Game balance¶
Game balance is the deliberate tuning of rules, resources, risks, rewards, and player options so a game produces its intended distribution of viable strategies, difficulty, and competitive outcomes.
Core Idea¶
Game balance is the deliberate adjustment of a game's rules, numerical parameters, resources, risks, rewards, and available options so play produces the intended experience.[1] What counts as balanced depends on the design target: competitive fairness, an appropriate difficulty curve, viable strategic diversity, a sustainable in-game economy, or a controlled pattern of advantage and disadvantage may each be relevant.[2]
Balancing works by changing relations among game elements and observing their consequences in play. Designers may alter costs, damage, probabilities, rewards, encounter strength, resource flows, feedback loops, or win conditions; a buff increases an element's utility, while a nerf decreases it.[3] Static balance concerns the configuration established before play, whereas dynamic balance concerns how advantages, resources, players, and opponents interact as play unfolds.[4] Testing and post-release data can expose dominant strategies, marginalized options, runaway positive feedback, or difficulty that mismatches the intended audience, prompting another tuning cycle.[5]
Balance does not require numerical equality or identical chances in every game.[6] An asymmetric game, simulation, or deliberately unfair encounter can be balanced if the asymmetry supports its intended roles and the strategies meant to work remain meaningfully usable.[7] Conversely, surface symmetry does not guarantee balance when one option dominates or a nominal choice has no practical consequence.[8] Game balance is therefore a design-relative property and activity, not a single universal formula and not merely the broad idea of equilibrium.[9]
Structural Signature¶
Sig role-phrases:
- the playable rule system — mechanics, resources, goals, and win or loss conditions define the game whose relations are being tuned.
- the declared experience target — fairness, difficulty, viable strategy diversity, economic stability, or another intended pattern supplies the criterion for balance.
- the player-and-situation population — skill level, role, mode, match phase, and encounter context determine where option performance is assessed.
- the actionable option set — strategies, abilities, items, roles, and routes are compared for meaningful usability rather than numerical sameness alone.
- the coupled value relations — costs, power, probabilities, rewards, counters, resource flows, and feedback loops determine each option's effective value.
- the observed play distribution — selection, conditional success, counterplay, progression, and accumulation reveal dominance, marginalization, or runaway advantage.
- the diagnosis-to-parameter link — an imbalance claim identifies which rule relation plausibly produces the observed departure from the target.
- the tuning intervention — a buff, nerf, cost change, encounter adjustment, matchmaking rule, handicap, or other edit changes an identified relation.
- the adaptation-and-retest cycle — subsequent play is checked for direct effects, indirect strategy shifts, economic responses, and newly created imbalances.
- the design branch — static or emergent, symmetric or asymmetric, competitive or cooperative, and PvP or PvE settings admit different balance criteria.
- the evaluative boundary — equal numbers or win rates do not by themselves establish balance, and balance metrics cannot independently determine fun, fairness, or the proper design target.
What It Is Not¶
- Not numerical equality among options. Equal costs, damage values, or probabilities can still produce dominance or meaningless choices when counters, timing, and coupled resources differ.
- Not necessarily symmetry or equal chances. Role-asymmetric games, simulations, handicaps, and deliberately difficult encounters can be balanced relative to their intended player roles and experience.
- Not established by an even aggregate win rate. Player skill, selection bias, matchup, phase, and metagame adaptation can hide unusable options or conditional dominance behind one summary number.
- Not the same as a game-theoretic equilibrium. A mixed-strategy equilibrium is a formal property of strategic response, while game balance is a design-relative judgment and tuning activity across rules, difficulty, economy, and experience.
- Not a fixed property independent of a design target. Fairness, viable strategic diversity, progression, economic stability, and intended difficulty can impose different and sometimes competing criteria.
- Not guaranteed by one buff or nerf. Changing an isolated parameter can redistribute strategies, counters, and resource flows, requiring play-based retesting for direct and indirect imbalances.
Scope of Application¶
Game balance applies wherever game designers deliberately tune interacting rules, options, resources, risks, rewards, or challenges against a stated target for play, rather than merely describing equal numbers or favorable outcomes.
