Renju Presented by JungYun Lo National Dong Hwa University Department of Computer Science and Information Engineering Artificial Intelligence Laboratory 2004/12/02

Renju2 Outline The rules of Renju Threat-Space Search Proof-Number Search Reference

Renju3 The rules of Renju (1) Opening –the players are preliminary black and preliminary white –The player who is preliminary black puts three stones on the board - two black ones and one white stone. This start of the game is called the opening

Renju4 The rules of Renju (2) The first move is always in the centre (marked on the board) with the black stone! The second stone is white put in the 3x3 square around the first move. The third stone is again black and put in the area of 5x5 intersections around the first move. Direct openings Indirect openings

Renju5 The rules of Renju (3) When the first player has put all the three stones on the board, the second player can choose the color of the stones she wants to play with. When the fifth move. The player with black stones puts two fifth moves on the points, which she/he considers as the best ones. White player takes one of the moves away and makes a move in his/her turn.

Renju6 The rules of Renju (4) The forbidden moves for black –Double threes –Double fours –Overlines

Renju7 The rules of Renju (5) How could black win? –Four-three

Renju8 Proof-Number Search Proving the true value of the root Using two criteria to expand next node –The potential range of subtree values –The number of nodes which must conspire to prove or disprove that range of potential values Enable pn-search to treat efficiently game trees with a non-uniform branching factor.

Renju9 Threat-Space Search (1) A winning threat sequence consists of threats. –Reducing the size –More efficient After a four, one defensive is possible After a three, two or three are possible

Renju10 Threat-Space Search (2) Definitions –The gain square of a threat is the square played by the attacker –The cost squares of a threat are the squares played by the defender, in response to the threat –The rest squares of a threat are the squares containing a threat possibility; the gain square expected –Threat A is dependency on threat B, if a rest square of A is the gain square of B

Renju11 Threat-Space Search (3) a b c d e f g h i j k l m n o e15 is a gain square with e15: cost square is d15 rest squares are a15, b15 and c15 After the moves e15 and d15 playing i11 creates a four (rest square e15,f14 and g13) thus the gain square i11 is dependent on gain square e15

Renju12 Threat-Space Search (4) Definitions –The dependency tree of a threat A is the three with root A and consisting of dependent nodes only –Two dependency trees P and Q are conflict, if within dependency tree P a threat A exists and within dependency tree Q a threat B, in such a way that The gain square of A is cost square in B Vice versa A cost square in A is also cost square in B

Renju13 Threat-Space Search (5) a b c d e f g h i j k l m n o The dependency tree of threat i11 is the four with gain square i11. It also the only child of root of dependency tree of threat e15. Threat with gain square e15 ( cost square d15) and threat with gain square d15 ( cost square e15) are conflict

Renju14 Threat-Space Search (6) a b c d e f g h i j k l m n o

Renju15 Reference Renju International Federation – Go-moku and Threat-Space Search (1993) –L.V. Allis, H.J. van den Herik, M.P.H. Huntjens –Report CS 93-02, Department of Computer Science, Faculty of General Science, University of Limburg. Maastricht, The Netherlands Solving Renju (2001) –Janos Wagner, Istvan Virag –ICGA march 2001 Combining Proof-Number Search with Alpha-Beta Search (2001) –Mark H.M. Winands, Jos W.H.M. Uiterwijk – Proof-number search (1994) –L. V. Allis, Maarten van der Meulen and H. J. van den Herik –Artificial Intelligence vol.66 Issue.1 pp

Renju16 Thanks for your attention!