Agent Heuristics: Probabilities and Dynamic Synergies

0. Core Concepts and Constants

Required Constants

  • LANDING_PROB (PROB_CAER): 1/54 (Probability of landing on a specific square, excluding jail).
  • TOTAL_TURNS: 500 (Used as a baseline to calculate remaining turns).
  • AUCTION_ROI_CTE: 0.75 (Safety margin to ensure ROI in maximum bids).
  • FANTASY_CTE: 0.0 (Expected net value of an unknown fantasy card).

Core Concepts

  • Expected Visits: Landing Probability * Number of Opponents * Remaining Turns.
  • Dynamic Reserve: The highest rent currently chargeable by any opponent on the board.
  • Rent Delta: The gross change in rent income (including monopoly multipliers or station/bridge scaling) when gaining or losing a property.

1. Jail

  • EV_ExitJail: Sum of EV of unowned buyables - Expected rent paid to others' properties - Bail cost (if applicable).
  • EV_StayInJail: -EV_ExitJail.

2. Buying and Special Moves

  • Buyables (Properties/Bridges/Servers): EV = (Rent Delta * Expected Visits) + Block Value - Buy Price+Mortgage Value (Residual Value)
  • Block Value: Evaluated ONLY if an opponent already owns properties of the same group. Weighted by the number of opponents.
  • Trams:
  • Take Tram: EV = Uniform average EV of the next 12 linearly connected squares - Travel cost.
  • Skip Tram: EV = Uniform average EV of the next 12 linearly connected squares from the current position.

3. Square Selection

The square with the highest expected value is chosen. * Opponent's Property EV: -Current Rent owed.

4. Business and Construction

  • Build: EV = (Projected rent increase * Expected Visits) - Build price.
  • Demolish: EV = Refund (Build price / 2) - (Rent loss * Expected Visits).
  • Unmortgage: EV = (Rent Delta gained * Expected Visits) - Cost (Buy price / 2).
  • Mortgage: EV = Cash gained (Buy price / 2) - (Rent Delta lost * Expected Visits). (Note: Rent Delta automatically factors in the monopoly multiplier impact).

5. Auctions

  • Max ROI Bid: (Square Buying EV + Buy Price) * AUCTION_ROI_CTE.
  • Budget: Current Money - Dynamic Reserve.
  • Max Bid: Minimum between Budget and Max ROI Bid.
  • Real Bids: Distributed across MaxBid or 0 (not to bid).

6. Liquidation and Surrender

  • Liquidate: Handled inherently by EV sorting. Demolishing/mortgaging monopolies generates massive negative EV due to the Rent Delta penalty, forcing the agent to liquidate low-value single properties first.
  • Surrender: Executed only if there are absolutely no other actions available to raise funds.

7. Trades

  • EV_Trade: Own Net Benefit - (Rival Net Benefit / Number of Opponents).
  • Net Benefit: (Money Gained + EV_properties_gained) - (Money Lost + EV_properties_lost).
  • Propose (Initiative): Identify target properties and generate random offers prioritizing maximum EV_trade. Offer value is capped at 80% of the target's buying EV to ensure profitability.
  • Decision: Accept or propose exclusively if EV_Trade > 0.