- Competitive player-versus-player games. Designers can tune factions, classes, characters, weapons, maps, matchmaking, and counters toward the intended distribution of viable strategies and competitive advantage.
- Player-versus-environment games. Enemy strength, encounter composition, resource availability, and progression can be adjusted to an intended difficulty curve without requiring equal chances between player and environment.
- Cooperative games. Role utility, shared challenges, resource demands, and contribution opportunities can be balanced so that cooperation does not collapse into one mandatory role or tactic.
- Single-player games. Combat, puzzles, economies, and progression can be tuned to the intended audience's challenge and learning path, including deliberately uneven encounters.
- Asymmetric games. Unequal roles, abilities, information, or objectives can still be balanced when each role has meaningful agency and the asymmetry serves the declared design target.
- Strategy games. Units, factions, technologies, build orders, maps, and counter cycles can be assessed for dominant strategies, marginalized choices, and phase-specific advantage.
- Role-playing games. Character classes, abilities, equipment, advancement, encounters, and party composition can be tuned across different levels and play styles.
- Action and fighting games. Move properties, damage, timing, mobility, character matchups, and execution demands can be adjusted against competitive and accessibility targets.
- Collectible and deck-building games. Card costs, effects, combinations, rarity, formats, and rotation policies can be tested for deck diversity and disproportionate strategic dominance.
- Massively multiplayer and live-service games. Patches, buffs, nerfs, new content, and player adaptation can be evaluated repeatedly as metagames and virtual economies change after release.
- In-game economies. Sources, sinks, prices, scarcity, acquisition effort, and item utility can be tuned where resource accumulation and exchange affect progression or strategic choice.
- Dynamic difficulty systems. Encounter parameters or assistance can respond during play when the design target calls for adaptation to observed player performance.
- Playtesting and telemetry analysis. Selection rates, conditional success, counterplay, progression stalls, and player segments can inform diagnoses without treating any single metric as proof of balance.[10]
- Post-release balance patches. Designers can trace a suspected imbalance to a rule relation, intervene through a buff, nerf, cost, reward, or matchmaking change, and retest direct and indirect effects.[11]
- Board, card, tabletop, and digital game design. The abstraction applies across game media when formal rules and player options can be adjusted against an intended play experience; the relevant parameters need not be encoded in software.
Clarity¶
Game balance separates equality from fitness to a declared play experience. Symmetric numbers can still yield a dominant strategy or meaningless choice, while asymmetric roles or deliberately difficult encounters can be balanced when their advantages, counters, risks, and rewards support the intended experience. “Balanced” therefore has no useful verdict until competitive fairness, difficulty, strategic diversity, economy stability, or another target is named.
The term also distinguishes static configuration from behavior that unfolds during play. Initial costs and statistics may look comparable while feedback loops, resource accumulation, player skill, or phase transitions create runaway advantage; buffs and nerfs alter those relations rather than simply moving isolated numbers. The design question becomes: which options are meant to remain viable for which players and situations, and what observed play pattern shows that the current rules meet or miss that target?
Manages Complexity¶
A game may contain hundreds of interacting costs, powers, probabilities, rewards, counters, resource flows, and player choices whose value changes with skill and situation. Balance turns that sprawl into a declared target and a smaller set of relations to monitor: option viability, risk–reward and power–cost curves, counter structure, success and selection rates, difficulty progression, and reinforcing or limiting feedback. Designers can read off dominant strategies, options with no meaningful use, runaway advantage, or encounters that miss the intended audience, then trace those outcomes back to tunable rules rather than isolated numbers alone.
The frame keeps major branches visible: static versus play-emergent balance, competitive fairness versus player-versus-environment pacing, symmetric versus role-asymmetric design, and transitive progressions versus intransitive counter cycles. Buffs, nerfs, matchmaking, handicaps, randomization, and dynamic difficulty intervene at different points in that structure. Compression stops before any metric proves that a game is fun or fair. Win rates depend on player skill, pick rates, metagame adaptation, and sample composition; subsystems interact; aesthetic and narrative goals matter; and a deliberately unequal or slightly unstable arrangement may be part of the intended experience.
