Brothers Mohammed Imran, 33, and Mohammed Irfan, 36, stole the money over three days in 2005.
Before the offence, they regularly competed against high-rollers, including Microsoft chief Bill Yates and millionaire entrepreneur Kerry Packer, at Las Vegas's top casinos.
One of their regular haunts was the Bellagio Hotel, made famous in the film Ocean's 11.
In the scam, the pair used information given to them by "an insider" after Halifax and Bank of Scotland overhauled their autoteller programming system following their merger three years ago. About 400 staff in Scotland and England helped implement the changes.
Imran Bashir, prosecuting, told Glasgow Sheriff Court an "error" in the system later became apparent although it was not known if it was deliberate.
"What is clear is that a member of staff … had communicated information of this fault to either of the two accused or other persons," he said.
The glitch allowed Imran and Irfan, both from Cumbernauld, to overcome the security of ATMs by simply using one expired Halifax Bank of Scotland Keycard.
The court heard that, between 29 May and 1 June 2005, they made some 380 withdrawals at cash points across Glasgow – including one at the city's Riverboat Casino.
The bank eventually became aware of the scam and the card being used was traced to a newsagent in the city's Charing Cross, owned by Shahana Shad, Imran's sister-in-law. She admitted being a customer of the bank, but said she had never received the card.
Mr Bashir said: "CCTV was obtained from the cash machines involved. The accused were seen approaching various cashlines."
Their homes were later raided and 14,480 was found in a safe belonging to Imran. A further 140,160 was discovered in Irfan's safe.
The brothers were originally charged with stealing a total of 486,320. However, prosecutors accepted their guilty pleas to taking 154,640.
The court heard both men were successful poker players, with Irfan ranked 19th and Imran 32nd in the 2005 World Series of Poker.
However, their crime has left them banned from every casino in the UK and there is virtually no chance of them being granted a visa to play again in the United States.
John Hamilton, defending Irfan, said he had carried out the "donkey work" for others, whom both accused refused to name.
He went on: "His familiar association with money may have been the root of this behaviour. It is the exposure of being with others that are wealthy and, income or not, this can be extremely tempting."
Sheriff Robert Anthony said the sentence would have been two years but for their guilty pleas. He told them: "Your parts involved a substantial course of criminal conduct. It must have taken some time and effort to perpetrate this offence."
Last month, a source close to the investigation said that the brothers planned to use the stolen cash to play the world's best poker players.
She added: "You need serious cash to take on some of these guys in Las Vegas, and an opportunity to get involved in a scam like this was a godsend for Imran and Irfan.
"The cash could have gone a long way, but, in this case, it was just one very big gamble too far and they lost out big time."
HBOS declined to comment on the case last night.
WINNER TAKES ALL
THE World Series of Poker (WSOP) is the largest poker tournament in the world.
Held annually in Las Vegas, it lasts over a month, attracting thousands of entries to over 50 events, including all the major varieties of poker.
The series culminates in the Main Event – the $10,000 buy-in no-limit Texas Hold 'Em tournament.
The winner gets a multi-million-dollar prize, a gold bracelet and their picture is placed in the Gallery of Champions.
But it was the unexpected win by an amateur, Christopher Moneymaker, who won the Main Event at the 2003 WSOP, which is generally credited for being one of the main catalysts for the poker boom.
Mr Moneymaker was working as an accountant when he won a seat into the Main Event through a $39 satellite tournament at the PokerStars online poker card room.