Ping-Hung Lin

Relevance-Zone-Oriented Proof Search for Connect6

Wu and Huang (Advances in Computer Games, pp. 180-194, 2006) presented a new family of k-in-a-row games, among which Connect6 (a kind of six-in-a-row) attracted much attention. For Connect6 as well as the family of k -in-a-row games, this paper proposes a new threat-based proof search method, named relevance-zone-oriented proof (RZOP) search, developed from the lambda search proposed by Thomsen (Int. Comput. Games Assoc. J., vol. 23, no. 4, pp. 203-217, 2000). The proposed RZOP search is a novel, general, and elegant method of constructing and promoting relevance zones. Using this method together with a proof number search, this paper solved effectively and successfully many new Connect6 game positions, including several Connect6 openings, especially the Mickey Mouse opening, which used to be one of the popular openings before we solved it.

Job-level proof-number search for connect6

This paper proposes a new approach for proof number (PN) search, named job-level PN (JL-PN) search, where each search tree node is evaluated or expanded by a heavy-weight job, which takes normally over tens of seconds. Such JL-PN search is well suited for parallel processing, since these jobs are allowed to be performed by remote processors independently. This paper applies JL-PN search to solving automatically several Connect6 positions including openings on desktop grids. For some of these openings, so far no human expert had been able to find a winning strategy. Our experiments also show that the speedups for solving the test positions are roughly linear, fluctuating from sublinear to superlinear. Hence, JL-PN search appears to be a quite promising approach to solving games.

Job-Level Proof Number Search

This paper introduces an approach, called generic job-level search, to leverage the game-playing programs which are already written and encapsulated as jobs. Such an approach is well suited to a distributed computing environment, since these jobs are allowed to be run by remote processors independently. In this paper, we present and focus on a job-level proof number search (JL-PNS), a kind of generic job-level search for solving computer game search problems, and apply JL-PNS to solving automatically several Connect6 positions, including some difficult openings. This paper also proposes a method of postponed sibling generation to generate nodes smoothly, and some policies, such as virtual win, virtual loss, virtual equivalence, flagging, or hybrids of the above, to expand the nodes. Our experiment compared these policies, and the results showed that the virtual-equivalence policy, together with flagging, performed the best against other policies. In addition, the results also showed that the speedups for solving these positions are 8.58 on average on 16 cores.

A Volunteer-Computing-Based Grid Environment for Connect6 Applications

This paper presents a volunteer-computing-based grid environment or called a desktop grid environment for Connect6 applications. The Connect6 application described in this paper is to let professional Connect6 players to develop or solve openings, based on two programs, NCTU6 and Verifier. NCTU6 is to make Connect6 moves, written by the team led by Wu [19][21]. NCTU6 Verifier (abbr. Verifier), modified from NCTU6, is to verify whether one player wins in a given game position, or to generate the defensive moves if not winning in the position. Since both NCTU6 and Verifier consume huge amount of computation resources and requires on-demand responses, we design a desktop grid environment that provides players with on-demand computing through dynamic resource provisioning. The underlying desktop grid achieves high throughput computing by harvesting the idle CPU times on desktop computers connected to the Internet.

Temporal Difference Learning for Connect6

In this paper, we apply temporal difference (TD) learning to Connect6, and successfully use TD(0) to improve the strength of a Connect6 program, NCTU6. The program won several computer Connect6 tournaments and also many man-machine Connect6 tournaments from 2006 to 2011. From our experiments, the best improved version of TD learning achieves about a 58% win rate against the original NCTU6 program. This paper discusses three implementation issues that improve the program. The program has a convincing performance in removing winning/losing moves via threat-space search in TD learning.

On drawn k-in-a-row games

In 2005, Wu and Huang [9] presented a generalized family of k-in-a-row games. The current paper simplifies the family to Connect(k, p). Two players alternately place p stones on empty squares of an infinite board in each turn. The player who first obtains k consecutive stones of his own horizontally, vertically, diagonally wins. A Connect(k, p)game is drawn if both have no winning strategy. Given p, this paper derives the value kdraw(p), such that Connect(kdraw(p), p) is drawn, as follows. (1) kdraw(2) = 11. (2) For all p ≥ 3, kdraw(p) = 3p+3d+8, where d is a logarithmic function of p. So, the ratio kdraw(p)/p is approximate to 3 for sufficiently large p. To our knowledge, our kdraw(p) are currently the smallest for all 2 ≤ p < 1000, except for p = 3.

Dependency-Based Search for Connect6

Allis proposed dependency-based search (DBS) to solve Go-Moku, a kind of five-in-a-row game. DBS is critical for threat space search (TSS) when there are many independent or nearly independent TSS areas. Similarly, DBS is also important for the game Connect6, a kind of six-in-a-row game with two pieces per move. Unfortunately, the rule that two pieces are played per move in Connect6 makes DBS extremely difficult to apply to Connect6 programs. This paper is the first attempt to apply DBS to Connect6 programs. The targeted program is NCTU6, which won Connect6 tournaments in the Computer Olympiad twice and defeated many professional players in Man-Machine Connect6 championships. The experimental results show that DBS yields a speedup factor of 4.12 on average, and up to 50 for some hard positions.