Honestly, I don’t know where these ideas come from (and for that I apologize).
I was taking out a caffeinepill this morning and I happened to drop it and instead of it landing on one side, it landed standing up. I’m sure the astute ones here know where I’m going with this.
Ever since I’ve been a kid I’ve learned and recited that when flipping a coin and letting it land there’s a 50-50 chance it will either result in heads or tails. But what about the fact that it could theoretically land standing up? So taking that into account it’s no longer a 50-50 chance of heads or tails, rather a 49.999999-49.999999* chance. Am I correct in assuming this?
I’ve never seen this done, and I’m sure none of you have either. But wouldn’t it be so cool and satisfying if you accomplished the feat?
***** I chose that very number of nines by random, but I’m sure you guys get the point.
All probabilities are just human models of real life anyway. I’d think of the coin odds as “It’s 50-50 for heads or tails, for all practical purposes”
There’s always the odds that the aliens will take that moment to invade, mistake the coin for an actual leader / monarch and abduct it in the hope of undermining our ability to govern ourselves.
Depends on how you’re approaching the problem. Someone could grab the coin out of the air before it lands, too. What about that? Of the coin could land in that crack between the baseboard and the shoe molding. Or it could drop into the heating vent, in which case you’re in some kind of Schroedinger’s cat situation until you pry open the vent and fish it out.
Point is, when we talk about flipping a coin, we simplify the problem by ignoring unlikely outcomes. We even ignore any asymmetries in the coin itself that might prejudice the outcome.
Now, if you want to include “landing on an edge” as a third outcome (or dropping behind the shoe molding, or whatever) then you can, but assigning the correct probability for such an unlikely outcome is tricky. Much easier to round off the 50/50 and be done with it.
Actually, I did once see a flipped coin come up “edge”. We were deciding which team would have first possession in a basketball game, or some such, and the coin landed on the gym floor, rolled on its edge to the wall, hit the wall, and stopped.
This may be true, but neither bumping off the edge nor spinning is the same as flipping. All US coins are close enough to 50-50 as to be indistinguishable for any practical purpose.
For the purposes of flipping a coin, what matters is that the probability of either side are the same. The probability of an “edge” is irrelevant as long as you know how to handle that unlikely case. Even if you are flipping a tuna can with a really high chance of landing on edge, all you have to do is agree to flip those again.
In RPGs, we often needed to roll d7 or d9. We just rolled a higher die (d8 or d10) and rolled again the invalid results (8 or 10).
I once heard a lecture by a magician/probabilist (he began his career as the first, then switched to mathematics. He claimed that it is virtually impossible to flip a coin fairly. His definition of a flip was to launch it off the edge of a finger straight up and catch it on the way down (obviously other modes are possible). The problem, as I understand it, is to make the axis of spin perpendicular to the edge of the balancing finger. If you can make it less that 45 deg, the coin will appear to spin, but never actually turn over. Things do not change much if you use the NFL flip (coin lands on the ground).