Abstract Reasoning¶
From observed play patterns to a balance diagnosis, the designer compares the intended experience with strategy selection, success conditional on skill and situation, available counters, resource accumulation, and difficulty progression. High use alone does not imply dominance, and an even win rate does not prove meaningful choice: a popular option may be accessible but counterable, while two apparently equal options can differ because one is never rational to choose. A diagnosis becomes specific when it identifies the rule relation that turns a cost, reward, timing window, or feedback loop into the observed marginalization or runaway advantage.
Balancing then proceeds as a counterfactual intervention. From changing one cost, probability, cooldown, reward, encounter parameter, or counter to a predicted redistribution of viable choices and outcomes, the designer states which target should move and which populations or game phases should be monitored. A nerf to an item may reduce its direct power yet also alter acquisition incentives, team composition, and an in-game economy; therefore pre/post comparison must trace indirect adaptations rather than attribute every change to the edited number.[12] The verdict remains design-relative. Asymmetry can meet a role-based target, deliberate hardship can meet a PvE target, and no play metric alone establishes fun, fairness, or the proper target.
Knowledge Transfer¶
Within game design, balance knowledge transfers literally across competitive, cooperative, single-player, and live-service games when the intended experience is declared and rules, options, resources, risks, rewards, counters, and difficulty are tuned against observed play. The cargo that carries intact is target population and skill, viable strategy set, selection and success conditional on context, counter structure, economy flows, progression, and patch or test intervention. Diagnostics transfer by changing one parameter and checking whether dominance shifts, choices become meaningful, or new feedback loops appear.
Beyond games, the honest case is (B) shared constrained-tuning mechanism. Markets and engineered systems also adjust interacting parameters, but the home-bound cargo is players, rules, strategies, win conditions, difficulty, and intended play experience. Equality of numbers, equal win rate, popularity, or asymmetry alone neither proves nor refutes balance. The stopping boundary is the declared design target: without it, “balanced” is an evaluative metaphor (A) rather than a testable game-design judgment.
Examples¶
Canonical¶
Rock–paper–scissors provides a minimal balanced option structure.[13] Rock defeats scissors, scissors defeats paper, and paper defeats rock, so no option is unconditionally strongest.[14] If a designer changed the rules so that rock also defeated paper, rock would dominate both alternatives and rational players would have little reason to choose either one.[15] Restoring the three-way counter cycle would repair strategic viability without making the options identical.[16] The example shows why balance can arise from coupled relations rather than equal numerical strength: every option has a use, a counter, and a vulnerability relative to the declared target of meaningful choice.[17]
Mapped back: The three rules form the playable rule system, and meaningful strategic choice is the declared experience target. Rock, paper, and scissors are the actionable option set, whose win–loss cycle supplies the coupled value relations. Making rock beat both rivals creates an interpretable departure in the observed play distribution; restoring the counter relation performs the tuning intervention without confusing balance with numerical sameness under the evaluative boundary.
Applied / In Practice¶
The cooperative video game Left 4 Dead uses an AI Director that changes encounters in response to player progress.[18] Rather than fixing every enemy appearance before play, the system monitors how the group is advancing and introduces events or creatures under rules intended to shape tension and encourage cooperation.[19] If a team is struggling, relentless escalation could make recovery impossible; if it is never pressured, the intended pacing disappears.[20] Designers can playtest the resulting encounter distribution, adjust the Director's parameters, and then observe how teams change their behavior.[21] The target is not equal power between survivors and enemies but a deliberately controlled cooperative difficulty curve.[22]
Mapped back: Cooperative survival play is the playable rule system, and paced tension is the declared experience target for the player-and-situation population. Director rules and encounter pressure instantiate the coupled value relations, while team progress supplies the observed play distribution. Parameter changes are the tuning intervention and renewed playtesting is the adaptation-and-retest cycle within the design branch for cooperative PvE play.
