# Exact dimensions of a 3-sided coin? **URL:** \ **Category:** Factual Questions\ **Created:** [September 23, 2008, 3:14pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840 "2008-09-23T15:14:11Z")\ **Posts on this page:** 12\ **Page:** 2
**Author:** ![Sapo](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@Sapo](https://boards.straightdope.com/u/Sapo)\ **Post date:** [September 24, 2008, 12:36am UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/21 "2008-09-24T00:36:15Z")
OP checking in. In my OP I did expect the fat coin to be a fair d3. Master Blaster did a good job of explaining why a fat coin could not be a fair d3. After that I insisted in the best approximation I could get with the fat coin anyways. The other better d3s are well known to me and I am not particularly interested in them at this time. If it matters, the scenario I was trying to solve was having to roll a d3 in a lost-in-the-woods situation, where you have some cans among your rations. This is why I can take the floor to be soft and not given to the can bouncing and rolling. Anyways, the question is more academic than practical. So, are we agreeing that d/h=1.5 is close enough? This sounds like a fairly easy to find can model. Time to go to the supermarket with a measuring tape. ---
**Author:** ![Shalmanese](https://avatars.discourse-cdn.com/v4/letter/s/45deac/32.png) [@Shalmanese](https://boards.straightdope.com/u/Shalmanese)\ **Post date:** [November 14, 2008, 7:12pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/22 "2008-11-14T19:12:12Z")
> [@Shalmanese](#): > > I did a computer simulation of this once. The answer is, given sufficient distance to fall, the height needs to be ~1.33 \* the radius. Sorry for resurrecting a zombie thread but I was digging through my old video collection and I realized I meant to upload a video of my simulation but never did. Anyway, here’s me [rolling 100 three sided coins](http://www.youtube.com/watch?v=WFG1OP5OmAw) ---
**Author:** ![muttrox](https://avatars.discourse-cdn.com/v4/letter/m/a8b319/32.png) [@muttrox](https://boards.straightdope.com/u/muttrox)\ **Post date:** [November 14, 2008, 9:19pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/23 "2008-11-14T21:19:32Z")
I don’t see why a tuna can shape couldn’t be fair. I see that it’s not a straightforward calculation. But couldn’t you experimentally flip a bunch of different tuna cans 10,000 times and see what shapes empirically gives you the right results? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 14, 2008, 10:07pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/24 "2008-11-14T22:07:28Z")
Yes, but the empirically correct result would depend on things like what surface you’re flipping them onto. The optimum shape would be different for a hard surface or a bouncy one or a squishy one. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [November 14, 2008, 10:44pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/25 "2008-11-14T22:44:31Z")
This made me wonder about the fairness of ten sided dice. Are they really as likely to roll onto any adjacent face, or are they less likely to switch from a “north” face onto a “south” face? ---
**Author:** ![toadspittle](https://avatars.discourse-cdn.com/v4/letter/t/c0e974/32.png) [@toadspittle](https://boards.straightdope.com/u/toadspittle)\ **Post date:** [November 14, 2008, 10:52pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/26 "2008-11-14T22:52:56Z")
> [@Sapo](#): > > OP checking in. > > In my OP I did expect the fat coin to be a fair d3. Master Blaster did a good job of explaining why a fat coin could not be a fair d3. After that I insisted in the best approximation I could get with the fat coin anyways. The other better d3s are well known to me and I am not particularly interested in them at this time. > > If it matters, the scenario I was trying to solve was having to roll a d3 in a lost-in-the-woods situation, where you have some cans among your rations. This is why I can take the floor to be soft and not given to the can bouncing and rolling. Anyways, the question is more academic than practical. > > So, are we agreeing that d/h=1.5 is close enough? This sounds like a fairly easy to find can model. Time to go to the supermarket with a measuring tape. Boy, you’re a SERIOUS gamer if you’re looking to keep playing D&D when lost in the woods. 🙂 ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [November 14, 2008, 11:46pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/27 "2008-11-14T23:46:24Z")
> [@Lumpy](#): > > This made me wonder about the fairness of ten sided dice. Are they really as likely to roll onto any adjacent face, or are they less likely to switch from a “north” face onto a “south” face? You might be able to come up with a way to roll it so that it would tend to land either north or south. But with a regular die you can do this too. If you drop it without rolling, with the six on top, you can get it to roll sixes more often, just from the cases when it lands flat and doesn’t roll. If you shake it loosely in your hand before rolling, the tendency to switch from north to south, and from south to north, will cancel out. ---
**Author:** ![Sapo](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@Sapo](https://boards.straightdope.com/u/Sapo)\ **Post date:** [November 15, 2008, 10:15am UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/28 "2008-11-15T10:15:44Z")
> [@Shalmanese](#): > > Sorry for resurrecting a zombie thread but I was digging through my old video collection and I realized I meant to upload a video of my simulation but never did. > > Anyway, here’s me [rolling 100 three sided coins](http://www.youtube.com/watch?v=WFG1OP5OmAw) Cool. Did you get the results from these rolls? I don’t see too many falling on edge. ---
**Author:** ![Sapo](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@Sapo](https://boards.straightdope.com/u/Sapo)\ **Post date:** [November 15, 2008, 10:17am UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/29 "2008-11-15T10:17:08Z")
> [@toadspittle](#): > > Boy, you’re a SERIOUS gamer if you’re looking to keep playing D&D when lost in the woods. 🙂 Call it LARP, if you want. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [November 15, 2008, 2:49pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/30 "2008-11-15T14:49:45Z")
> [@Lumpy](#): > > This made me wonder about the fairness of ten sided dice. Are they really as likely to roll onto any adjacent face, or are they less likely to switch from a “north” face onto a “south” face? It is trivial to make fair even sided die. Construct 2 n-sided pyramids and glue the bases together. The picture on the left [here](http://en.wikipedia.org/wiki/Pentagonal_trapezohedron) seems to show a related 10-sided die. The bases are not aligned, so some rounding has been done to the edges. An less rounded version is shown on the left but note the sides are not flat. To get an odd sided fair die, construct one with twice as many sides and pair up sides. Whole lot easier, and more accurate, than futzing with tuna cans. It all comes down to symmetry. Can you rotate/flip/etc. the die from one face up to another face up so that it looks exactly the same except for labelling? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 15, 2008, 7:09pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/31 "2008-11-15T19:09:55Z")
> [@](#): > > The picture on the left here seems to show a related 10-sided die. The bases are not aligned, so some rounding has been done to the edges. An less rounded version is shown on the left but note the sides are not flat. The skew of the two pyramids is so that there’s a flat face on top when it lands, instead of an edge. This does not require rounded edges or curved faces; what it does require is non-triangular faces (they come out kite-shaped). ---
**Author:** ![Shalmanese](https://avatars.discourse-cdn.com/v4/letter/s/45deac/32.png) [@Shalmanese](https://boards.straightdope.com/u/Shalmanese)\ **Post date:** [November 15, 2008, 11:25pm UTC](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840/32 "2008-11-15T23:25:22Z")
> [@Sapo](#): > > Cool. Did you get the results from these rolls? I don’t see too many falling on edge. Yeah, the answer was in the quote: h = 1.33r. In that simulation, it was 33.35% side after 50,000 simulations. [Previous page](https://boards.straightdope.com/t/exact-dimensions-of-a-3-sided-coin/464840.md?page=1)