Pacific

Hawaii

Chee-Fah was played in Hawaii, often spelled Che Fa. It was forbidden in 1886.
Pakapio was played too.

Hawaiian dictionary By Mary Kawena Pukui, Samuel H. Elbert

hua : winning word in the Chinese gambling game of chee-fah.
kiko : To draw or guess the winning number in chee-fah, a Chinese gambling game.
kī.pā : Chinese gambling game chee-fah; to play this game.
wā.wahi panakō : To break the bank, as in chee-fah or other games.

Presstime in paradise: the life and times of The Honolulu advertiser, 1856-1995

Most attention was focused on wide-open gambling in a soon-restored Chinatown, often with police passing in front of the known "dens" but saying they had no power to interfere.
The most popular game was che fa, in which players picked one of thirty-six words on a sheet (eg, dog, man, arm) and winners were drawn at random. An Advertiser reporter witnessed the way in which four out of five chefa "banks" announced the outcome, with dozens of bicyclists racing down principal streets shouting or holding aloft placards with winners' names, while police, said the paper, conveniently vanished.

Hawaiian national bibliography, 1780-1900, Volume 4; Volumes 1881-1900 edited by David W.. Forbes

William O. Smith, who assumed the position of Attorney General as of Attorney General as of January 17, 1 893 , reports on the two-year period ending March 31, 1894. He notes the unsettled state of public affairs following the January 1893 revolution, which necessitated an increase in the police force and entailed larger expenses than usual. "Great credit is due to the Police Department of the Islands ... for the manner in which public peace has been preserved" Smith remarks briefly on prisons and prison inspectors, criminal prosecutions, and alien immigrants. He says that "the carrying on of Lotteries such as paka pio, che fa and similar games of chance" had become a great evil in the community, but were now considerably reduced.

Revised laws of Hawaii: comprising the statutes of the Territory, consolidated, revised and annotated : Hawaii, Walter Francis Frear, Arthur A. Wilder, Albert Francis Judd 1905

Message from the President of the United States: transmitting the report of the Hawaiian Commission, appointed in pursuance of the "Joint resolution to provide for annexing the Hawaiian Islands to the United States," approved July 7, 1898, Volume 3727

CHAPTER 217.# GAMBLING.

Sec. 3172. Lottery denned. A lottery is any scheme for the disposal or distribution of property by chance among persons who have paid or promised to pay any valuable consideration of the chance of obtaining such property or a portion of it, or for any share or any interest in such property upon any agreement, understanding or expectation that it is to be distributed or disposed of by lot or chance, whether called a lottery, raffle, che fa, pakapio, gift enterprise or by whatever name the same may be known.

New Zealand

In New Zealand, from the stories I've found, only Pakapoo was played.

On a roll: a history of gambling and lotteries in New Zealand By David Grant

The earliest Chinese miners brought their own form of lottery. Pakapoo (in Chinese, Pak kop piu) originated during the Han Dynasty in 187 BC. In New Zealand, pakapoo tickets bearing 80 Chinese characters from the Thousand Character Classic were sold for sixpence. The purchaser marked off ten of the characters and returned the ticket to the seller, who noted the marks in a duplicate book and then returned it to the 'bank' (in the goldfields era usually a store-keeper's back room) where the drawing took place. Tickets were removed one by one from a jar or basket until one of those drawn had a number corresponding with a ticket that had been purchased. This was the winning ticket. Originally prizes were traditional Chinese items from the shop, but as the game became popular among Europeans as well, money prizes became more common.

Pakapoo was enormously popular among Chinese in colonial New Zealand. In their bigger communities such as Round Hill (Canton), there could be up to five lotteries a day. Store-keepers employed ticket-sellers who walked from claim to claim selling tickets and, after the lottery was drawn, delivered prizes to lucky winners. Their role was crucial in keeping the operation solvent. They received half the profit from the organiser, and one-tenth of the winner's prize. In good times there was never any shortage of such jobs. The Chinaman's Hill community, near Tuapeka, played host to some 50 transient chinese at anyone time. Most were failed miners for whom selling pakapoo tickets was welcome employment.

Unfolding history, evolving identity: the Chinese in New Zealand By Manying Ip

GAMBLING IN HAINING STREET
For non-Chinese, one of the main attractions of the street was pakapoo (sometimes spelt pak-ah-pu). Although indecipherable to most of its players, the 80 Chinese characters printed on the ticket are the beginning of an ancient prose poem describing the world and its creation. The poem is composed of 1000 Chinese characters, with no two repeated. It is entitled the 'Thousand Character Classic', a primer that all Chinese children once learnt to read and write from.

The name pakapoo comes from 'bak gap biu', white pigeon tickets. Originating during the Han Dynasty in 187 BC,49 it has been compared by many to modern-day Lotto or Keno, except that the odds were much better. Players marked up to ten choices with a brush dipped in ink, and a copy was made and kept by the agent. There were several draws a day, and winnings were paid in proportion to the number of characters that corresponded with the master ticket, with 20 out of the 80 characters being drawn elsewhere at a place called 'the bank'. Copies of this ticket were marked and sent by the bank, via runners, back to the agent. In this way the agent knew if he had sold a winning ticket and was able to greet the winning client with the news.

After a fire in a disused shop on the corner of Haining Street, workmen found hundreds of draw tickets blowing about, each about 600 mm square with a single character on them. In 1905 and 1907 it was reported that, for an outlay of six pence, it was possible to win between one shilling and £70.