Searching with Analysis of Dependencies in a Solitaire Card Game

Abstract

We present a new method for taking advantage of the relative independence between parts of a single-player game. We describe an implementation for improving the search in a solitaire card game called Gaps. Considering the basic techniques, we show that a simple variant of Gaps can be solved by a straightforward depth-first search (DFS); tuming to variants with a larger search space, we give an approximation of the winning chances using iterative sampling. Our new method was designed to make a complete search; it improves on DFS by grouping severa! positions in a block, and searching only on the boundaries of the blocks. A block is defined as a product of independent sequences. We describe precisely how to detect interactions between sequences and how to deal with them. The resulting algorithm may run ten times faster than DFS, depending on the degree of independence between the subgames.

Determining Solvability in the Birds of a Feather Card Game

“…As a result, there is less emphasis in BoaF on efficient moves as there is on accurate moves, and algorithms accordingly focus more on intelligent move selection and pruning of the search space. This logic relates to work on deadlock patterns by Paul and Helmert (2016), and is strikingly similar to ideas proposed by Helmstetter and Cazenave (2003). In fact, many parallels exist in limitations and patterns based on state positions in BoaF and Gaps (Helmstetter and Cazenave 2003).…”

“…This logic relates to work on deadlock patterns by Paul and Helmert (2016), and is strikingly similar to ideas proposed by Helmstetter and Cazenave (2003). In fact, many parallels exist in limitations and patterns based on state positions in BoaF and Gaps (Helmstetter and Cazenave 2003).…”

“…Multidimensional planning is most evi-dent in multi-player games such as checkers (Samuel 1959), chess (Campbell, Hoane Jr., and Hsu 2002), and Go (Silver et al 2016), since the strategy of the solver is dependent upon an unknown sequence of opposing moves. However, planning is still necessary in relaxed, single-player versions of these games, as well as games such as FreeCell (Paul and Helmert 2016;Elyasaf, Hauptman, and Sipper 2011) and solitaire (Bjarnason, Tadepalli, and Fern 2007;Helmstetter and Cazenave 2003), where optimal play may be defined by various independent factors. BoaF may also be included in this group, as many similarly independent properties of stacks exist.…”

A Two-Phase Optimization Algorithm For Mastermind

“…Similar clustering techniques are employed in sampling and clustering [24] and block search [30]. Sampling and clustering [24] uses clustering rules based on the idea of distance between points, to identify clusters of initial points which would lead to the same local optimum.…”

“…Examples of these algorithms based on local search are genetic algorithms [16], simulated annealing [17], Tabu search [18,19], Ant Colony optimization [20] and iterated greedy [21]. On the other hand, examples of algorithms based on constructive methods are iterative sampling [22], HBSS [23], sampling and clustering [24], selective-sampling simulation [25], adaptive sampling [26,27], GRASP [28,29], block search [30] and Monte-Carlo tree search [31]. The main difference between these algorithms is the mechanisms used to guide the tree search.…”