Dreidel is Not Fair

December 4, 2015 at 6:47 am Leave a comment

Dreidel

play an online version of dreidel at the Jewish Outreach Institute (but turn the sound off)

Is dreidel fair?

The rules of dreidel are straightforward. At the beginning of each round, players put one coin into the pot. (For young kids, the “coins” are actually chocolate pieces in the shape of a coin and wrapped in gold foil. This is known as geld, and as far as I’m concerned, chocolate is a currency to kids.) Players then take turns spinning the dreidel, and a reward is earned based on which of the four Hebrew letters appears on top when the dreidel stops spinning:

  • Nun: nothing.
  • Hey: half the pot.
  • Gimel: all of the pot.
  • Shin: put one in.

Play continues clockwise, with each person spinning the dreidel until Gimel occurs and all coins are removed from the pot. At that point, everyone antes another coin, and a new round starts with the next player.

Officially, a player is out of the game when she or he has no coins left to contribute to the pot, and the game ends when one person has all the coins. But practically speaking, the game often ends much earlier, because players get bored and quit or, in the case of very young kids, the game lasts beyond bedtime and the children are pulled away by their parents.

No matter how the game ends, though, it’s not fair.

The following table is courtesy of Paul J. Nahin (Will You Be Alive 10 Years from Now?, Princeton University Press, 2014, p. 81). It shows the amount, over the long run, that each player will win during a dreidel game.

Player
1 2 3 4 5
Number
of
Players
2 1.143 0.857
3 1.361 0.956 0.680
4 1.617 1.102 0.757 0.524
5 1.900 1.267 0.855 0.580 0.398

In other words, the first player has a significant advantage over the others. In a game of five players who start with 10 coins each, the first player will finish the game with 19 coins, on average, whereas the fifth player will finish with just 4 coins. That’s if the game ends early. If played until one person gets all the coins, then the first player is five times more likely to win than the fifth player.

This disparity in odds is likely the reason that an unofficial rule of dreidel is that the youngest player goes first, the second-youngest player goes second, and so on.

The word dreidel is Yiddish and means “to turn around.” Because the dreidel is, after all, a top.

Explicit LyricsThis fact is not lost on comedian Lewis Black, who has some thoughts on the matter.

Happy Chanukah!

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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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