Of course you get a larger refund if you commit tax fraud. Both "single" and "Head of Household" are filing statuses for *unmarried* persons (or considered unmarried - which you are not). If you have been filing improperly "for years" I would suggest that you seek out a tax professional to help you to correct those returns before the IRS figures it out - the penalties can be high.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**