## Bar Chart: Success Rate ### Overview The image is a bar chart comparing the success rates of five different methods (GPT4, Expert, PAL, ToT, and Ours) across three tasks (Game of 24, MGSM, and Checkmate-in-One) and their average. The y-axis represents the average accuracy in percentage, ranging from 0 to 100. ### Components/Axes * **Title:** Success rate * **Y-axis:** Average accuracy (%) with scale from 0 to 100 in increments of 10. * **X-axis:** Categories: Game of 24, MGSM, Checkmate-in-One, and Average. * **Legend:** Located at the top-right of the chart. * GPT4 (Blue) * Expert (Orange) * PAL (Gray) * ToT (Yellow) * Ours (Light Blue) ### Detailed Analysis Here's a breakdown of the success rates for each method across the tasks: * **Game of 24:** * GPT4 (Blue): 27% * Expert (Orange): 36% * PAL (Gray): 61% * ToT (Yellow): 71% * Ours (Light Blue): 98% * **MGSM:** * GPT4 (Blue): 85% * Expert (Orange): 76% * PAL (Gray): 87% * ToT (Yellow): 84% * Ours (Light Blue): 96.8% * **Checkmate-in-One:** * GPT4 (Blue): 48.2% * Expert (Orange): 53.4% * PAL (Gray): 36.4% * ToT (Yellow): 78.4% * Ours (Light Blue): 93.4% * **Average:** * GPT4 (Blue): 67.13% * Expert (Orange): 71.82% * PAL (Gray): 70.12% * ToT (Yellow): 84.57% * Ours (Light Blue): 95.15% ### Key Observations * "Ours" consistently achieves the highest success rates across all tasks and the average. * GPT4 performs the worst on "Game of 24" and "Checkmate-in-One" but shows improvement on "MGSM". * The "ToT" method shows a strong performance, consistently ranking among the top performers. * The "Expert" method shows a relatively consistent performance across all tasks. * The "PAL" method shows a relatively consistent performance across all tasks. ### Interpretation The chart demonstrates a comparative analysis of different methods in terms of success rate across various tasks. The "Ours" method significantly outperforms the other methods, suggesting its superior effectiveness in these tasks. The performance variation across tasks highlights the strengths and weaknesses of each method in different problem-solving scenarios. The average success rates provide an overall performance indicator, further emphasizing the superiority of the "Ours" method.

\n ## Bar Chart: Success Rate Comparison ### Overview This bar chart compares the success rates of four different models – GPT4, Expert, PAL, and “Ours” – across three distinct game-solving tasks: Game of 24, MGSM, and Checkmate-in-One. An overall average success rate is also presented. The y-axis represents the average accuracy in percentage, ranging from 0 to 100. ### Components/Axes * **Title:** "Success rate" (positioned at the top-center) * **X-axis:** Game/Task Name (labeled: "Game of 24", "MGSM", "Checkmate-in-One", "Average") * **Y-axis:** Average accuracy (%) (labeled, ranging from 0 to 100, with increments of 10) * **Legend:** Located at the top-center, identifying the models by color: * GPT4 (Blue) * Expert (Orange) * PAL (Gray) * Ours (Yellow) ### Detailed Analysis The chart consists of four groups of bars, one for each task/average, with each group containing four bars representing the success rate of each model. **Game of 24:** * GPT4: Approximately 98% (visually, almost reaching 100%) * Expert: Approximately 85% * PAL: Approximately 76% * Ours: Approximately 71% * The trend is a decreasing success rate from GPT4 to "Ours". **MGSM:** * GPT4: Approximately 96.8% (visually, very close to 100%) * Expert: Approximately 87% * PAL: Approximately 84% * Ours: Approximately 84% * GPT4 has the highest success rate, followed by Expert, and PAL and Ours are tied. **Checkmate-in-One:** * GPT4: Approximately 93.4% * Expert: Approximately 78.4% * PAL: Approximately 53.4% * Ours: Approximately 48.2% * The success rate decreases significantly from GPT4 to "Ours". **Average:** * GPT4: Approximately 95.15% * Expert: Approximately 84.57% * PAL: Approximately 70.12% * Ours: Approximately 67.13% * GPT4 has the highest average success rate, followed by Expert, PAL, and "Ours". ### Key Observations * GPT4 consistently outperforms all other models across all tasks and in the overall average. * The "Ours" model generally has the lowest success rate, except for MGSM where it ties with PAL. * The largest performance gap between models is observed in the "Checkmate-in-One" task. * The success rates for all models are relatively high, generally above 60%, indicating a good level of performance overall. ### Interpretation The data suggests that GPT4 is the most effective model for solving these game-solving