Uniform and Non-uniform Probabilities
A standard deck of 52 playing cards includes four suits—clubs diamonds hearts spades—each with 13 cards ranging from 2 to 10, plus a Jack, Queen, King, and Ace, colored red for hearts and diamonds, and black for clubs and spades, usually accompanied by two jokers, with cards featuring standardized face designs and index labels, and designed for durability with uniform backs to prevent recognition.
Drawing a specific card like the Ace of Spades from a full deck has a fixed probability of 1/52, but this changes as cards are drawn and not replaced, leading to non-uniform probabilities with each draw. Each new card drawn from a deck reshapes the landscape of possible outcomes, influencing decisions such as betting, holding, or folding in games like poker.
A standard six-sided dice (d6) is a symmetrical cube with each face displaying a unique number of dots from 1 to 6, opposite faces summing to seven, traditionally made from materials like plastic, wood, or bone, and is compact and easy to roll, making it widely used in board games, role-playing games, and educational activities for random number generation.
Each face of a six-sided dice (d6) has an equal chance of landing, maintaining uniform probabilities that simplify strategic calculations in games and models. the steady probabilities mean that outcomes can be anticipated based on equal odds—less about adapting to a changing game state.
Adjustments network with decision-making across chance and context. The nature of their probabilities shapes how games are structured and experienced differently by players.
The target of a ranged attack roll partially obscured by terrain or other models, the shooter may receive penalties to their hit rolls, further decreasing the probability of a successful hit. Suffering from injuries or certain spell effects have reduced abilities, impacting their chances to hit or be hit, thereby modifying the probability calculations yet again.
The probabilities become non-uniform when considering attrition in a skirmish game and the various modifiers applied based on the scenario, such as terrain effects, unit abilities, or tactical advantages, which modify the likelihood of hitting, wounding, or avoiding damage. Systems seem to drift away from being uniform.
A combination of uniform and non-uniform probabilities in a single system, where some aspects of the system operate with fixed probabilities and others with variable probabilities.
Probabilities are undefined or the system is too complex to categorize solely as uniform or non-uniform, possibly due to lack of information or a state of flux.
