Described below is a modified version of Zombie dice ( http://www.sjgames.com/dice/zombiedice/ ) which the kids and I play.
As in the original game, the idea is to sequentially roll sets of 3 specialty dice (described below and in the link above) until you either voluntarily stop rolling or bust.
There are green, yellow an red dice whose faces show:
Green: 3 brains, 1 shotgun blasts, 2 footsteps
Yellow: 2 brains, 2 shogun blasts, 2 footsteps
Red: 1 brain, 3 shotgun blats, 1 footsteps
After each roll, you accumulate either brains (you ate your victim's brains) or shotgun blasts (victim shot you); footsteps are neutral (victim ran away).
If you choose to stop rolling, you get 1 point for each accumulated brain. You bust when you accumulate 3 shotgun blasts and receive no points in that game.
Instead of picking the dice blindly from a bag, as called for in the original version rules, we let the players pick which 3 dice to roll of any color available.
Obviously, nobody in his right mind would roll anything other than the green dice, since they have the most brains and least shotgun blasts.
We modified the rules by somewhat arbitrarily awarding 1 point for each green die, 2 points for a yellow die and 5 points for a red die.
So, the riskier the dice you select to roll, the more points you stand to get. This introduces a nice risk/reward element to the game.
Here is where you come in. I don't know whether our 1:2:5 point ratio is the fairest, that is, the one that balances the risk/reward of each die color.
So: What should be the fair point value of each color die?
I don't know whether one can calculate the desired values. Naturally, I could do a simulation by rolling, say, 1,000 games with each color dice and tallying the average number of brains accumulated right before the bust for each color; then, I would derive a factor by which to the yellow and red dice that equates the average outomes of the three colors.
Also, I could but now don't have the tools (e.g., a BASIC interpreter) to write a simulation program, or the time to manually do the simulation.
What say you is the right green:yellow:red ratio?
BK asked: "For one's turn must the same 3 dice be rolled each time or may one switch back and forth?"
LB says: No, you can switch dice.
After each roll (except if you bust, of course) you:
Keep the brains.
Keep the shotguns.
Return the footsteps to the dice cache.
Pick any 3 dice from the dice cache, if you want to roll again, and roll.
Note that as a game progresses and players accumulate brains and shotguns--depleting the dice cache--there will be times when a player's dice choice is limited by the dice then remaining in the cache. However, this does not happen often (we actually use 2 sets of Zombie dice and may even buy a couple more so there will always be plenty to pick from). Also, when there are fewer than 3 dice left in the cache, we replenish it by writing down on a Post-it the number of brains each player has and returning back to the cache their brain dice (could also do it for the shotguns be don't). So I think reasonable to disregard the dice depletion for our purposes.
Dr. Tim Chow suggested I ask y'all. http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=139865
I hope you find this problem interesting enough to give it a shot.
Thanks in advance for taking the time to read this message and for hopefully figuring out the answer to the problem.