Structural Tensions¶
T1: Competitive fairness versus intended asymmetry. Equal options or win probabilities can support fair competition, yet asymmetric roles, factions, or encounters may be central to the intended experience. Diagnostic: evaluate whether each side has meaningful agency toward its role-specific objective rather than demanding surface equality.
T2: Strategic diversity versus comprehensibility. Increasing viable options can prevent a dominant strategy while also raising the cognitive burden of learning interactions and anticipating opponents. Diagnostic: test whether additional choices create distinct workable plans or merely obscure a small set of effective ones.
T3: Static tuning versus emergent metagame. Pre-release parameters establish an initial possibility space, but player discovery, coordination, and evolving conventions can change which strategies dominate. Diagnostic: compare designed affordances with observed high-level play over time before declaring the configuration settled.
T4: Responsive adjustment versus rule stability. Buffs and nerfs can correct harmful dominance quickly, while frequent changes undermine mastery, comparability, and player trust. Diagnostic: ask whether the identified imbalance is robust enough—and costly enough—to justify resetting learned expectations.
T5: Population-wide equity versus skill differentiation. A change that equalizes outcomes for average players may erase expert counterplay, whereas tuning for experts can make ordinary play inaccessible. Diagnostic: stratify balance evidence by skill, mode, and coordination level rather than averaging incompatible populations.
T6: Challenge versus accessibility. Difficulty can produce tension and achievement but becomes exclusionary or frustrating when players lack intelligible paths to improvement. Diagnostic: distinguish demanding execution or judgment from opaque feedback, unavoidable failure, or mismatched audience assumptions.
T7: Telemetry versus design judgment. Usage and win-rate data reveal patterns at scale, yet selection effects, novelty, and unmeasured experience make those metrics incomplete design targets. Diagnostic: connect a quantitative imbalance to the intended play experience and validate the interpretation through controlled tests or qualitative evidence.
T8: Game Balance autonomy versus reduction to Game Design. Game Balance is a strict specialization of the immediate domain-specific parent Game design: the playable rule system, design target, option set, and play population specify the carrier and inputs; iterative observation, diagnosis, parameter tuning, and retesting instantiate the parent's prototype–observe–tune operation; and preservation of the declared play experience supplies the invariant, recognition test, consequence, and failure boundary. Game Design carries that complete interactive-system design signature, but it does not require comparative option viability, counter structure, runaway-feedback diagnosis, or buffs and nerfs directed at balance targets. Diagnostic: Does the case satisfy Game Design's complete carrier–iteration–invariant structure while also preserving the balance-specific diagnosis-to-tuning relation, or does broad game-system design remain after that residual is removed?
Structural–Framed Character¶
Game balance occupies the framed pole because no game is balanced without a declared experience target, a chosen player population, and design judgments about which outcomes and options ought to remain viable. Its evaluative_weight is high: fairness, challenge, accessibility, strategic diversity, economic stability, and fun can pull in different directions, and the design target determines which distribution counts as success. Its human_practice_bound is high because designers create the rules, interpret play evidence, choose buffs or nerfs, and decide when retesting is sufficient. Its institutional_origin is moderate; studios, competitive communities, and publishing practices stabilize metrics and patch processes, but no single institution constitutes balance across games. Its vocab_travels score is low to mixed: tuning, counters, feedback, and viable options travel, while players, metagames, win conditions, difficulty curves, buffs, and nerfs remain game-specific. Under import_vs_recognize, balance is largely imported as a design perspective: the same play distribution can be judged differently under different legitimate experience targets.
The exact immediate parent Game design is the in-domain umbrella because game balance performs iterative observation and rule-system tuning while specializing that practice to comparative option viability and declared balance targets. The smallest positively reviewed Prime skeleton is Balance: countervailing elements are redistributed through a balancing mechanism toward a proportion-sensitive target. The cross-domain reach belongs to that Prime. Game balance keeps the playable rule system, player population, metagame response, and design-relative criteria that neither parent supplies in full.
Its character: framed pole; structural tuning supports disciplined comparison, but target selection and the meaning of a satisfactory play distribution remain human design commitments.
