220,000 at age 65 just to pay for medical costs that are not covered by Medicare, according to Fidelity Benefits Consulting. Plus, they’d need to put aside an additional $150,000 to pay out-of-pocket for long-term supports and services, according to my Urban colleague Melissa Favreault and Judith Dey of the Department of Health & Human Services.

That’s $370,000 in savings at age 65—more than twice what a typical older couple has squirreled away. And it doesn’t include what they’ll need for routine day-to-day expenses such as housing, transportation, food, utilities, clothing, and the like.

That’s the average. Now, think about nearly one out of every ten 65-year-olds who will spend more than $250,000 out-of-pocket for long-term care before they die.

The great paradox is that those turning 65 today will receive generous government benefits over their lifetimes, according to my Urban Institute colleagues Gene Steuerle and Caleb Quackenbush. And a couple turning 65 in 2030 stands to receive almost $2 million in lifetime federal retirement benefits, at least according to current law. These estimates are based on a couple where each spouse earns average wages from age 22 to 65.

Keep in mind that the Medicare portion of those benefits ($422,000 for a middle-income couple turning 65 this year) goes to medical providers or insurance companies, not to the seniors themselves. They will get about $616,000 in lifetime Social Security cash benefits (and will have paid $543,000 in Social Security payroll taxes).

As generous as those Medicare benefits seem, they do not pay for many costs typically incurred by older adults. Seniors still must pay copayments and deductibles, as well as premiums (which are growing significantly for those with high-incomes). Many choose to purchase Medicare Supplement (Medigap) insurance to help with those out-of-pocket costs, but those policies carry additional premiums.

And Medicare does not pay for long-term supports and services at all. It does pay for some rehab and nursing care after a hospital discharge and for specialized care such as hospice. But for the most part, when it comes to personal assistance at home, nursing home care, or assisted living, seniors are on their own.

The work by the researchers at Kaiser and Urban (Gretchen Jacobson, Christina Swope, and Tricia Neuman from Kaiser and Karen Smith from Urban) shows that many people will still fall far short of what they’ll need in old age. Their definition of income is very broad, including not only Social Security, but pensions, income from financial and housing assets, IRA withdrawals, and the like.

The work of all these researchers tells a complex story—two stories really. The first is that the government has promised seniors who retire at age 65 very generous health and retirement benefits. The second is, despite that largess, many older adults will have far fewer resources than they’ll need to finance out-of-pocket medical and long-term care costs.

In our era of overly simplistic soundbites, it is often hard to keep two seemingly-contradictory ideas in mind at the same time. But when you think about the well-being of older adults in the US, it is essential to acknowledge both stories: Yes, seniors are in line for generous government benefits. And, yes, those benefits won’t be enough to see many of them through their old age, especially if they have serious health problems.