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Tree-based ensemble algorithms (TEAs) have had a transformative impact in various fields. However, when they are applied to real-time critical problems such as medical analysis, existing TEAs fall short of two-fold issues. The first is the trade-off among model interpretability, accuracy, and explainability. Second, traditional TEAs perform dramatically worse when the number of contributing features to model accuracy is small in comparison to the total number of features. We address the aforementioned issues in this paper and propose a novel "eXplainable Reasonably Randomised Forest" (XRRF) algorithm. The XRRF consists of four conclusive steps: learning performance, intrinsic interpretability, model accuracy, and explainability. The proposed forest algorithm is evaluated on three real-world problems (medical analysis, business analysis, and employee churn), a hybrid artificial dataset, and twenty multidisciplinary benchmark problems with varying characteristics. The experimental results demonstrate that the XRRF outperforms the six mainstream and two cutting-edge black-box and white-box algorithms, respectively. [ABSTRACT FROM AUTHOR]