The game traditionally played with the dreidel is unfair, as Ben Blatt showed by simulation and Robert Feinerman showed analytically, but this is assuming that all four sides of the top are equally likely to come up when it is spun. The Nemiroffs took this one step further and checked whether the four sides of the dreidel are equally likely to come up. They took three dreidels and spun them (800, 1000, and 750 times respectively) and showed that these dreidels were unfair even in this more basic sense.
Interestingly, the patterns seem to tell a story about how the dreidels the Nemiroffs used were flawed. I reproduce their Table 1 here (and yes, they had a dreidel with Christmas imagery on it…)
|Driedel||ג (gimel)/ Santa||נ (nun)/ candy cane||ש or פ (shin or pei) / tree||ה (he) / snowman||total spins|
The letters נ (nun) and ה (he) appear opposite each other, as do ג (gimel) and whichever of ש or פ (shin or pei) is used. So what we see here is that:
- on the “old wooden” dreidel and the “santa” dreidel, two sides opposite each other are preferred – perhaps the dreidel is slightly wider in one direction than the other
- on the “cheap plastic” dreidel, one side is preferred and the side opposite it is dis-preferred – perhaps the dreidel is slightly heavier on one side or the handle is slightly off-center.
Presumably dreidels are allowed to be so unfair because nobody is playing dreidel for high stakes, so there’s no real incentive to construct the things properly.