Splitting a card is tricky, but very simple once you have the knack.
Although, there's quite a few occasions when literally sticking the shim to the back or front of a card with no cover is acceptible. Simply don't show the shimmed side.
I've performed an effect for a number of years which uses a shimmed card prepared in such a way. The shim allows me to pick up the card and whatever card is above (a selection) by placing a card box which has a very thin neo inside... and nobody ever sees the shim.
Card splitting is a trial and error thing... here's some basics...
(NOTE: I don't believe I'm breaking any laws by explaining this, as it's a method which I've known for donkey's yonks which is basically my own perception on how it's done... if I need my knuckles wrapping and this should be edited, please let me know...)
Splitting a card - Seige's method
Firstly, decide which face you want to split off. Bicycle cards are basically three layers... the front, the back, and a card middle. They're all laminated together, but believe me, there are 3 separate elements (at least!).
In this example, I'll be taking off the FACE of the card—discarding the centre layer and back of the card as one (i.e. the centre layer and back will always remain attached)...
So, step one is to soften the card's corner. Hold the card as in fig 1, and tap the corner on a hard surface a few times, moving around the corner's curve until it starts to look a bit frayed.
Next, using a fine blade (I use a No.10 Swann-Morton scalpel... get one, it's essential to your magi's toolkit!), gently separate the layers you want to separate (fig 2). In this case, I want to separate the FACE from the BACK+CENTRE... leaving the back and centre as one.
Tip: DO NOT use the blade to cut... use it to gently separate the cards.
After a while, you'll end up with about a 1/4 inch of card split. FROM THIS POINT you will keep the PART YOU WISH TO KEEP totally flat.
ALWAYS move the UNWANTED layers AWAY from the KEPT layer...
You'll now start splitting by placing the card on a flat surface with the part to keep FACE DOWN. At all times, you will hold the part you want to keep flat, as you gently pull the OTHER PART away, peeling back as you go (fig 3). As you peel further (SLOWLY) you need to advance the fingers holding the 'kept' layer flat, making sure you're as close to the unseparated crease as you can. (fig 4).
After a while, you'll get the hang of it. BUT DON'T GET COCKY... keep going slowly, and try to always keep going at the same angle/direction. (fig 5).
All the way to the bitter end, just go slow, and peel the UNWANTED layers away, never peel the kept layer. If at any point the layer looks like it's thinning or the unwanted layers are starting to tear up, use the blade to fray the card at that point to keep the layers separate.
Finally, VOILA (fig 6), you have a split card. In some cases, BOTH parts of the split are usable.
This method works whether you're keeping the single or double layer.
I've literally just done this as we speak, and even with taking pictures, the whole split took less than 2 minutes.
What now?
You can half-split the card and add a shim. Just a small amount. Or add a magnet. Whatever you like. I recommend a VERY thin layer of rubber cement to put the whole thing back together. Then, put it inside a big hardback book and weight it flat... leave it for a few hours, and you've got a perfect shimmed card.
How to split a playing card by Chris Jones