Collaborative robots and machine learning-based virtual agents are increasingly entering the human workspace with the aim of increasing productivity and enhancing safety.

Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required. This paper presents a more efficient and straightforward algorithm: Linear TreeShap. Like TreeShap, Linear TreeShap is exact and requires the same amount of memory.

We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes into skill leverage K and luck leverage L. Applying this to 30 games reveals a continuum from pure chance (coin toss, S = -1) through mixed domains such as backgammon (S = 0, Sigma = 1.20) to pure skill (chess, S = +1, Sigma = 0). Poker exhibits moderate skill dominance (S = 0.33) with K = 0.40 +/- 0.03 and Sigma = 0.80. We further introduce volatility Sigma to quantify outcome uncertainty over successive turns. The framework extends to general stochastic decision systems, enabling principled comparisons of player influence, game balance, and predictive stability, with applications to game design, AI evaluation, and risk assessment.

Learning to autonomously execute long-horizon procedures from natural language remains a core challenge for intelligent agents. Free-form instructions such as recipes, scientific protocols, or business workflows encode rich procedural knowledge, but their variability and lack of structure cause agents driven by large language models (LLMs) to drift or fail during execution. We introduce Procedure Aware DynaMic Execution (PADME), an agent framework that produces and exploits a graph-based representation of procedures. Unlike prior work that relies on manual graph construction or unstructured reasoning, PADME autonomously transforms procedural text into executable graphs that capture task dependencies, decision points, and reusable subroutines. Central to PADME is a two-phase methodology; Teach phase, which focuses on systematic structuring, enrichment with executable logic of procedures, followed by Execute phase, which enables dynamic execution in response to real-time inputs and environment feedback. This separation ensures quality assurance and scalability, allowing expert knowledge to be encoded once and reliably reused across varying contexts. The graph representation also provides an inductive bias that reduces error accumulation in long-horizon reasoning, underscoring the importance of structured procedure modeling for reliable agent-driven automation. Empirically, PADME achieves state-of-the-art performance on four diverse benchmarks, including ALFWorld and ScienceWorld. These results demonstrate that agents equipped with graph-based procedure representations offer a powerful intermediate abstraction for robust and generalizable execution.

Collaborative robots and machine learning-based virtual agents are increasingly entering the human workspace with the aim of increasing productivity and enhancing safety.