Yahtzee probability

[geroldsh]

Hello.
I have a probability question that someone may be able to help me with. I've written a Yahtzee program that comtains several different Yahtzee games. I also wrote my own version. It contains regular Yahtzee with a color variety. In the color variety there are six different colors that are randomly assigned to each face of the five dice on each roll. A regular Yahtzee contains the same value on each of the five dice and is awarded 50 points. I award 50 points for five dice with the same color (flush). I am not sure of the probability of rolling a Color Yahtzee: that is five dice with the same value and also the same color. I currently award 150 points for it. Can anyone show me how to calculate the probability of rolling the combination above (there are a total of three rolls to achieve this combination of values and color. Dice can be placed in a hold state (not rollable) or a free state (rollable ). Thats for any help.

[damasterjo]

try this
http://mathforum.org/library/drmath/view/52174.html
and this
http://mathworld.wolfram.com/Yahtzee.html

[geroldsh]

Thanks, damasterjo, for the links. I'm not seeking information on the basics of the game; I have already written my program in VB 2005 that works very nicely. You can play the following games of Yahtzee: Standard, Triple, Swedish, Kismat, Maxi, and my own variety called Rainbow. Basically, I just want to award enough points for a roll consisting of five dice with the same value (for instance 4,4,4,4,4) and also the same color (red,red,red,red,red). On any given roll, each dice face can have a random color (red, cyan, yellow, green, blue, or purple), and also a random value (1,2,3,4,5,6). So, I guess you have a one in six chance of rolling a 1 and a 1 in six of rolling a red. Is that a one in 36 chance of rolling a red 1?

[bilm_ks]

Yes, one dice six colors 6*6 = 36 cases. With five dices 36^5. So one in 36^5 chance for 4,...,4 and red,...,red but much better chances for 1,2,3,4,5 and red,...,red((36^5)/5! cases)