// Functions for predicting lottery or Keno probabilities.

// balls is the number of total balls to draw from
// drawn is the number of balls actually drawn from the above pool
// chosen is the number of balls chosen by the player
// matches is the number of balls chosen by the player that match drawn balls
lottery[balls, drawn, chosen, matches] :=
{
   binomial[chosen, matches] * binomial[balls-chosen, drawn-matches] /  binomial[balls,drawn]
}



/* Powerball Examples:

   NOTE:  The rules below may change.  The rules were changed for the
   2015-10-07 drawing and later, and may change.  For official payoffs see:

   http://www.powerball.com/powerball/pb_prizes.asp

   Powerball draws five white balls out of a drum with 69 balls and one red
   powerball out of a drum with 26 red balls.  To win the grand prize, you
   must match the 5 hite balls (in any order) and the red powerball.

   To calculate the odds of winning the grand prize, you would do:
   lottery[69, 5, 5, 5] * 1/26

   To calculate the odds of matching 5 white balls but NOT the powerball (this
   is a $1 million prize):
   lottery[69, 5, 5, 5] * 25/26

   To calculate the odds of matching exactly 4 white balls AND the powerball:
   lottery[69, 5, 5, 4] * 1/26

   To calculate the odds of matching exactly 4 white balls but NOT the
   powerball: 
   lottery[69, 5, 5, 4] * 25/26

   ...

   To calculate the odds of matching 1 white ball and matching the powerball:
   lottery[69, 5, 5, 1] * 1/26

   To calculate the odds of matching no white balls but matching the powerball:
   lottery[69, 5, 5, 0] * 1/26

   To calculate the odds of matching nothing at all:
   lottery[69, 5, 5, 0] * 25/26
*/