The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include, as subclasses, the scoring games considered by Milnor (1953), Ettinger (1996) and Johnson (2014. We present the structure of GS and the techniques needed to analyze a sum of guaranteed games. Firstly, GS form a partially ordered monoid, via defined Right-and Left-stops over the reals, and with disjunctive sum as the operation. In fact, the structure is a quotient monoid with partially ordered congruence classes. We show that there are four reductions that when applied, in any order, give a unique representative for each congruence class. The monoid is not a group, but in this paper we prove that if a game has an inverse it is obtained by 'switching the players'. The order relation between two games is defined by comparing their stops in any disjunctive sum. Here, we demonstrate how to compare the games via a finite algorithm instead, extending ideas of Ettinger, and also Siegel (2013).
We show how to use recursive function theory to prove Turing universality of finite analog recurrent neural nets, with a piecewise linear sigmoid function as activation function. We emphasize the modular construction of nets within nets, a relevant issue from the software engineering point of view.
For games of complete information with no chance component, like Chess, Go, Hex, and Konane, some parameters have been identified that help us understand what makes a game pleasant to play. One of these goes by the name of drama.
Briefly, drama is linked to the possibility of recovering from a seemingly weaker position, if the player is strong enough. This is an important requirement to prevent initial advantages to be amplified into unavoidable and thus uninteresting victories. Drama is a feature that arguably good board games should have, since it is relevant in the perception of the play experience as pleasant.
Despite its intrinsic qualitative nature, we suggest the adaptation of the concept of drama to games of pure chance and propose a set of objective criteria to measure it. Some parameters are here used to compare Goose-like games, which we compute via computer simulation for some well-know games. A statistical analysis is performed based on the play of millions of matches done by computer simulation. The article discusses correlations and patterns found among the collected data. The methodology presented herein is general and can be used to compare other types of board games.
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