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The success or failure of many card tricks depend on the belief by the audience that the deck has been fairly shuffled. If they suspect a stacked or prearranged deck.. you're fried.
This false cut is one of the very best, it's simple, and it only requires a small bit of acting.
Hold the deck in your weak hand in a mechanics grip. For the uninformed, that means instead of holding it in your palm, you hold the deck above your palm, holding it with your thumb on the left long side (assuming you're left handed) and your fingers along the right long side. This gives you access to both the top and the underside of the deck.
Reach with your strong hand and, using your thumb and middle finger, secure a lower side grip on the bottom half of the deck. Just imagine that you're reaching over to take the top half off the deck, but, you take the bottom half instead. As soon as the bottom half has cleared the deck... FREEZE. Look at the spectator and make some kind of statement.
" I am going to try to find your card in a very fair way.." for example. You can even gesture slightly with the half pack in your strong hand. Looking at the spectator will almost always prompt them to look at you for a moment as well. It's this pause in the action that makes the spectator momentarily forget that the strong hand pack came from the bottom of the deck. Now, bring this half somewhat over the top of the weak hand half and lay it on the table.
Not a big, fancy move. Just a steady and confident move.
As soon as you place the strong hand half on the table, reach out with the same hand and take the weak hand half out of the weak hand, using the same thumb and middle finger, and place it on top of the half already on the table.
Of course, all you've accomplished is to take the bottom half of the deck and set it on the table, then, take the top half and put it on top. You have changed absolutely nothing regarding the order of the deck.
If you do this with a steady and deliberate motion, but pausing just long enough to distract the spectator, you will almost fool yourself. It's surprising how convincing this simple false cut can be...