I conceptuallized a low level mechanic that is likely to be engaging for players, but i havent figure out how to actually put it into practice in an actual game design. The game has to be simple content wise, because i dont havem uch time to create it, its for a marathon. Here are the mechanics:

This game mechanic revolves around a system where players manage resources (R), score (S), and time (T) through strategic investment in actions. Here's how it works:
### 1. Game State Variables:
   - R (Resources): This is the player's current pool of resources, which can represent points, currency, or any in-game asset.
   - S (Score): Tracks the player's progress or achievement level.
   - T (Time/Turn Counter): This increments with each action the player takes, allowing for a time-based or turn-based system.
### 2. Player Actions:
   - At each time step (T), the player selects an investment level (I_T), which is how many resources they commit to an action.
   - The investment level must stay within a set range [I_min, I_max] and cannot exceed the player's current resources (R).
### 3. Reward Calculation:
   - Each action yields a reward W_T, calculated by a function f(I_T, P_T), where:
     - I_T is the player's investment.
     - P_T is a progressive multiplier that increases with consecutive successful actions, enhancing rewards for streaks of successful investments.
   - The multiplier P_T increases each turn by a small increment δ, starting from a base value P_base.
### 4. Risk Factor:
   - Every action has a chance of failure based on a failure probability F_T.
   - F_T increases with higher investment levels I_T and a growing multiplier P_T, calculated by an exponential function F_T = 1 - e^{-\alpha I_T P_T}, where:
     - α is a scaling factor.
     - As the player increases investment or extends a successful streak (higher P_T), failure risk rises significantly.
### 5. Outcome Determination:
   - A random check determines if an action succeeds or fails based on the failure probability F_T.
     - Success: The player gains resources and score:
       - R_{T+1} = R_T - I_T + W_T (Resources updated after accounting for investment and reward).
       - S_{T+1} = S_T + W_T (Score increases).
       - P_T increases further, incentivizing streaks.
     - Failure: The player loses the invested resources and the multiplier resets:
       - R_{T+1} = R_T - I_T (Only investment lost).
       - P_T resets to its base value, reducing future rewards.
       - There may be additional penalties.
### 6. Resource Regeneration:
   - Each turn, the player receives a passive resource gain r, preventing total resource depletion and allowing them to recover after failures.
### 7. Objective:
   - The goal is to maximize score (S) through careful management of resources and investment decisions.
   - Players must balance the escalating rewards from higher investments and consecutive streaks with the increasing risks of failure.
### 8. Interaction of Components:
   - Investment Level (I_T): Higher investments yield larger rewards but also increase the risk of failure. Players must decide how much to risk based on their resources and the likelihood of success.
   - Progressive Multiplier (P_T): Successive actions without failure boost rewards but also increase failure risk. The player is incentivized to continue streaks for higher rewards but must be cautious of mounting risks.
   - Failure Probability (F_T): As I_T and P_T grow, the risk of failure rises exponentially, demanding strategic risk management.
   - Resource Management (R_T): Players need to avoid running out of resources while making the most of each turn. The passive gain ensures that the game continues even after failures.
This mechanic creates a dynamic tension between reward maximization and risk management, where players must navigate the fine line between aggressive investment and careful conservation of resources.


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One challenge is that i need the players feel a sense of agency, not just like they are pressing butons without any control