The government wants to reduce the number of poker machines in Canberra from 4985 to 4000 by July 2020, in line with its parliamentary agreement with the Greens.

A discussion paper released this week suggests clubs could be forced to hand back about a third of the total each year - 320 or so a year, with the first tranche in March 2018. But it also suggests a gentler option that starts more slowly to give clubs a chance to adjust, so they would hand back 230 in 2018, 350 a year later and 410 in 2020.

The paper models that option, with most clubs set to lose about 20 or 21 per cent of machines overall. The smallest clubs, with fewer than 20 machines, would be exempt.

The biggest club in town, the Vikings group, would lose 150 of its 715 machines, to end up with 565.

The Southern Cross Club, which has 680 machines, would lose 144.

The Labor club group, which has 475 machines and is owned by the Labor Party, would lose about 99 machines, ending up with 376.

And the CFMEU-owned Tradies, with 467, would lose 103.

The government paper says poker machines were introduced in 1975 and by the end of 2006, numbers had hit the cap of 5200. The ACT was recognised as having the highest number of gaming machines per head of population in the country, and the second highest spend.

In 2011, the government introduced a target of 4000, but without a firm way of getting there.

In 2015, it introduced a trading scheme, allowing clubs to buy and sell machines, with one machine forfeited for every four traded. But that has seen only a small reduction, with 5022 machines when the scheme began and 4985 now, of which 4502 are in operation.

The discussion paper said some clubs had suggested the new 4000 limit only apply to poker machines in operation, not to machines in storage. But given there would be nothing to stop clubs bringing machines back on to the floor, that would provide no guarantees of meeting the 4000 target.

Another option would force big clubs to hand back more than small clubs, with clubs owning more than 200 machines handing back 24 per cent, and clubs with up to 100 machines handing back 16 per cent. Clubs with fewer than 20 would still be exempt. Some clubs suggested this would be fairest mechanism, the paper said.

Seven clubs have more than 200 machines, the biggest being the Dickson Tradies, the Belconnen Labor club, and the Southern Cross Club in Woden.

Industry group Clubs ACT is urging a cap of 280 machines for any single venue. The government discussion paper mentions the idea of a cap, and points out that Victorian clubs are capped at 105 machines, South Australian clubs at 40, and Queensland clubs at 300. But it doesn't model the option.

Clubs ACT's 280 cap would only hit a few clubs - the Tradies, which has 347, the Belconnen Labor club, with 301, and the Southern Cross Club in Woden with 295. The Vikings and Raiders would be untouched, despite being some of the biggest pokie owners in the city, albeit across a number of venues.

Another suggestion is a hand-back based on profits, with clubs making less than $8000 per machine exempt, clubs making an average of $8000 to $25,000 from each machine handing back 16 per cent of machines, clubs making $25,000 to $38,000 handing back 20 per cent , and clubs making more than that handing back 24 per cent. But the paper said the bigger clubs could add more machines to the floor to reduce their average revenue per machine, making the option unfair.

Analysis of profits in 2015 suggests this option would hit the Labor clubs hard, with Labor operating the most profitable machines in the city, earning well over $50,000 from each machine a year. The Raiders, Hellenic and Southern Cross clubs also operated very profitable machines.

Yet another option would be to change the trading scheme, so one machine was forfeited for every three traded, or one machine for every two traded, but the paper said based on the limited trading in the past two years that option wouldn't reduce numbers fast enough to reach 4000 by mid 2020.

Gaming minister Gordon Ramsay, who invites feedback till September 18, said the paper was not about whether the government should reduce numbers, with that decision already made. It was about how to get there.