Well, I did a bit of digging around online, and found out some interesting things about the ‘Greed$’ game I told you about yesterday. Apparently, there’s a version of it that you just play with ordinary dice, but somebody figured that they could put Greed into practice and make a buck by selling the customized dice and pre-printed score cards. And it’s based on an older folk dice game called Farkle.
The good thing about this is that there’s already a fair bit of analysis up on the web regarding Farkle probabilities, such as this helpful post on the Solarium blog, and a Farkle Fun page with a whole bunch of supporting math.
I’ve drawn on their work to attempt an analysis of the four-die case. There’s still a mistake in my numbers somewhere, because the probabilities are adding up to 1.02461 😦 I may have to write a quick die-rolling simulator, as Greg at the Solarium did, to see where the error lies.
But what I’ve got suggests that in Greed$, the immediate expected value of rolling 4 dice is something like 134 points, and the chance of zilching out is only 15.74%, suggesting that the break-even point is much more than you could possibly bank with two dice, therefore, unless you’ve already reached the point where you’re certain to win the game, it’s a good idea to roll those dice.
And, interestingly enough, that expected gain from 4 dice is just about 50 points more than the expected gain from 3 dice, suggesting that if you have a choice between banking a G as a third die, or re-rolling it, you’d be better off to reroll; it’ll pay back on average just on immediate scores, it’ll reduce your chances of zilching out from 27.8% to 15.7% (which could save you whatever else you have banked,) and it gives you the option to re-roll or bank if you roll a single point die out of four.
Okay, I think that’s it for tonight. And do let me know if you’d rather I get back to blogging about writing, instead of continuing to geek out over dice and probability math. Who knows, I might oblige you.