A drawing from a hat will decide control of the Virginia House of Delegates.

That random draw will determine the winner of the 94th House District in Newport News — and with it whether Republicans retain a 51-49 majority in the 100-member chamber or whether the chamber becomes evenly split 50-50 between Republicans and Democrats, requiring a power-sharing arrangement.

The drawing became necessary after a three-judge panel determined Wednesday that the election Nov. 7 between incumbent Republican Delegate David E. Yancey and Democratic challenger Shelly A. Simonds resulted in a tie.

Following a recount on Tuesday, Ms. Simonds appeared to have captured the seat by one vote over Delegate Yancey, who has served three terms in the House of Delegates.

However, the one-vote lead for the Newport News School Board member and former teacher evaporated Wednesday when the judges found that a ballot cast for Delegate Yancey should not have been discarded and would be added to his vote tally.

The judges’ finding: Both candidates received 11,608 votes, leaving the race to be settled with a rarely used procedure to settle a race — the drawing of lots.

When it will happen has yet to be decided. However, state law requires the three-member state Board of Elections to take on the chore.

Board Chairman James Alcorn indicated when the date is set, the board likely would use the same procedure as in selecting the order of the names on the ballot. The board puts the names in a hat, and then allows a neutral party to pick.

In this case, both names will go into the hat, and the first name drawn will be the winner, Mr. Alcorn said Wednesday.

A victory for Ms. Simonds would represent a step toward an expansion of Medicaid for low-income adults, a priority for Gov. Terry McAuliffe and his successor, Dr. Ralph S. Northam, who will take office next month.

With a 51-49 majority, Republicans could maintain their four-year blockade to the expansion of the health insurance program. An evenly split House could make that more difficult.

Still, the Republican margin, assuming a win, would be a far cry from the 2017 session, when Republicans held 66 seats in the 100-member chamber and could advance or kill any bill they wanted. The only saving grace for Democrats was the fact a Democratic governor held the veto pen and they had enough votes to uphold his vetoes.

During the Nov. 7 election, Democrats picked up 15 more seats in the House that are now held by Republicans. The winners will take their seats in early January when the legislature convenes.

The GOP still holds a 21-19 majority in the Senate, so there is no certainty that expansion could pass the full legislature.

However, a 50-50 split would appear to provide more room for a deal to be hashed out between the GOP and Dr. Northam.

Two other recounts are to take place this week — in the 68th House District in Richmond that Democrat Dawn Adams won by more than 300 votes, and in the 28th House District in Stafford County that Republican Bob Thomas won by more than 100 votes. Both winners are expected to maintain their majorities once the recounts are completed.

However, the result in the 28th House District might not be final. Several voters who were among 147 people given the wrong ballots are asking a federal court to hold a new election.