Kleinman settlement equations
Join Date: Feb 2016
Posts: 2
Hi All,
I am currently reading Danny Kleinman's "Vision Laughs at Counting". On page 238 he calculates settlement values, but I'm afraid I can't resolve the final equation.
So let:
Cube = Q
Winning Rolls = W
Losing Rolls = L
Therefore, the settlement value can be calculated as : Q(W-L)/36.
Now, since L = (36-W) the above equation can read: Q(W-(36-W))/36.
However, I don't understand the next step, viz:
The above equations can be stated as: (QW/18)-Q, apparently.
Can anyone show me, in detail, how we get from equation 2 to equation 3, please?
No doubt a ten year-old could solve this, but...................
Many thanks.
Join Date: May 2004
Posts: 1,954
Are you really supposed to be able to do all this over the board?
I'd recommend just skipping all this and playing the game to a conclusion. Or take a guess. You won't win any popularity contests with your fellow chouette players if you're stopping the game to do these calculations.
Join Date: Jan 2003
Posts: 4,623
I have no idea what you are trying to do here and Robertie is probably correct to say this is a pointless exercise, but here is the math you are struggling with.
Q*(W-(36-W))/36
Q*(W-36+W)/36
Q*(2W-36)/36
(2WQ-36Q)/36
2WQ/36-36Q/36
WQ/18-Q
Join Date: Feb 2016
Posts: 8
I agree with Bill Robertie too.
Join Date: Jan 2016
Posts: 30
I've not seen this formula before but it looks quite neat. (QW/18)-Q When I plug in a tied game where there are 18 winning shots on a 2 cube the settlement is (2*18/18)-2 = 0, and when all the shots are winners the settlement is (2*36/18)-2 = (2*2)-2 = 2 which is what you would expect. With 24 winning shots (2*24/18)-2 = 0.67. This is trivial and you should just play it out, but what if your playing 5 players and the cube is turned to 16. I think that could be a different story. Settlement in that case would be (16*24/18)-16 = 5.33.
Join Date: Feb 2016
Posts: 2
Thank you all for taking the time and effort to reply to my post.
I would not delay a game by trying to figure out such equations, but I really did want to know what the answer was. Many thanks, MarkD, for the explanation. I knew I was being extra stupid.
Nonetheless, I believe it is important to be able to figure out settlements accurately. After all, settlements are part of the game and, as Trunky points out, there may be times when the numbers will be large.
Again, many thanks to all.
