In the demimonde of Kabukicho, a warren of striptease bars, cabaret clubs and brothel fronts that makes up Tokyo's main red-light district, the night manager of the Parisienne Café frets about the yakuza. Japan's biggest organized-crime group, the Yamaguchi-gumi, with 23,400 members, split last month.

On Sept. 5, more than a dozen of its factions gelled into a new, rival outfit. A yakuza shootout with Chinese mobsters in the Parisienne killed one gang member and injured more. The café's manager now fears the risk of renewed warfare.

The police are bracing themselves for violence up and down Japan. At the time of the last yakuza split, in 1984, two dozen gang members died in territorial battles.

In the past few years, firebombings, death threats and murders by gangs have eroded the public's tolerance of the gangs.

For all that, the yakuza remain largely legal. Membership is no crime. Mobsters commute to official headquarters, proffer business cards and have pension plans. Its boss, Shinobu Tsukasa, portrays the group as a refuge for the marginalized.

The split has partly to do with the economy. Two decades of Japan's flirting with deflation has made it harder to extort money from businesses.

Criticism over Tsukasa's leadership was a factor too. Other factions have long resented the dominant position of his Kodo-kai, the most ambitious yakuza group that has tried to expand beyond its base in Nagoya. Mobsters in the port cities of Kobe and Osaka were left with slimmer pickings as industry declined.

Kodo-kai also fell out with the police. Rather than cooperating with the cops, as other factions do, it started intimidating them. The police appear even to be helping the breakaway group, which will call itself the Kobe Yamaguchi-gumi.

Many Japanese dare to hope that the split is a sign that the yakuza are diminishing. They are a source of a certain embarrassment, and America has been critical of their semi-tolerated status.

Since 2009, local governments have enacted organized-crime exclusion ordinances, making it illegal for businesses to pay extortion money to the yakuza or do business with them. These ordinances are having an effect.

Still, signs of strong yakuza presence surface often. Tokyo's Olympic Games in 2020 is a tempting honey pot. There have been questions about a link between Tsukasa and the vice president of Japan's Olympic Committee.

In October 2013, a financial watchdog caught a part of Mizuho, a huge banking group, lending generously to yakuza. Mobsters have long been involved in finding lowly workers for nuclear-power plants, including for the cleanup at the site of the 2011 nuclear disaster.

Curiously, yakuza see themselves as victims. They complain of growing discrimination against their members and bemoan the bullying of their children. Perhaps to garner popularity, they are trying to take advantage of growing sentiment against Prime Minister Shinzo Abe.

The Yamaguchi-gumi's website warns that under Abe the country risks heading back to pre-second world war thinking. It is a new line from a force that used to help Abe's Liberal Democratic Party (LDP) quash unions and left-wing demonstrators in the 1950s and '60s.

Back then the LDP used openly to get money from yakuza bosses. Many a politician still attends monthly dinners in honor of the local yakuza boss in some discreet, high-class ryotei restaurant.

It is not clear whether such time-honored rituals will now suffer a brief period of disruption.

Copyright 2013 The Economist Newspaper Limited, London. All Rights Reserved. Reprinted with permission.