The engravings on most coins are not exactly the same on both sides. Wouldn’t this cause a tiny bias when tossing coins to measure 50/50 probability. A United States penny has Abraham Lincoln on one side and the Lincoln Memorial on the other side. I can’t imagine that both sides would contain the exact same amount of metal on both sides. So are virtually all actual coins not usable for probability experiments?
I found a paper on this, apparently it’s more likely to land on the side it starts on, most of it has to do with how it’s flipped judging by the abstract. However, it also says that a natural/perfect flip is about 1% more likely to land on the side that was face up when you started.
On the other hand, if you put a coin on edge on the table and spin it, it can have considerable bias, as great as 80-20 for some coins. So if anyone ever offers to bet you on the outcome of a spun coin, don’t take it.
A coin-toss coin could not be exactly the same on both sides either. Why would it be any different from a money coin?
I can see how the difference in weight on each side would affect a spin, as Chronos notes. But how would it be relevant in a toss?
You mean a metal disc made especially for tossing? I guess you are right that it could not be exactly the same on each side: for one thing, you need to be able to tell the sides apart. However, it would not be difficult to make it a lot closer to being truly fair than a money coin is.
Even if the paper Jragon found is right, it is not really to the point of the OP’s question. I am not sure I believe it anyway, though. For one thing, why are they apparently not seeing any effects of the differences between the two sides, the sorts of effects Chronos is talking about in spinning? (I did not read all through, but from the photo it looks like they used regular quarters.) Also, the fact that the authors are all mathematicians makes me wonder whether they really know how to set up an experiment like this properly, and control properly for possible biases in the apparatus.
ETA: I am not exactly sure how to answer Rigmarole’s question, but it certainly seems to me that it ought to make a difference. It is possible to make deliberately biased tossing coins, is it not?
You mean homogeneous flat cylinders where the only bias comes from the engravings on the sides? From my ignorance I cannot really see how you could put some serious bias to them.
Casinos make a lot of money on 51:49 odds, so you don’t really need that serious a bias to make out like a bandit.
It could be that they’re not seeing those effects because they’re simply not there, or are so small that they might as well not be. I suspect that the spinning bias depends more on irregularities in the edges than on the faces (for instance, if the coin is actually a frustrum of a long cone, rather than a true cylinder).
How about making your fake coin out of two discs, of different metals with different densities, welded or otherwise stuck together? (If necessary it could then be plated with a thin metal layer for disguise.)
US cents with the Lincoln Memorial have Abraham Lincoln on both sides, though you might have to use a magnifier to see him in the Memorial.
In watching the ceremonial coin tosses in the last round of bowl games, it seemed to me the tossing was poorly done. In some cases, there was barely a half-turn.