I believe I've seen reports that discussed a spike in lottery ticket sales when it's positive EV; I think there are some people that do watch for that and behave accordingly. Putting your "actually risk neutral" investment money into it isn't a terrible idea, but whether or not you have that investment money depends on your situation.

[edit] That is, you should split your financial resources into "expected to be needed in the next 3 months," "expected to be needed in the next year," "expected to be needed in the next 5 years," "expected to be needed in the next 20 years," and "risk neutral." How much of your current income flow to put into each of those buckets depends on your projected income, projected consumption, and so on, and is a fairly complicated calculation if you want to do it carefully. Even so, eyeballing it is better than not running those numbers.