Gaming Dice Geometry for Low-Probability Outcomes
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Solution Overview
Problem
Existing gaming dice do not effectively incorporate low probability results to introduce novel and surprising outcomes or modifiers during gameplay, lacking the ability to balance different probabilities on their sides.
Innovation Solution
The gaming dice are designed with truncated or chamfered corners to create lower probability results on specific sides (2, 4, or 8) while maintaining balanced core sides of higher probability, resulting in 8, 10, 12, or 14-sided dice configurations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If truncated or chamfered corners are added to create low probability sides, then the dice introduces novel and surprising results with different probabilities, but the dice structure becomes more complex and the manufacturing difficulty increases
Solution Approach 1:
The dice is segmented into two distinct types of sides: six larger congruent sides and additional smaller truncated sides. This segmentation allows each side type to serve different probability functions, with the larger sides providing higher probability outcomes and the smaller truncated sides providing lower probability outcomes, thus achieving varied probability distribution while managing structural complexity
Solution Approach 2:
The dice incorporates asymmetric side sizes where truncated corners create smaller landing surfaces compared to the six larger congruent sides. This asymmetry in surface area directly translates to different landing probabilities, with smaller surfaces having lower probability of being selected, thereby introducing novel probability outcomes without requiring completely redesigning the entire dice structure
2Adaptability or versatility
If truncated corners are used to create lower probability sides, then the dice produces surprising results, but the manufacturing precision requirements increase
Solution Approach 1:
The truncation is applied locally only to specific corners of the dice rather than uniformly to all corners. This local quality approach allows precise control over which sides become low-probability outcomes while maintaining standard manufacturing tolerances for the remaining congruent sides, thereby reducing overall manufacturing precision requirements while still achieving the desired probability distribution
3Reliability
If the dice maintains a balanced core of six congruent sides, then the core sides remain fair and reliable, but the overall dice structure becomes more complex with additional truncated sides
Solution Approach 1:
The dice merges two functional elements into a single structure: six congruent sides that maintain traditional fairness and reliability, and additional truncated sides that provide low-probability outcomes. By combining these elements into one integrated dice body rather than using separate components, the design achieves varied probability distribution without proportionally increasing overall structural complexity
Data Source
AI summary
This is a novel gaming dice invention that incorporates low probability results, called “Low Probability Dice,” invented by Benjamin M. Timp for the purposes of board games, role-playing games, or other dice playing games of chance. By combining different sizes of landing planes, some of the results have lower probabilities of landing face up.