# Probability based Proof Number Search

### Zhang Song, Hiroyuki Iida, H. van den Herik

#### Abstract

Probability based proof number search (PPN-search) is a game tree search algorithm improved from proof number search (PN-search) (Allis et al., 1994), with applications in solving games or endgame positions. PPN-search uses one indicator named “probability based proof number” (PPN) to indicate the “probability” of proving a node. The PPN of a leaf node is derived from Monte-Carlo evaluations. The PPN of an internal node is backpropagated from its children following AND/OR probability rules. For each iteration, PPN-search selects the child with the maximum PPN at OR nodes and minimum PPN at AND nodes. This holds from the root to a leaf. The resultant node is considered to be the most proving node for expansion. In this paper, we investigate the performance of PPN-search on P-game trees (Kocsis and Szepesvári, 2006) and compare our results with those from other game solvers such as MCPN-search (Saito et al., 2006), PN-search, the UCT solver (Winands et al., 2008), and the pure MCTS solver (Winands et al., 2008). The experimental results show that (1) PPN-search takes less time and fewer iterations to solve a P-game tree on average, and (2) the error rate of selecting a correct solution decreases faster and more smoothly as the iteration number increases.

Download#### Paper Citation

#### in Harvard Style

Song Z., Iida H. and van den Herik H. (2019). **Probability based Proof Number Search**.In *Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-350-6, pages 661-668. DOI: 10.5220/0007386806610668

#### in Bibtex Style

@conference{icaart19,

author={Zhang Song and Hiroyuki Iida and H. van den Herik},

title={Probability based Proof Number Search},

booktitle={Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2019},

pages={661-668},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007386806610668},

isbn={978-989-758-350-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - Probability based Proof Number Search

SN - 978-989-758-350-6

AU - Song Z.

AU - Iida H.

AU - van den Herik H.

PY - 2019

SP - 661

EP - 668

DO - 10.5220/0007386806610668