About 2 years ago, after competing (and losing all 3 of my matches) in a tournament, I asked my Sensei for some feedback. His advice was super helpful, but the one thing that stood out was that he noticed, that as dominant lefty, somewhere in middle of one of my matches I switched to playing right-handed. He told me that I should have stayed lefty and played to my strengths. I explained to him that the reason why I didn't play left-handed was because my opponent was holding down his right lapel to prevent me from getting a grip (My sensei pointed out that this is illegal according to tournament rules, and he should have received a Shido penalty, but he did it discretely so that the refs didn't notice). Nonetheless, I continued to practice the left-sided technique even harder, to the point where I almost exclusively fight left-handed at tournaments and Randori.
There is a lot of benefit to being a lefty in Judo. Opposing grips make it easier for me to get in closer to my opponents (and vice versa as well). In addition, many Judoka do not practice throws from both sides, and even when they do, they don't practice their throws against an opposing grip! In Uchikomi, for example, when I switch sides to practice the opposite side techniques, my uke usually switches sides too - unless I tell him not to.
This puts me at a psychological advantage - at least with people of equal experience and skill. I often find people are more reluctant to let me take my grip than to allow my grip and test the waters so to speak.
Needless to say, after some time, people catch on. I noticed on many an occasion in Randori that as my opponents were trying to thwart my left-handed gripping, they would open themselves up to right-handed techniques - but, being out of practice, its hard to capitalize.
That coupled with the fact that the makeup of our dojo for the summer is heavy on people smaller, lighter, and less-experienced than myself, (Please, I am not trying to be arrogant. I am a 5'10.5", 215 lb, Brown-belt, I have gone up against green and yellow belts who are much shorter and weigh at least 50 lbs less) I have started to play right-handed against them. I think that this works out well for both of us because, as beginners, they can simply go out and practice their right-hand techniques, and not be thrown off by my grip. It also takes away some of my experience advantages, because I haven't played righty in a while. I think that this is a great example of mutual benefit and welfare.
Hopefully after a few more weeks, I will feel confident to switch sides against the big folks, and the brown and black belt squad.