No, putting extra choices won't diminish your chances of getting your first choice -- the lottery isn't trying to maximize everybody's happiness or anything. All it does is try to put everybody in his or her first choice, and if you don't put a second choice and you don't get lotteried into your first choice, you won't get a HASS-D assignment.
Selecting 1, 5, and 6 would be the same as selecting 1, 2, and 3, and neither option will make it less likely that you'll be lotteried into 1. If there are a few courses you'd be willing to take, it's to your advantage to select all of them in the lottery.
I should probably note also that if you don't get your first-choice HASS-D, the odds are still good that you can take the class. You just have to show up on the first day of class with an add/drop form -- since a decent number of students who are lotteried in will end up deciding to take other classes, there are almost always enough spots for people who weren't lotteried in. (My fiance got through MIT without ever entering the HASS-D lottery.

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