The head of a secretive "Punters Club" which uses sophisticated software to make thousands of calculated online bets across the globe each day, allegedly made more than $36 million over three years from the venture but did not declare a single cent of it to the Australian Taxation Office, court documents reveal.

The Tax Office is pursuing Zeljko Ranogajec - who now calls London's 1 Hyde Park apartments home - over the millions of dollars in profits he secured as the biggest stakeholder in the 17-member club between 2004 and 2006.

MONA founder David Walsh. Credit:Scott Gelston

The Tax Office argues that the club is effectively a multinational business and has launched proceedings against a number of members. These include the high-profile owner of Tasmania's Museum of Old and New Art, David Walsh.

Set up in 1987 by a group of ex-maths students from the University of Tasmania, the club is a highly sophisticated operation that uses complex algorithms to calculate the odds in thousands of horse and greyhound races, the Tax Office says.