I think a lot of people are a little confused with what the OP is saying.
He says he is right handed but holds the deck with his left hand and performs everything with his left hand. Which is the standard way of doing it if you are right handed. If you are left handed or just learned differently then you would hold the deck in your right hand and perform everything opposite from what it is taught in books.
Now on to doing things the "wrong way", I do believe there is a wrong way and for everyone who is going to argue later that making things more difficult than they actually are isn't "wrong", YES IT IS! And for everyone that says adding more moves then there needs to be doesn't make it wrong, YES IT DOES! And before anyone says but if we don't do things that are more difficult we won't ever get better I am not meaning harder sleights. I am all for learning more difficult sleights. What I mean is making more movements than needed to accomplish a certain sleight. Why would you make more movements to do the same thing you can accomplish in less movements? If you are performing magic the "standard way" (as in mechanics grip in the left hand) IMO I think it is wrong to switch hands to do one or two sleights or even to do an overhand shuffle. The stuff is designed to work from one grip and transition straight into the sleight or the shuffle. If you are holding a deck in mechanics grip in your left hand and you "have to" switch hands to do the sleight easier, you will have to re-grip the deck at least three more times to get it in the correct grip than you would normally. To me, if I had to switch hands to do an overhand shuffle it wouldn't be worth the effort. It would be more worth my time to learn the stuff the right way, and yes there is a right way.
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*Lesson time* I want everyone reading this to take out a deck of cards and overhand shuffle normally and then hold the deck in your normal mechanics grip and then take the deck into your opposite hand and try to overhand shuffle. So what I mean by this is if you normally hold the deck in your left hand for mechanics grip you will do so as normal. Now, for an overhand shuffle, you would normally grip the deck from underneath in a biddle grip type grip and start pulling the cards off of the deck with your left thumb and catch them in your left hand, but what I want you to do is go from left hand mechanics grip and figure out how to re-grip the deck to shuffle the deck where you are pulling the cards off with your right thumb into your right hand.
I know the shuffle itself will be difficult to do just because of using the opposite hand than you are used to. What I want you to see is how sloppy and difficult the transfer of the deck from your normal mechanics grip, to the grip you would use to execute the overhand shuffle into your right hand really is.
For me to do a normal overhand shuffle all I have to do, from mechanics grip, is release the grip with my left middle, ring and pinky fingers and place them on the face of the deck to lift the deck into the grip to shuffle. One move and I am ready to shuffle. If I transfer from left hand mechanics grip to my right hand to shuffle them I have to first let go of my grip with my left index finger, take the deck in biddle grip with my right hand, turn my left hand into a short end mechanics grip, then drop my right hand down to catch the cards I am shuffling. That's 4 moves to accomplish the same action I normally do in 1. Not only that, if you are using the overhand shuffle as a control, because of your new angles from switching hands, you would have to turn your entire body around to the opposite direction so you don't flash.
*Lesson learned*
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It just doesn't make sense to me to learn everything in a certain grip and then switch hands for a couple sleights, regardless of how much easier it is to perform the sleight if you switch hands. It would look fishy to me. (This next sentence is really confusing but it is what some of you guys are saying you do while performing) Let's say we have a person who is normally right handed, but performs magic as a lefty (which means his mechanics grip is in his right hand and he perform his sleights with his right hand). I see this magician performing as a lefty during his entire routine and then he switches grip to a righty grip to perform one sleight. Not only is this magician having to switch hands and grips and all else he now has new angles that he hasn't had for anything else in his routine. Really though, it just seems like too much work to switch the deck in to the other hand to perform one sleight when you can just put in the time and learn it the correct way and not have to switch hands.
All of that being said, there is no statement anyone can make that can justify doing what I just talked about.
There is a wrong way.
Like I said before, more movements = wrong