"We're going to play a new game," the pilot announced-"airline roulette."

He then offered any passenger on the overbooked jet in Chicago$150 to leave the plane and catch a later flight to Washington.

When one woman got up to leave, the other passengers applauded. But she soon returned after deciding she did not have enough of guarantee on the next flight.

The captain then upped the ante. He offered $175 to anyone who would leave the plane. There were no takers and the plane took off for Washington.

This scene at Chicago's O'Hare last week is being repeated all over the nation as airlines try to comply with the latest Civil Aeronautics Board effort to cut down the number of passengers who are involuntarily and unceremoniously "bumped" off flights.

Although the airlines have been bidding for volunteers since September, the procedure has come to public attention recently as passengers grumble and scramble for alternative reservations in the wake of the strike by the International Association of Machinists against United Airlines, the nation's largest domestic carrier.

In Washington, the biggest impact of the United strike has been felt by would-be passengers on Northwest Airlines which is the only other airline serving many cities in the Midwest. The airline also claims it has smaller computer capacity for making reservations than many of the other carriers. The result, according to interviews this week at National Airport, has been a host of horror stories of stranded travelers, long waits and complicated reroutings by computers under siege.

Oddly enough, the strike has not exacerbated the overbooking problem. Airline and CAB officials say that the strike actually may have eased the problem as the number of "no-shows" increases because travelers are unable to get through to airlines on crowded telephone circuits to cancel reservations.

However, the strike has made some passengers reluctant to take advantage of the airline's cash offer to lure them off overcrowded flights because of the difficulty in getting a seat on the next plane.

But the bidding system still works for many airlines. On a recent American Airlines flight from Chicago to Des Moines, an agent came aboard the crowded plane and announced there were five too many passengers with confirmed reservations. Who would be willing to get off for $100, plus hotel and dinner and a guarantee of being in Des Moines by 10 the next morning? Three passengers got up immediately. When the ante was raised to $125, two more left.

Just before the strike, one story circulating at the CAB told of an airline that was seeking seven volunteers for $50 to get off a flight and found that 20 had stampeded off the plane. Not knowing how to decide which of the 20 to pick, the airline decided to pay all of them $50 and the plane actually left the gate with some empty seats.

Under the CAB rules, the airlines are required to seek volunteers who will agree to be bumped in return for payment of the airline's choosing before any passengers are bumped against their will. Passengers who are involuntarily bumped, however, are also entitled to an increased amount of compensation. They must be given the flight to their destination, plus the full value of one-way ticket, up to a maximum of $200 even if they are booked on another flight within minutes.

If the airline cannot provide alternative transportation that gets bumped passenger to his or her destination within two hours of the originally scheduled arrival time, the airline must double the compensation, up to $400.

Those airlines conducting auctions generally stop the "bidding" at the point at which they are legally obligated to pay. According to CAB statistics, about a third of those now bumped off flights are volunteers, but some airlines are doing better than others.

A CAB official waiting for someone at Dulles Airport watched a few minutes while a Trans World Airlines employe comiserated with a passenger who held a confirmed reservation. The airline official told the passenger it was too bad that they had oversold the flight to San Francisco - the last one that night - but those things happened sometimes. Only after the CAB official stepped in and explained to the would-be passenger what his rights were did the TWA manager give instructions to a ticket agent to write him the check he was entitled to - $400.

But for many passengers, delays can be a matter of days.

At National Airport this week, Cleveland horse trainer David Frey described his wait at the Northwest Orient ticket counter as "worse than the gas shortage." Frey said it took him a week recently to fly from Monterrey, Claif., to Cleveland. "I ended up in Buffalo, by way of Toronto," he said, shaking his head.

At Washington's Capital Hilton Hotel, the Northwest ticket counter has been jammed every day since April 1. CAPTION: Picture 1, Luggage stacked in a waiting area at National Airport Monday: a host of horror stories of stranded travelers, long waits and complicated reroutings.; Picture 2, Bob Knox and his daughter Lois wait in line while his sister-in-law, Kathy Schnider, goes for her ticket at National Airport. She and her children were seated separately on their American Airlines plane. Photos by Fred Sweets-The Washington Post