tasks, demonstrating a significantly higher success rate compared to the other models. The "Expert" model performs reasonably well, consistently ranking second. PAL and "Ours" exhibit lower success rates, with "Ours" generally being the least effective. The substantial difference in performance on the "Checkmate-in-One" task could indicate that this task is particularly challenging and highlights the strengths of GPT4 in handling complex strategic problems. The relatively high success rates across all models suggest that the tasks are not overly difficult, but GPT4's consistent superiority indicates a significant advantage in problem-solving capabilities. The fact that "Ours" ties with PAL on MGSM suggests that the model may have specific strengths in that particular task. The chart provides a clear comparison of the performance of different models, allowing for a quantitative assessment of their effectiveness in game-solving. This information could be valuable for researchers and developers seeking to improve the performance of AI models in similar domains.

## Bar Chart: Success Rate Comparison Across Tasks ### Overview This is a grouped bar chart titled "Success rate" that compares the performance of five different methods or models across three specific tasks and an overall average. The performance metric is "Average accuracy (%)". ### Components/Axes * **Chart Title:** "Success rate" (centered at the top). * **Y-Axis:** Labeled "Average accuracy (%)". The scale runs from 0 to 100 in increments of 10. * **X-Axis:** Represents four distinct categories or tasks: 1. Game of 24 2. MGSM 3. Checkmate-in-One 4. Average * **Legend:** Located in the top-right corner. It defines five data series by color: * **GPT4:** Dark blue square. * **Expert:** Orange square. * **PAL:** Gray square. * **ToT:** Yellow square. * **Ours:** Light blue square. * **Data Labels:** Each bar has its exact numerical value displayed at the top. ### Detailed Analysis The chart presents the following data points for each task category. The trend within each task group is generally ascending from left (GPT4) to right (Ours), with some variation. **1. Game of 24** * **Trend:** Clear ascending trend from GPT4 to Ours. * **Data Points:** * GPT4 (Dark blue): 27% * Expert (Orange): 36% * PAL (Gray): 61% * ToT (Yellow): 71% * Ours (Light blue): 98% **2. MGSM** * **Trend:** Ascending trend, with "Ours" achieving the highest score. "Expert" slightly outperforms "GPT4". * **Data Points:** * GPT4 (Dark blue): 85% * Expert (Orange): 87% * PAL (Gray): 76% * ToT (Yellow): 84% * Ours (Light blue): 96.8% **3. Checkmate-in-One** * **Trend:** Ascending trend from GPT4 to Ours, with a significant jump for "ToT" and "Ours". * **Data Points:** * GPT4 (Dark blue): 48.2% * Expert (Orange): 53.4% * PAL (Gray): 36.4% * ToT (Yellow): 78.4% * Ours (Light blue): 93.4% **4. Average** * **Trend:** Consistent ascending trend from GPT4 to Ours. * **Data Points:** * GPT4 (Dark blue): 67.13% * Expert (Orange): 71.82% * PAL (Gray): 70.12% * ToT (Yellow): 84.57% * Ours (Light blue): 95.15% ### Key Observations 1. **Dominant Performance:** The method labeled "Ours" (light blue) achieves the highest accuracy in every single category, including the overall average. 2. **Task Variability:** The relative performance of the other methods varies by task. For example, "PAL" is the second-best on "Game of 24" but the worst on "Checkmate-in-One". 3. **Significant Gains:** The performance gap between "Ours" and the next-best method is most pronounced in the "Game of 24" (27 percentage points higher than ToT) and "Checkmate-in-One" (15 percentage points higher than ToT) tasks. 4. **Consistent Ranking:** In the "Average" column, the final performance ranking from lowest to highest is: GPT4 < PAL < Expert < ToT < Ours. ### Interpretation This chart is designed to demonstrate the superior performance of a proposed method ("Ours") against several established baselines (GPT4, Expert, PAL, ToT) across a diverse set of reasoning or problem-solving tasks. The "Game of 24" is a mathematical puzzle, "MGSM" likely refers to a multilingual grade-school math benchmark, and "Checkmate-in-One" is a chess tactic problem. The consistent top placement of "Ours" suggests it is a more robust and effective approach for these types of challenges. The "Average" column synthesizes this advantage, showing a clear, incremental improvement over the other methods, with "Ours" achieving a 95.15% average accuracy. The chart effectively argues for the state-of-the-art capability of the presented method.

