ghoulish game, prompted by the announcement of third-quarter operating losses even greater than record second-quarter losses, was being played last month in private by New York banking regulators and in public by the media. Question: How long would it take mutual savings banks to go broke if present economic trends continued?

Answer: Almost a third of New York City's savings banks would run out of surplus funds in two years or less, a couple within two quarters or less. Though a few strong institutions could withstand that magnitude of losses for 10 years or more, for the city's savings banks as a whole, average life expectancy was about three years. Since the third-quarter figures came out, one of the city's remaining 36 savings banks has been merged out of existence by the government authorities. Two more mergers are imminent.

During the current quarter interest rates have dropped sharply. How much the decline is cutting operating losses remains to be seen. Yet, unless interest rates fall further, and more important, remain at low levels for an extended period, the deadly erosion of the thrift industry will continue, according to New York State Superintendent of Banks Muriel Siebert.

Savings banks and savings and loan associations in her state suffered operating losses of over $1.2 billion during the first nine months of this year. The more numerous savings banks accounted for the major portion, $897 million. Of the 105 New York state-chartered savings banks, 97 were in the red. Third-quarter losses of $372 million were 23 percent more than in the second quarter. Three New York City savings banks were marginally profitable. Net worth or surplus fell to $4.4 billion, 17 percent below the December 1980 level. Withdrawals exceeded deposits by $11.4 billion during the first nine months. At the end of September the banks had total assets of over $65.8 million.

As for New York savings and loan associations (plus a handful of federally chartered savings banks) insured by the Federal Savings and Loan Insurance Corp. (FSLIC), losses for the first three quarters totaled $352.7 million. Net worth was down by 25 percent from December 1980. Savings outflows through September totaled $1.76 billion. Mortgage activity declined by 41 percent during the period to $237 million. At the end of the third quarter they had assets of $26.8 billion.

During the first half of 1981, New York state S&Ls had the second worst return-on-assets ratio of any of the 50 states, Puerto Rico, Guam and the District of Columbia, according to a survey by the Federal Home Loan Bank Board; Puerto Rico had the worst return-on-assets ratio. New York's total loss was $1.45 per $100 of assets, compared with 49 cents for the nation as a whole.

Two major mergers involving the city's thrifts were engineered by state and federal regulators during the disastrous third quarter. West Side Federal Savings and Loan of New York and Washington Savings and Loan of Miami were merged with Citizens Savings and Loan of San Francisco. Between them the New York and Florida S&Ls were losing almost $10 million a month, and their net worth was near zero. Citizens is a subsidiary of the National Steel Corp. of Pittsburgh, which agreed to invest $75 million in the two savings institutions over three years. The FSLIC will provide an estimated $10 million a month in subsidies.

Greenwich Savings Bank, which had losses of $21 million during the third quarter and would have gone broke by next February, was merged with another New York thrift, Metropolitan Savings Bank, at an estimated cost to the Federal Deposit Insurance Corp. of $465 million. At the same time, a separate intrastate-assisted $2.2 billion merger in September involved Franklin Society Federal S&L of New York City and First Federal S&L of Rochester. More recently, Empire State Federal Savings and Loan in White Plains, which had a $4.3 million loss in the first half, was merged into Erie Savings Bank of Buffalo.

Back in the city, Central Savings Bank, which would have exhausted its reserves in six months, was merged with Harlem Savings Bank Dec. 7 at a cost to the FDIC of $160 million. The insurers are still seeking merger partners for New York Bank for Savings and Union Dime Savings Bank.

The West Side Federal and Greenwich mergers made history of a sort. West Side Federal was involved in the first interstate merger since federal regulators changed the rules last spring to aid troubled S&Ls by permitting suitors to come from out of state. Greenwich marked the first time in the annals of New York State banking regulations that a state-chartered mutual savings bank required federal assistance in working out a merger.

But as Siebert said, "If I thought that Greenwich were the first and the last of the supervisory mergers, I would not be here today" at a press conference publicizing the plight of banks.

Why does New York have such a sorry record? Saul B. Klaman, president of the National Association of Mutual Savings Banks, cited the state's unrealistically low usury ceiling of 10 1/4 percent, which was overridden by federal statute at the end of 1979. Moreover, mortgage loans were made under great political pressure at below-market rates for quite a while, he said.

Other important factors are customer sophistication on interest rates and the resulting cutthroat competition among 35 banks in the city. Siebert remarked: "Many people think the 'thrift problem' is a 'New York City problem.' " Indeed, giveaway campaigns there--ranging from toasters to "bring-a-friend" bonuses to sky-high interest rates on promotional investment plans--give the appearance the Big Apple's banks are either foolish or desperate or both.

Just because New York City is the brashest and the baddest doesn't mean the problem is not serious elsewhere. Take the very different example of California. Nine out of the country's 10 largest savings and loan associations are located in California. Although that state has 195 thrifts, or 5 percent of the institutions nationwide, they command 20 percent of the assets.

Not only are they the biggest with $126.3 billion in assets, California S&Ls are among the best. Collectively, they had a higher return on assets during the first half of 1981 than did 38 other states, the District of Columbia, Puerto Rico and Guam.

But "best" is a relative term in this terrible year for thrifts. According to the Federal Home Loan Bank of San Francisco, California S&Ls lost $232 million in the first half of the year, followed by a third-quarter loss of $261 million. Total operating losses for the year to date: almost half a billion dollars. This contrasts with positive earnings of $152 million in the fourth quarter of 1980.

California's performance during the first half meant an operating loss of 38 cents for every $100 of assets. By the third quarter, California losses soared to an annualized rate of 82 cents per $100. Nationally, it was 84 cents.

