Gamers everywhere, rejoice: researchers have discovered that it is possible to transform any shape 鈥� from dragons to kittens 鈥� into a fair die, making it suitable for playing games that rely on random outcomes.
鈥淲e started from the idea of: 鈥業f you look at an object, can you tell its resting probabilities?鈥欌�� says at Carnegie Mellon University in Pittsburgh, Pennsylvania. In other words, if you roll a particular shape, what is the probability it lands in a particular orientation?
To answer this question, Crane and his colleagues developed a geometric model to compute the resting poses of any object. Rather than physically simulate the object, the model maps the corners, edges and faces of that object onto a sphere, allowing the researchers to describe how it would fall under gravity before coming to rest. For example, if a corner is the first part of the object to touch the ground, it will then fall onto an edge determined by the position of its centre of mass, and from there onto a face.
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鈥淭he big deal about what we鈥檙e doing is that we can just bypass the simulation entirely and understand these probabilities from a much simpler geometric picture,鈥� says Crane. That then enables the design of odd-looking dice, by tweaking a shape until its resting positions match the desired probabilities.
Using their model, the researchers 3D-printed seven unusual designs. These included armadillos and kittens, both designed to land in one of three orientations with equal probability, and more exotic concepts, like a single die with probabilities equivalent to rolling two standard six-sided dice.
To test each of the dice, the team dropped them from the same height onto a hard wooden floor between 100 and 1000 times, with different people throwing the dice to limit bias, and counted how often they landed in each orientation. The probabilities produced by these real-world tests came within 3 or 4 per cent of those predicted by their model.
at Oklahoma State University says the work is 鈥渧ery cool鈥� but isn鈥檛 鈥渘ecessarily a silver-bullet solution to designing weird dice鈥�. For example, the team鈥檚 method doesn鈥檛 incorporate the effects of momentum, friction or bouncing when rolling dice. 鈥淚t鈥檚 more like they are 鈥� very efficiently 鈥� predicting where a die ends up if you put it down with a random orientation on a non-slip surface in low gravity. It slowly falls over and rolls down to land, without slipping or bouncing,鈥� he says.
鈥淐harming as it might be, it has very little to do with real dice rolling under real circumstances,鈥� says at Stanford University, as the number of real-world tests is too small to draw significant conclusions. Crane says the work is not an 鈥渋deal solution鈥� to the problem, but he was surprised by how momentum seemed to play only a small role in the outcome of rolling the dice.
