In this work we study the following problem, from a computational point of view: If three points are selected in the unit square at random, what is the probability that the triangle obtained is obtuse, acute or right? We provide two convergent strategies: the frst derived from the ideas introduced in [2] and the second built on the combinatorics theory. The combined use of these two methods allows us to address the random triangle theory from a new perspective and, we hope, to work out a general method of dealing with some classes of computational problems.

Starting from a very simple economic scenario, we build on it a game and then we introduce a general strategy able to reduce a regression problem to an equivalent binary classification problem. This reduction scheme (that we call adaptive reduction or also dynamic reduction) can be also used to derive a new boosting algorithm for regression problems named bOOst^d. The bOOst^d algorithm is very simple to implement, and it can use any learning algorithm with no priori assumptions. We present a conjecture for bOOst^d performances, which ensures a little error on training set. More important we can also provide a very good theoretical upper bound for the generalization error. We give a set of preliminary experimental results that seems to confirm our conjecture for bOOst^d performances on training set and the theoretical assumptions for the generalization error. We also provide a possible justification of why boosting often does not overfit. Finally, we leave some open problems and argue that in the future an adaptive single boosting (with an unique code) algorithm for binary, multi class and regression problems can be derived.