Death by Plastic Caltrop? Death To Plastic Caltrop!

Man, do I hate d4's. I stepped on an old untumbled d4 once, and it was bloody murder, but that's not why I hate d4's.

• I hate them because they don't roll like normal dice.
• There's a single motion that makes a d6 bounce a couple times, and a d12 or d20 roll across the table. Most of us have that motion as muscle memory, and we do it automatically. (I know one gamer who just can't roll dice, but that's another story). But apply that same motion to a d4, and it just flops onto the table and lays there.
• As a result, you have to think before you roll them. You either have to really bounce them around in your hollow cupped fists, or throw them high into the air and impart a spin. Anecdotal evidence over the years tells me that most gamers can't parse the motion of rolling d4s at the same moment they are doing math. In a really rules-light game it's no big deal. But if you have to add numbers together, apply modifiers, or choose the highest die, the parts of the brain the get used to do so are not the same as the part of the brain reminds you to roll your d4 differently. Either you roll them the wrong way, or it slows down the process as you transition between dice and math.
  
• Rolling them the wrong way results in the same number getting rolled again and again. It's an honest mistake, almost never is it cheating. It's the just the reality of how the d4 fails to tumble if thrown with the wrong motion.
• That it has only 4 sides compounds that. A d20 that never flips more than one adjacent side wouldn't be a problem, since the "20" is next to the "2", the "8" and the "14". There'd still be plenty of variation from roll to roll.
• What's more, if someone rolls a "20" on, say, 5 consecutive rolls of a d20, you know the odds are seriously against it, and they know it too. You can suggest they need to shake the dice more, without it sounding like an accusation of cheating. Hell, if you think they are cheating, you can say it to their face, and they'll forgive you for thinking that, 'cause it looked mighty suspicious. But, "4" on 5 consecutive rolls, given all the above factors, doesn't strike most people as all that unlikely. But the chances are actually less than 1/10th of a percent. Most people just don't realize the odds are that extreme. Roll 5d4 a thousand times, and you'll probably get that maximum total (5 fours) just once - assuming the dice are being rolled in a truly random fashion, and d4s rarely are.

So, we have all that related die-rolling trouble, and we compound it with a variety of other minor strikes against the d4.

• Most games want you to roll high, but these are the smallest / lowest-rolling standard dice. Your own psychology is wired to get excited when you roll high, but again, you can't.
• Rolled in multiples, d4s create very steep bell curves. Fewer but larger dice create a more gentle curve.
• d4s come in top-reading and bottom-reading variants which can be disorienting if borrowing or mixing dice.
• That same variance makes it harder for a GM to casually spotcheck a player's rolls from a distance. As I said on the first list, it's harder to document cheating via d4s since a bunch of 4s doesn't stand out like a bunch of 20s does - so making it harder to surreptitiously read the dice sure doesn't help the situation.
• Q-workshop accidentally produced some beautiful but defective dice with bottom-reading d4s that escaped quality control since the numbers were so strangely placed. We used to have some at the games store I managed. They looked cool, till you rolled a 4...or was it a 2... well, these twos sides say "4"... but that one says "2". Grrr... I paid $20 for these?!?
  
• And yes, they hurt if you step on them.

For all those reasons, I hate d4s. When I'm designing / homebrewing game systems, I avoid d4s if at all possible. When I'm making characters, I avoid any powers or stats that will force me to roll a d4.