More bad news showed up in the net new-savings column. California savers withdrew $995 million more than they deposited during the first quarter. By the second quarter that figure jumped to $2.4 billion and held there for the third quarter as well. Contrast that with a gain of $529 million during the last quarter of 1981.

In the same nine-month period, net worth (assets minus liabilities) declined from $6.8 billion to $6.4 billion. The state's S&Ls had a net-worth-to-deposits ratio of 7.2 percent in September, down from 7.6 percent last December. Yet it was considerably above the national average of 5.9 percent reported at the end of June, and well in excess of the 4 percent required by federal regulators. That is not to say there are no S&Ls in serious trouble in the state; in June the Federal Home Loan Bank Board reported 17 mainly small, new S&Ls had ratios under 4 percent.

Sanford C. Bernstein & Co., which tracks major California stock associations, predicts that H.F. Ahmanson, parent company of the largest S&L in the country, Home Savings, will have a loss of $2.55 per share in 1981 compared with a profit of $2.34 the previous year.

The second largest, Great Western, will show a loss of 20 cents per share compared with a profit of $1.74 last year. Great Western's relatively good performance of a $2.4 million profit in the third quarter is due in part to two unusual items: An Internal Revenue Service settlement of $5.5 million and repurchase of $53 million in Great Western mortgage-backed bonds at $40 million. First Charter, which owns American Savings, will have a loss of $1.95 per share versus a gain of $1.32 in 1980.

Glendale Federal, which recently became the country's fourth-largest S&L when it acquired First Federal Savings and Loan Association of Broward County, Fort Lauderdale, Fla., in a supervisory merger, was said by the Federal Home Loan Bank Board to have suffered a loss of $8 million during September. California Federal, the next largest federally chartered S&L, declined to give figures but acknowledged its share of red ink during the third quarter.

Mortgage loan activity declined from $4.3 billion in the fourth quarter of 1980 to $2.5 billion in the third quarter of this year. October activity was off 25 percent from September. Bernstein & Co. reported that the third-quarter flow of mortgage credit in that state approximated only 5 percent of outstanding portfolios at an annual rate. In other words, mortgage activity during the third quarter was running at 15 to 20 percent of its average during the previous decade. "The flow of mortgage credit has essentially been shut off in California," said the firm.

The above figures indicate that the situation in California, unlike New York, did not take a dramatic turn for the worse until the third quarter. Prior to that, the Golden State's S&Ls on the whole had weathered the crisis rather well for a variety of reasons. These include a period of sustained real estate growth longer than anywhere else in the country, no usury statutes, and a greater percentage of mortgage banking activity than in any state except Texas. With a rapid turnover of their portfolios, California S&Ls were not saddled with low-yielding mortgages to the degree their eastern colleagues were.

Moreover, according to William Popejoy, who switched jobs this month from president of Far West Savings and Loan to president of Financial Federation Inc., for a long time S&Ls in his state did not pay out cash dividends, and by keeping their earnings in reserve, built up capital positions that have seen them through this crisis. Financial Federation showed a loss of $9 million during the third quarter compared with a profit of $1.8 million in the same quarter of 1980.

Two other factors also contributed to the success of California thrifts: The ability of state-chartered S&Ls to invest directly in real estate and to make variable rate mortgages (VRMs). Federally chartered S&Ls only gained the power to make variable rate mortgages in 1979, four years after the state thrifts did. (Federally chartered S&Ls cannot yet invest directly in real estate, whereas California recently upped the percentage of portfolio state-licensed S&Ls can invest from 5 to 12 percent.)

How much help variable rate mortgages were to California S&Ls is a subject of debate. Until recently, when the ceiling was lifted, state-licensed S&Ls were allowed to raise the interest rates on VRMs by just one-half percentage point a year, or 2 1/2 percentage points over the life of the loan. In the words of Linda Tsao Yang, California's Savings and Loan Commissioner, "It's a nice nest egg. Every half-point adjustment means $100 million additional a year." Thirty percent of California's mortgages are VRMs.

Yet only half the state-chartered thrifts offered VRMs, countered Popejoy who thinks they were not a major factor. Even James Montgomery, president and chairman of Great Western, which has 60 percent of its portfolio in VRMs, remarked, "The VRM wasn't variable enough to protect us." He meant lenders couldn't raise mortgage payments enough to cover their increased cost of funds.

Also on the minus side was the 1978 Wellencamp court decision prohibiting state-chartered S&Ls from exercising due-on-sale clauses--that is, preventing buyers from assuming existing low-interest mortgages. Mortgages without the clause were difficult to sell in the secondary market. The case has now embroiled federal S&Ls and is headed for the Supreme Court.

Another factor affecting profitability and growth is charter. During much of the past decade, the innovative freedom conferred on California S&Ls by a state license kept the industry there prosperous. Then the California federals exerted pressure on Washington to give them parity with the state S&Ls on things such as variable rate mortgages and real estate equity investments, so the advantage of a state charter was removed. Also state regulators have tried to impose stricter rules on branching within California.

Now, given the lure of interstate branching before them, many large California S&Ls claim state charters hinder growth and are rushing to convert to federal charters. If the big S&Ls change charters, the state's Department of Savings and Loans will have insufficient funds as well as less clout. State commissioner Yang, anxious to preserve the dual charter system, deplores this rush to de facto federalization without Congressional debate on whether it is desirable.

With the decline of interest rates during the fourth quarter, is the Golden State now out of the woods? The same factors that mitigated California S&Ls' losses through the first half of this year make analysts relatively optimistic about next year. Allan G. Bortel of Shearson/American Express in San Francisco projects that the state's S&Ls will break even by March, a couple of months ahead of the rest of the nation, provided Treasury bill rates stay in the 9 to 9 1/2 percent level. He forecasts an industry wide profit of $1 billion to $1.5 billion next year, with California accounting for a quarter of it.