Republican Greg Abbott is leading Democrat Wendy Davis by 8 points in a hypothetical matchup for Texas governor, but it’s a statistical dead heat among women, according to a Texas Lyceum Poll of registered voters released Wednesday.

Abbott, the attorney general, leads Davis, a state senator from Fort Worth, 29 percent to 21 percent in the poll, with a whopping 50 percent undecided. The poll has a margin of error of +/- 3.47 percentage points.

Abbott’s lead shrinks to 2 points, within the margin of error, when only women are counted. In that slice of the electorate, Abbott had 25 percent and Davis was at 23 percent, with 51 percent undecided.

Davis, who is expected to announce her campaign for governor on Thursday, leads Abbott 36 percent to 10 percent among black voters and 22 percent to 18 percent among Hispanic voters in the poll. Abbott has a lopsided lead over Davis among independents — 18 percent to 8 percent — but in that group, 74 percent are undecided.

Cal Jillson, a political scientist at Southern Methodist University, said he found the gender gap “intriguing.” Given the fact that white Texans make up two-thirds of the electorate and routinely give 70 percent or more of their votes to Republicans, Davis needs to peel off white suburban women from Abbott if she has any hope of winning.

He said Democrats in the last several elections have generally lost statewide races by 12 to 16 percentage points in Texas, so she’s ahead of the game at this point. But with so many people undecided, Jillson said Davis is vulnerable to a negative ad campaign that would define her before she can define herself. It doesn’t help that her opponent has the biggest war chest in Texas politics.

“How does Davis break even with Abbott among the 50 percent who don’t know, when he’s got $22 million and she’s got $1 million?” Jillson said. “The odds are pretty long.”

A poll over the summer, conducted by Public Policy Polling, also had Abbott leading by 8 points.