The heavy drinking sessions were held to encourage senior staff to "speak more freely", it was claimed. They would often begin mid-evening and end between 1-3am.
Blue is suing Ashley over a claimed agreement made at just such a meeting in 2013 at the Horse and Groom pub in Central London.
He claims Ashley agreed to pay him millions if he could help double the firm's share price. That duly happened the very next year.
However, Blue said he only received GBP1m. Ashley denies the claim.
"These meetings were like no other senior management meeting I had ever attended in all my years of investment banking experience," Blue said.
Fish and chips and kebabs would be delivered after the pub's usual closing time, Blue claimed.
"On one such evening, in front of his senior management team, Ashley challenged a young Polish analyst in my team, Pawel Pawlowski, to a drinking competition.
"The pair drank pints of lager, with vodka 'chasers' between each pint.
"The first to leave the bar area for whatever reason was declared the loser.
"After approximately 12 pints and chasers Pawel apologised profusely and had to excuse himself," said Blue.
"Ashley then vomited into the fireplace located in the centre of the bar, to huge applause from his senior management team."
"Ashley was like no other client that anyone at Merrill Lynch had ever come across," he said describing how even outside the pub he had an unconventional approach to every day business events.
"By way of example, his ability to express boredom and frustration during client meetings knew no limits, including various episodes where he would lie underneath meeting room tables to 'have a nap'," he claimed.
Ashley's legal counsel said it was an "opportunistic try-on," reported The Guardian, and the notion that Ashley had made such a valuable agreement during a drinking session at the pub was "remarkable".
The hearing continues.