## Bar Chart: Success Rate ### Overview The chart compares the average accuracy (%) of five AI models (GPT4, Expert, PAL, ToT, Ours) across four games: Game of 24, MGSM, Checkmate-in-One, and an Average. The "Ours" model consistently achieves the highest accuracy, while performance varies significantly for other models depending on the game. ### Components/Axes - **X-axis**: Games (Game of 24, MGSM, Checkmate-in-One, Average) - **Y-axis**: Average accuracy (%) (0–100 scale) - **Legend**: - Blue: GPT4 - Orange: Expert - Gray: PAL - Yellow: ToT - Light Blue: Ours - **Bars**: Grouped by game, with values labeled on top of each bar. ### Detailed Analysis #### Game of 24 - **GPT4**: 27% (blue) - **Expert**: 36% (orange) - **PAL**: 61% (gray) - **ToT**: 71% (yellow) - **Ours**: 98% (light blue) #### MGSM - **GPT4**: 85% (blue) - **Expert**: 87% (orange) - **PAL**: 76% (gray) - **ToT**: 84% (yellow) - **Ours**: 96.8% (light blue) #### Checkmate-in-One - **GPT4**: 48.2% (blue) - **Expert**: 53.4% (orange) - **PAL**: 36.4% (gray) - **ToT**: 78.4% (yellow) - **Ours**: 93.4% (light blue) #### Average - **GPT4**: 67.13% (blue) - **Expert**: 71.82% (orange) - **PAL**: 70.12% (gray) - **ToT**: 84.57% (yellow) - **Ours**: 95.15% (light blue) ### Key Observations 1. **Ours Dominates**: The "Ours" model achieves the highest accuracy in all games and the average, with a 98% success rate in Game of 24 and 95.15% overall. 2. **GPT4 and Expert**: These models show inconsistent performance. GPT4 peaks at 85% in MGSM but drops to 27% in Game of 24. Expert performs best in MGSM (87%) but struggles in Checkmate-in-One (53.4%). 3. **PAL**: Underperforms in Checkmate-in-One (36.4%) but improves in other games (61–76%). 4. **ToT**: Consistently strong, with 71–84.57% accuracy, but lags behind "Ours" in all cases. 5. **Checkmate-in-One Challenge**: All models except "Ours" show significant drops in this game, suggesting it is particularly difficult. ### Interpretation The data demonstrates that the "Ours" model outperforms existing benchmarks (GPT4, Expert, PAL, ToT) across all tested games, indicating superior adaptability or optimization. The stark drop in GPT4 and Expert performance in Checkmate-in-One highlights potential limitations in handling complex or niche tasks. The "Ours" model’s consistent dominance suggests it may incorporate novel strategies or architectural improvements. The Average row reinforces this trend, with "Ours" achieving a 95.15% accuracy compared to the next highest (ToT at 84.57%). This chart underscores the importance of model-specific tuning for game success rates.