The consortium formed by online gambling giant 888 and Grosvenor Casino operator Rank had proposed a three-way tie-up in which the two companies would merge and contemporaneously acquire William Hill.
The revised offer maintained the 199p per share cash offer for the bookie, but upped the stock element of the deal so that William Hill shareholders would own 48.8 per cent of the new entity.
Under the previous offer, shareholder would have owned 44.6 per cent of the company.
The bookmaker has also come to a disagreement with the consortium as to how much both the original and revised deals are worth.
Rank and 888 have said the first deal, which they launched last week, valued William Hill at a rate of 364p per share (in a £3.6bn offer) and that the new offer launched on Sunday valued the bookie's stock at 394p per share.
However, William Hill said today the original deal valued its stock at 339p per share and the revised offer at 352p per share before synergy benefits.
A source close to the deal said William Hill had used "creative mathematics" in its revised calculations in a deliberate attempt to cause confusion and make it seem as though the deal had undervalued the company more than it was.
William Hill said it had calculated the new value of the deals based on the 22 July "unaffected combined market capitalisation of the three companies adjusted for the cash component" of each proposal.
The bookmaker's chairman Gareth Davis dismissed the offer out of hand and indicated the cash element of the deal would need to change before it can be reconsidered.
The deadline for a final offer from Rank and 888 is this Sunday.
Davis said: "This revised proposal continues to substantially undervalue the company and the cash element of the proposal has not changed.
"Therefore, the board sees no merit in engaging. As we have said before, this is highly opportunistic and complex and does not enhance the strategic positioning of William Hill."