How such a sweet deal came to pass was unraveled more than a decade ago by Joyce Purnick, a columnist for The New York Times.

Pleading hard times and high costs in the early 1980s, a ragged era in the city, the Garden said it needed concessions from its unions and tax breaks from the city. Edward I. Koch, who was mayor at that time, said in 2002 that he believed he had agreed in 1982 to a tax exemption that would last for 10 years. But the language of the deal was read to mean that as long as the Knicks and the Rangers played their home games at the Garden for 10 years, the break would continue.

And so it has.

For the tax year that begins in July, the Garden will save “roughly $54 million” in property taxes, according to George Sweeting, the deputy director of the city’s Independent Budget Office. Last year, the savings were $17 million. In 2002, it saved $6.9 million. The deal is now worth nearly eight times more because the value of land in Manhattan has soared and because the Garden has invested heavily in renovating the building.

Cumulatively, the Garden has saved $350 million since 1982.

The arena is in a City Council district represented by Corey Johnson, who is the sponsor of a resolution asking the state to repeal the tax deal. Because it won wide support in the Council, a State Assembly committee will consider a bill next week to end the exemption, said David I. Weprin, a Queens assemblyman who has long supported a change.

For the Dolan family and other shareholders, having the Garden as a home arena has been a great financial success, regardless of how the teams have performed: Even with a 40-year streak of futility, the Knicks are regarded as the most valuable franchise in basketball, worth $1.4 billion; the Rangers are ranked the second most valuable hockey team, at $850 million.