# Alpha-Beta Pruning and Althöfer’s Pathology-Free Negamax Algorithm

## Abstract

**:**

## 1. Introduction

Yet, it should come as a surprise that the minimax method works at all. The static evaluation function does not exactly evaluate the positions at the search frontier, but, only provides estimates of their strengths; minimaxing these estimates as if they are true payoffs amounts to committing one of the deadly sins of statistics, computing a function of the estimates instead of an estimate of the function.

## 2. Review of Althöfer’s Algorithm

## 3. Review of Alpha-Beta Pruning

`m`), if that sibling returned a value greater than α. For example, consider the situation illustrated in Figure 3 where x had a child w prior to z. If w returns to x a value less than the α of x (e.g., $-4$), then the maximum value of an ancestor of z of x’s own parity will still be the α that x received from y. If, however, w returns to x a value greater than α (e.g., $-1$), then the maximum value of an ancestor of z of x’s parity will be the current value of x itself. Therefore, z will be passed a value of β equal to the negation of the value x received from w, which is a sibling of z.

## 4. Applying Alpha-Beta Pruning to Althöfer’s Algorithm

## 5. Concluding Remarks

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**MDPI and ACS Style**

Abdelbar, A.M.
Alpha-Beta Pruning and Althöfer’s Pathology-Free Negamax Algorithm. *Algorithms* **2012**, *5*, 521-528.
https://doi.org/10.3390/a5040521

**AMA Style**

Abdelbar AM.
Alpha-Beta Pruning and Althöfer’s Pathology-Free Negamax Algorithm. *Algorithms*. 2012; 5(4):521-528.
https://doi.org/10.3390/a5040521

**Chicago/Turabian Style**

Abdelbar, Ashraf M.
2012. "Alpha-Beta Pruning and Althöfer’s Pathology-Free Negamax Algorithm" *Algorithms* 5, no. 4: 521-528.
https://doi.org/10.3390/a5040521