Structural Core vs. Domain Accent¶
Game Balance is a domain-specific strict specialization within Game design, while the Balance Prime supplies its smallest portable skeleton: multiple weighted elements are deliberately redistributed against a declared target without requiring numerical equality.
What is skeletal (could lift toward a cross-domain prime). The portable Balance signature comprises countervailing elements, an aggregation relation, a proportion-sensitive target, a balancing mechanism, static or dynamic adjustment, and a disequilibrium failure mode. It recurs in at least three unrelated domains: mechanical balance distributes masses and lever arms to satisfy a torque condition, portfolio balance allocates assets against a risk–return target, and visual composition distributes perceptual weight to achieve coherence. Game balance fills those roles with options and strategies, coupled costs and rewards, a chosen experience target, buffs or nerfs and rule changes, iterative retesting, and dominance or marginalization as failure. Strip away players, mechanics, metagames, and win conditions, and the Balance skeleton remains.
What is domain-bound. The immediate in-domain umbrella is Game Design: intentional shaping of an interactive rule system through prototyping, observed play, tuning, and iteration. Game Balance narrows that practice to comparative option viability, difficulty, fairness, strategic diversity, or economic stability for a declared player-and-situation population. It adds coupled value relations, play-distribution evidence, diagnosis-to-parameter links, adaptation, and distinct competitive, cooperative, symmetric, and asymmetric branches. Remove the balance target and tuning objective while retaining the interactive design cycle, and Game design remains. Conversely, retain abstract redistribution but remove the playable rule system and observed player response, and one may have Balance elsewhere but not game balance.
Why this does not clear the prime bar. Balance owns the cross-domain weight–aggregation–target–adjustment structure, and Game design owns the broader practice in which the child is situated. Game Balance owns the design-relative choice of play target, the actionable option set, game-rule interventions, and metagame retesting. Removing those accents yields the portable Prime or the immediate domain parent; removing both the balancing structure and the game-design practice destroys the child's identity. Strict subsumption under Game Design is therefore exact, while the Prime test fails because players, rules, buffs, nerfs, and intended play distributions do not recur literally across at least three unrelated domains.
Instantiates / Related Primes¶
This entry is a kind of Game design.
Immediate domain parent — Game design (Game design). Strict subsumption is faithful: game balance performs the parent practice of intentionally shaping an interactive rule system through observation and iteration, while specializing it to tuning coupled rules, options, risks, resources, and rewards against a declared play-experience target. Removing that tuning objective leaves game design in general, but not game balance.
Instantiates — Balance (Balance). The option set supplies competing elements; costs, power, probabilities, counters, and rewards supply domain-specific weights and an aggregation relation; fairness, viable strategy diversity, difficulty, or economic stability supplies the declared target; and buffs, nerfs, rule edits, and retesting supply the balancing mechanism. Surface equality is not required, because asymmetric distributions can satisfy the target while dominance or meaningless choice supplies the failure mode. Collapse to Balance preserves deliberate redistribution toward a proportion-sensitive target but loses the playable rule system, player population, metagame response, and game-design criteria.
Decline — Design for Implementation (Design for Implementation). This Prime is reachable through Game design, but implementation feasibility is not the defining work of game balance. A balance intervention can tune play relations within an already implemented game without analyzing production, deployment, assembly, operation, or lifecycle constraints, so the current prose does not assert a separate direct relationship.
Relationships to Other Abstractions¶
Current abstraction Game balance Domain-specific
Parents (1) — more general patterns this builds on
-
Game balance is a kind of Game design Domain-specific
Strict subsumption is faithful: game balance performs the parent practice of intentionally shaping an interactive rule system through observation and iteration, while specializing it to tuning coupled rules, options, risks, resources, and rewards against a declared play-experience target.Removing that tuning objective leaves game design in general, but not game balance.
