The United Kingdom votes in a referendum Thursday on whether it will leave the European Union, or "Brexit." The decision could have major global economic and political ramifications.

There have been 65 polls of the British citizenry since HuffPost Pollster started tracking them on April 1, but polls arent providing much insight into which way voters will swing. The combination of pre-existing polling issues and a one-time special interest vote is proving particularly vexing to pollsters.

The HuffPost Pollster model estimates that if the election was held today about 46 percent of Britons would vote to leave the EU, and 45 percent would vote to remain. The probability that leave is in the lead is about 78 percent, but it wouldnt be surprising for the June 23 vote to go either way.

But those numbers have wavered -- just last week, the polls appeared to swing even farther toward leave. Polls since Member of Parliament Jo Coxs murder, which could have been connected to her outspoken support for staying in the EU , have inched back toward remain.

But the trajectory of the race is different depending on what polls you look at. Theres a substantial split between live interviewer polls and polls done over the internet, and splitting the polls along that cleavage results in completely different views how opinions have shifted.

In the live interviewer polls, "leave" the EU holds a substantial 6-point advantage -- a complete trend reversal from just a month ago. Remain was averaging a 10-point lead in mid-May.