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But a majority of city voters support a ballot measure to allow as many as seven casinos in New York State, according to a New York Times/Siena College poll.

The finding is good news for supporters of expanded gambling in the state, including Gov. Andrew M. Cuomo. New York City is home to about 40 percent of the state’s registered voters, and Election Day turnout in the city is expected to be higher than in many other parts of the state because of the race for mayor, so support for the casino measure in the city would greatly increase the odds of passage statewide.

Debate over the measure, which would amend the State Constitution, has been muted: A coalition of casino supporters, financed by about $3 million primarily donated by gambling interests, has begun airing television commercials in the city and on Long Island. There is little organized opposition.

The poll quoted the Nov. 5 ballot language, which lists only positive arguments for allowing casinos, such as promoting job growth and increasing education funding. After hearing that language, six in 10 likely voters said they would vote yes.

“That is a strong margin of victory for the gambling amendment,” said Steven A. Greenberg, a Siena College pollster. “If support is 60 percent in New York City, I am hard pressed to see how it could fail statewide.”

City residents, however, were less enthusiastic about opening a full-scale casino in the city, with 42 percent in favor and 50 percent opposed.

New York already has five full-scale casinos run by Indian tribes and nine slot machine parlors at racetracks. Mr. Cuomo and lawmakers have agreed that if the ballot measure passes, they would allow only four casinos at first, and all of them would be upstate.

In the new poll, New York City residents said they expected both positive and negative effects from expanded casino gambling.

Seven in 10 said they thought it was quite likely that the casinos would bring in significant new revenue for government.

“Just in my apartment building alone, twice a month they have buses come and take people to Atlantic City,” Albert Perrotto, 55, from Far Rockaway, Queens, said in a follow-up interview. “If they take them to upstate New York instead, it would be a shorter ride, and people would go upstate, and the revenue would come here instead. It makes a lot of sense to me.”

At the same time, six in 10 city residents said they thought it was most likely that new casinos would increase societal problems such as crime and compulsive gambling.

Quin Stratton, 23, who works for a credit-card processing center and lives in the Bronx, said she supported the amendment but would not want to see a full-scale casino developed in New York City. “If it’s in the city, it will attract people who don’t have a lot of money, and they will blow their whole paycheck,” she said.

“If the casinos are upstate, or far away, it’s harder,” Ms. Stratton added. “They would have to actually get into a car and would have to make that decision. If it’s in the city, then someone who gets off work will walk by and say, ‘Hey it’s a casino!’ and blow everything they just made.”

Mr. Cuomo, a Democrat, has promoted the casino measure as an economic boon to struggling upstate regions and has predicted that tourists could be lured beyond New York City by the new casinos. But city residents in the poll expressed little interest in traveling upstate to visit a gambling destination. Only about one-third of city residents said they would be likely to visit one of the new casinos, and two-thirds said it was unlikely they would do so.

The citywide poll was conducted on landlines and cellphones from Oct. 21 to 26 with 1,215 adults, including 701 likely voters. The margin of sampling error is plus or minus three percentage points for all adults and four percentage points for likely voters.