We went for the smallest experiment allowed by Google, which is 1000 people, at $0.10 per question, so $100.
The result: 65.9% heads.
I didn't realize this, but even though you pay for 1000 people, Google doesn't have demographic information on everyone who answers, and it throws out people it doesn't know about. Hence, this 65.9% is from 794 'respondents with demographics', and I'm not sure how to see what the remaining 206 people did. [EDIT: Jack Hebert says "To see all 1000 responses, click on the 'gear' icon then set 'Prefer weighted' to Off." He's right. Thanks Jack! He also mentioned that I can share the data. Apparently it is public by default, so here's the link.]
The demographics are cool though, and they automatically look for statistically significant differences among the demographics, called "Insights". It says "124 insights investigated. 2.5 false discoveries expected on average." There were indeed two insights, so they're probably both false: "Among women, those in the US South picked Heads more than those in the US Northeast." and "Among people in the US South, women picked Heads more than men."