Hierarchy paths (2) — routes to 1 parentless root
- Game balance → Game design → Design for Implementation → Constraint
- Game balance → Game design → Design for Implementation → Trade-offs → Constraint
Neighborhood in Abstraction Space¶
Game balance sits in a crowded region of the domain-specific corpus (30th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Strategic Games & Equilibrium Concepts (13 abstractions)
Nearest neighbors
- Cognitive Hierarchy Theory — 0.89
- Dominated Strategy — 0.89
- Correlated equilibrium — 0.89
- Max-dominated strategy — 0.89
- Evaluation function — 0.89
Computed from structural-signature embeddings · 2026-10-08
Not to Be Confused With¶
- Game design. Game design establishes a game's overall rules, content, interactions, and intended experience; game balance is the narrower activity of tuning coupled values and options against a declared target. Tell: ask whether the work is creating the playable system generally or diagnosing and adjusting relations that produce dominance, marginalization, runaway advantage, or mismatched difficulty.
- Fairness. Fairness evaluates whether players receive appropriate opportunities or treatment, while game balance may deliberately preserve asymmetry or unequal odds when those serve the intended experience. Tell: identify the stated design target rather than assuming that equal starting chances exhaust balance.
- Difficulty. Difficulty describes the challenge a game presents to a player or group; balancing can tune difficulty but also strategy diversity, role utility, resource economies, and counterplay. Tell: a difficulty adjustment becomes balance work only when related parameters are assessed against the intended play pattern.
- Symmetry. Symmetry gives players, roles, or options the same structure or resources; balanced play can instead arise from unequal but countervailing roles. Tell: compare effective uses, counters, and vulnerabilities rather than the surface equality of rules or numbers.
- A game-theoretic equilibrium. An equilibrium is a formal profile from which strategic deviation is not advantageous under specified payoffs; game balance is a design-relative judgment and tuning cycle. Tell: deriving a stable strategy profile does not by itself establish appropriate difficulty, fun, economic stability, or the intended range of viable choices.
- A dominant strategy. A dominant strategy is one option that performs at least as well across relevant opponent choices; it is a possible symptom of imbalance, not the balancing process itself. Tell: distinguish the diagnosed option relation from the intervention that changes costs, counters, rewards, or rules.
- A buff or nerf. A buff raises and a nerf lowers an element's utility, but either is only one possible tuning intervention and can create a new imbalance. Tell: require a diagnosis-to-parameter link and subsequent play-based retesting before treating the change as successful balancing.
- Matchmaking. Matchmaking selects or groups participants under eligibility and skill rules; it can support competitive balance without changing the game's option values. Tell: determine whether the intervention changes who plays whom or changes the rules, resources, abilities, and coupled values within play.
- Playtesting or telemetry. Play sessions and usage data reveal selection, success, progression, and counterplay patterns; they are evidence for balance judgments rather than balance itself. Tell: a metric matters only after controlling for population and context and linking the observed departure to a tunable rule relation.
- An in-game economy. Sources, sinks, prices, scarcity, and exchange constitute a game economy; economic balance is one branch of game balance when those flows are tuned against progression or strategic targets. Tell: an economy can exist without a balancing intervention, and balancing can concern systems with no exchange market.
- Player satisfaction. Enjoyment, engagement, or approval is an outcome designers may seek, but popularity alone does not identify which rule relation is balanced. Tell: ask what experience criterion is being evaluated and what actionable option or parameter relation plausibly controls it.
References¶
[1] Alexander Becker and Daniel Görlich, “What is Game Balancing?” ParadigmPlus 1(1) (2020) (source). registry ↩ Show verification details
Supported in partVerified against the work's full text
Collects and compares definitions of game balancing, framing it as adjusting a game's rules and parameters toward intended play outcomes.
“they define game balancing “as the modification of parameters of the constitutive and operational rules of a game (...) in order to achieve optimal configurations in terms of a set of goals, i.e. a parameter tuning problem.””
[2] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[3] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[4] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[5] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[6] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[7] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[8] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[9] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[10] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[11] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[12] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[13] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[14] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[15] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[16] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[17] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[18] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[19] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[20] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[21] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩
[22] Unverified encyclopedia synthesis; no authoritative source located for the claim as written. ↩