The latest vote count released Saturday by Snohomish County failed to make any significant difference in the bleak prospects for Referendum 88, which would have ended a two-decade ban on affirmative action in Washington state.

Snohomish County’s Saturday count added roughly 50,000 ballots to the statewide total. Opposition to the referendum in Snohomish County remained about constant, with nearly 55% of voters rejecting it.

After the Saturday tallies were added, the Secretary of State’s Office said the referendum was losing by nearly 13,000 votes, or 50.35 % to 49.65 %. The difference is not close enough to trigger a mandatory recount.

On Friday, two massive ballot dumps came in from King County where support for the referendum is strong, approaching 63% in favor. But it is almost impossible that enough support can be found in the comparatively small number of ballots still to be counted in King or other counties to push Referendum 88 into the winning column. King County will next release a vote count Tuesday.

The referendum was being approved by voters in only four counties — Jefferson, King, San Juan and Whatcom.

Correction: an earlier version of this story incorrectly stated Ref. 88 was passing in three counties.