This is for Classic SDG CSP T Ball:

Break-even prices for the first 22 relations.

Think of them as phase transitions (boiling point, freezing point)
of pure chemical substances.

Relation : bmax : f[bmax]
0 : 0.0 : 0.0
1 : 0.0 : 1.0
2 : 0.3333333333333333 : 0.14814814814814814 = 4/27
3 : 0.0 : 1.0
4 : 0.3333333333333333 : 0.14814814814814814 = 4/27
5 : 0.0 : 1.0
6 : 0.3333333333333333 : 0.2962962962962963 = 8/27
7 : 0.0 : 1.0
8 : 0.6666666666666666 : 0.14814814814814814
9 : 0.0 : 1.0
10 : 0.5 : 0.25
11 : 0.0 : 1.0
12 : 0.5 : 0.25
13 : 0.0 : 1.0
14 : 0.42264973081037427 : 0.38490017945975047
15 : 0.0 : 1.0
16 : 0.3333333333333333 : 0.14814814814814814
17 : 0.0 : 1.0
18 : 0.3333333333333333 : 0.2962962962962963
19 : 0.0 : 1.0
20 : 0.3333333333333333 : 0.2962962962962963
21 : 0.0 : 1.0
22 : 0.3333333333333333 : 0.4444444444444445

When we mix substance 1 and 22, there is a "chemical reaction"
and the boiling point goes down to: 27/64 = 0.421875.
The worst mixing ratio is 0.25 for 1 and 0.75 for 22.
How to reason about this will be when we leave the training
ground of T Ball.

See also:
/home/lieber/.www/courses/csu670/sp09/preparation/requirements-analysis/single-rel-preds