Mathematics

Comparative Math: Linked vs. Standalone Progressives

Analyzing the mathematics of wide-area progressive networks versus single-machine jackpots, and how each affects player strategy and expected value.

Comparative Math: Linked vs. Standalone Progressives

Progressive jackpots come in different architectures, each with distinct mathematical properties. Understanding the differences between standalone and linked progressives is crucial for advantage players seeking positive expected value.

Progressive Architecture Types

Standalone Progressives

Definition: Single machine with its own jackpot

Characteristics:

  • Jackpot funded only by that machine's play
  • Grows more slowly
  • Hit less frequently (by definition—one machine)
  • Reset value typically lower
  • Player can track individual meter
  • Linked (Wide-Area) Progressives

    Definition: Multiple machines contribute to shared jackpot

    Characteristics:

  • Many machines fund the jackpot
  • Grows more quickly
  • Hit more frequently (more machines = more attempts)
  • Higher reset values
  • Large maximum jackpots possible
  • Proprietary Networks

    Major networks include:

    NetworkOperatorScopeMegabucksIGTNevada-wideWheel of FortuneIGTMulti-casinoLocal progressivesIndividual casinosSingle property

    The Mathematics

    Contribution Rate

    Both types take from base RTP:

    Standalone example:

  • Base 9/6 JoB: 99.54% RTP
  • Contribution: 1.5% to meter
  • Effective base RTP: 98.04%
  • Linked example:

  • Base 8/5 JoB: 97.30% RTP
  • Contribution: 2.5% to meter
  • Effective base RTP: 94.80%
  • Meter Movement

    Standalone:

    $$\text{Meter increase per hour} = \text{Hands/hour} \times \text{Avg bet} \times \text{Contribution rate}$$

    Example: 600 hands/hour × $1.25 × 1.5% = $11.25/hour

    Wide-Area:

    $$\text{Meter increase} = \sum_{i=1}^{n} (\text{Machine}_i \text{ contribution})$$

    With 1,000 machines at similar rates: $11,250/hour network-wide

    Hit Frequency Comparison

    Standalone (Royal Flush progressive):

  • Single machine: ~1 Royal per 40,000 hands
  • At 600 hands/hour: ~67 hours between Royals (on average)
  • Wide-Area (1,000 machines):

  • Network: ~1 Royal per 40 hands played network-wide
  • Hit frequency: Multiple times daily
  • Individual player experience: Same as standalone
  • Expected Value Analysis

    Breakeven Calculation

    Standalone:

    $$EV = (\text{Base RTP} - \text{Contribution}) + \frac{\text{Meter}}{\text{Royal Probability} \times \text{Bet}}$$

    Example at breakeven:

  • Base: 98.04%
  • Need: +1.96% from progressive
  • At 5-coin $1: Need ~$3,136 meter for 100% EV
  • Wide-Area:

    Same formula, but:

  • Higher contribution (lower base)
  • Larger jackpots possible
  • More competition for the hit
  • Effective Hourly Value

    Standalone at breakeven:

  • EV per hand: $0
  • Plus: Exclusive access to meter
  • Minus: Slow meter growth
  • Wide-Area at breakeven:

  • EV per hand: $0
  • Plus: Larger potential jackpot
  • Minus: Competition from other players
  • Strategic Implications

    Standalone Advantages

    For advantage players:

    AdvantageReasonExclusive accessOnly you contribute when playingMeter controlCan estimate time to breakevenLower competitionNo other players hunting same jackpotPredictable growthSingle-variable calculation

    Wide-Area Advantages

    AdvantageReasonLarger jackpotsMore funding sourcesFaster growthMultiple contributorsLife-changing winsMaximum prizes higherMore frequent network hits(Though individual odds unchanged)

    Player Strategy Differences

    Standalone Strategy

    Monitoring:

  • Track individual meter
  • Calculate precise breakeven
  • Time play when +EV
  • Execution:

  • Exclusive play when advantageous
  • No time pressure from competition
  • Can leave and return
  • Wide-Area Strategy

    Monitoring:

  • Track network meter
  • Calculate breakeven for network
  • Assess competition level
  • Execution:

  • May need extended sessions
  • Competition creates time pressure
  • Consider multiple machine play
  • Casino Perspective

    Why Offer Each Type

    Standalone:

  • Lower maximum liability
  • Simpler accounting
  • Machine-level marketing
  • Local player loyalty
  • Wide-Area:

  • Large jackpot marketing value
  • Network effects (destination play)
  • Shared liability across properties
  • Progressive pools for smaller casinos
  • Contribution Differences

    Casinos structure differently:

    TypeTypical ContributionCasino ReserveStandalone1-2%20-50% of contributionWide-Area2-4%10-30% + network fees

    Variance Comparison

    Expected Wait Time

    For a Royal Flush progressive:

    Standalone:

  • Your expected wait: 40,000 hands
  • Your expected contribution before win: Proportional to meter
  • Variance: High (could be hand #1 or #100,000)
  • Wide-Area:

  • Your expected wait: Same (40,000 hands)
  • Network hit frequency: Much higher
  • But: You might not be the one who hits it
  • Psychological Factors

    FactorStandaloneWide-AreaHit visibilityOnly your machineCould be anywhereAnticipationPersonalCollectiveDisappointmentNo one else won "yours"Someone else got itCelebrationPersonalShared network event

    Practical Examples

    Scenario: $5,000 Standalone at Breakeven

  • Only you are contributing
  • Playing 600 hands/hour
  • Contributing $11.25/hour to meter
  • If you leave, meter grows only when others play
  • Return when still +EV
  • Scenario: $500,000 Wide-Area at Breakeven

  • 1,000 machines contributing
  • Meter growing ~$11,000/hour
  • Could hit any moment on any machine
  • Your individual contribution: Tiny fraction
  • Competition intense when +EV
  • Advantage Play Recommendations

    When to Focus on Standalone

  • Lower bankroll
  • Prefer predictable situations
  • Value exclusive access
  • Can monitor specific machines
  • When to Target Wide-Area

  • Seeking life-changing wins
  • Higher risk tolerance
  • Enjoy competition
  • Larger bankroll available
  • Hybrid Approach

    Many advantage players:

  • Monitor both types
  • Prioritize based on current opportunities
  • Adjust for competition levels
  • Consider all available options
  • The Evolution of Progressives

  • Mystery progressives (random trigger)
  • Multi-level progressives
  • Community jackpots
  • Must-hit-by progressives
  • Impact on Standalone vs. Linked

    New structures blur traditional lines:

  • Community jackpots: Linked play, individual triggers
  • Must-hit-by: Guaranteed hits creating clear +EV points
  • Multi-level: Combined standalone and linked features
  • Understanding the mathematical differences between progressive types enables informed decisions about where to invest time and money in pursuit of jackpots.