# Complex Hearts

The game of complex hearts, is pretty much like the regular old card game of hearts, except that scoring is modified slightly to include complex values. The origins of the game are from none other than Richard Garfield, Magic guru. The instructions first appeared in an issue of Games magazine.

**Complex Numbers**

You know what complex numbers are, right?

**Revised Scoring**

**Card values**

All s | 1 point |

Q | 13*i |

J | -10 |

10 | *2*i |

The 10 requires more explanation. Acquiring it, multiplies your score for a given hand by 2*i. For example, for a given hand, you took 5s, Q , and the 10 . Your score for this hand would be: (5 + (13*i))*(2*i) = -26 + 10*i.

**Shooting the moon (updated Jan 21, 1998)**

If you successfully shoot the moon (ie, you get all the hearts and
queen of spades), you can choose to do one of the following:

- subtract 13 + 13i from YOUR score.
- add 13 + 13i to everyone else's score.

(remember J is -10, and 10 multiplies score by 2i. )

The jack and 10 are independent of shooting the moon. If you get these too, it'll usually result in a detrimental effect on your score! So, for example, if you shoot the moon AND get the 10, then you will end up with 26 - 26*i to subtract from your score (or to add to everyone else's).

**Winner/Loser**

The first person with a score with magnitude 100 loses. The
magnitude, or absolute value, of a complex value is the square root
of the sum of the squares of the real and imaginary values:
given a complex number, a + bi, it's magnitude is
sqrt(a^{2} + b^{2})