Ok, I’m sure we’ve all used a coin to settle a difference at one time or another- with one side being ‘heads’ and the other side being ‘tails.’ This heads/tails thing suggests that flipping a coin results in 50% chance heads, 50% chance tails on each toss. But all coins have more than 2 sides, right? Take a U.S. quarter for example, it has Mr. Washington on one side and some other picture on the reverse side (eagle, state, etc). But a quarter also has a side lined with ridges. So this would make every toss not a choice between heads or tails, but of heads, tails and guts (well, maybe it could be called something different). So this would make every toss not a 50/50 chance, but more of a 49.5/49.5/1% thing. Am I making sense? Has anyone’s toss ended on this third side?
heads
| | guts?
tails
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In every coin toss I’ve ever heard about, “guts” would be considered an invalid result and would not count in the tally. Thus, the probability is still 50-50, heads-tails.
It also would depend on how you toss the coin. Most coin tossing I’ve seen is done by throwing the coin up, grabbing it mid-air, then placing it on a flat surface (without looking at it). With this method you would never have a chance of getting the “guts” result.
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I don’t think it’s possible. Even if the quarter does land on its side, there will be the momentum to have it continue and fall over.
While we’re on this subject, how do biased (as they’re referred to in my math book in the probability chapter) coins work? Sure, one side is weighted, but how does it cause it to land on that side? It’s not going to stop in the air and land straight down on that side.
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First, the odds of a coin coming up “guts” are way less than 1%. Presumedly everyone here has flipped a coin at least a few hundred times in their life. Has anyone ever had one spontaneously land on its edge? I think we can safely say “guts” is about as likely as having the coin achieve escape velocity. If you ever flip a coin and fail to get heads or tails, you can either follow PapaBear’s advice and reflip, or take it as a sign from God that you shouldn’t have been asking the question.
As for the bias in favor of the heads side, who says so? It appears to me that the two sides contain a pretty much equal amount of material. If one side is heavier, it might affect the outcome if you spun the coin. But when you flip it, the outcome is determined by which side of the coin hits the table. This is essentially unrelated to which side is heavier. In any event, the sides are too similar to make any possible bias anywhere near 2%.
As for fixing a coin toss, the three most common ways are using a rigged coin with two identical sides, learning to toss the coin so it makes a specific number of flips, and changing the side that’s up after it lands by sleight of hand.
I remember reading in one of those “incredible facts” type books, that a teacher in a probabilties class was flipping a coin to teach a lesson, and it landed guts.
I’ve heard the 51% probability for tails as well. I don’t remember exactly where I heard it, but it was a fairly reliable source, like Games magazine or a statistics manual. Or even the Straight Dope, but I can’t find it in the archives.
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More likely than landing on edge (“guts”???), would be that the coin rolls off the table and is lost under the couch.
The whole point of the coin toss is to have 50/50 odds, so any unusual result (lost coin, land on edge, coin hit by lightning while in air and melted into an unrecognizable blob, etc – any result other than a simple heads or tails) would be excluded.
Same as playing a board game, and you roll the dice and one die falls off the table. You don’t count it, you roll again.
There’s no good way to determine the odds of one of these eccentric results happening, except to stand there and flip a coin a zillion times and record any unusual results (defined as neither heads nor tails). Of course, if you’re flipping the coin while riding a bucking bronco near the edge of a high cliff during a thunderstorm, you’ll probably increase the prospects of getting results other than the simple heads or tails.
I have had a quarter land on its edge once. I don’t remember the reason that I was flipping it, but it landed on its edge and rolled into a groove on a table at a Dairy Queen. It leaned a little to one side, but it did not fall over. Without the groove, I doubt that it would ever do it again. My friends that were with me all laughed (we were pre-teens at the time) and could hardly believe it. Back to the topic of probabilities, the rarity of the coin landing on its edge will in essence still give a 50/50 chance of heads or tails; especially if you consider that most people whom I know catch the coin in the air and then flip it over onto the back of their hands.
I’ve been a casino croupier (ok, crap dealer) for 30 yrs, and on several occasions I’ve seen a chip thrown from the end of the table to the center and come to rest on its side! It’s a rare happening but not impossible. Also on 4 separate occasions I have seen two small cubes thrown over 12 feet, bouncing all over an area 4 ft wide, 14 ft long, and 2 ft deep… only to come to rest, one on top of the other! It’s called stacked dice. ( extremely rare ) Any thing can happen. Considering the 49.9%/49.9% is certainly not out of the question for a coin tossed onto a flat surface.
Im, you are basing the coin probability theory [CBT] on a US quarter, which can land on it’s side, and that factor changes the equation. The CBT is not based on this type of coin.
The number of combinations that a coin can have is two, heads & tails [so no coin has a tail on it anymore, that doesn’t change the theory]. The CBT assumes 2 sides.
NOTE: Theories are always trying to be disproven. If you have a computer simulation of a coin being flipped, it comes out close to 50/50 after a zillion flips, but that itself is no proof of probability [Which is just a theory it’s not a law yet, whew].