We know that human brains use patterns (or schemata) to figure out the world and decide what to do. This kind of cognitive activity takes place very quickly, which means we can react quickly to the world around us, as long as the pattern holds.
Here’s a pattern (or schema) that your brain may know: to put a card in a slot, use the narrow edge. If the card has a clipped corner, use that edge. Some examples:
This pattern is easy for your brain because of the physical cues—also known as affordance. The narrow edge + clipped corner say: “This side goes in.”
A pattern that’s harder for your brain to learn is the magnetic-stripe bank card. You have to think about which way the stripe goes. And it seems harder when you’re in a hurry, or when you feel less safe. Have you used an outdoor bank machine at night, with people hanging around?
Vancouver transit tickets are awful because they don’t follow the card-in-the-slot pattern correctly. As a passenger on the SkyTrain (overhead subway line), you must punch your ticket at the station entrance. The machines are placed so you must turn your back on the drug dealers and their customers who hang out in the subway. As with bank cards, these transit tickets fit four ways, but only one will punch the ticket, and it’s not the edge with the clipped corner. There’s a yellow arrow to assist, but while the arrow is clearly visible in daylight, it’s almost invisible in the yellow-tinged fluorescent lighting of most SkyTrain stations. Also, the yellow arrow must be face down, which is counterintuitive because then you cannot see it. In the photo (above, right), can you find the arrow on the ticket?
Did the designers consider how their ticket machines or bank cards would make passengers feel? Designing for emotion seems to have legs, these days, but it’s not a new idea.
Doing better. 
I wonder whether the designers of these systems (transit tickets, bank cards) considered all possible options. It’s a Five Sketches™ mantra: You get a better design when you first saturate the design space. This can include doing a competitor analysis to seek out other ideas. And there are other models for transit tickets. I’ve seen Paris subway tickets with the magnetic stripe in the middle, so passengers could insert the ticket face up or face down, frontwards or backwards. The more recent tag-on/tag-off technology used from London, UK, to Perth, WA, avoids the insert-your-card problem—though the overall experience may be worse, since failure to tag off means paying the highest possible fare.
As for bank cards, IBM’s designers must have modelled bank cards on credit cards, which had the magnetic stripe toward the top instead of in the middle. This doubles the customer’s chances of inserting the card incorrectly. An obvious question to have asked at the design stage: can we design a bank machine to read the card regardless of how it’s inserted?