Idle game economy, 120 days, one player who plays 5 sessions of 90 minutes per day. Core loop (one "run"): - A frog fights through floors. Each floor has 14 monsters (rising to 20 by floor 1000). Every 10th floor has a boss. - Monster health on floor f = 2.5 × (1 + f/400)^12 × 1.004^f. Monster damage grows the same way. - Killing monsters gives Coins: coins per monster = 1.07 × (monster health growth)^0.466. - Coins are only spent inside the run on run upgrades (damage, health, attack speed). Run upgrade prices grow 1.1× per level. Coins reset to 0 when the run ends. - Each floor gives Memories: memories per floor = 5.05 × (monster health growth)^0.303, ×5 on boss floors. - The run ends when the frog dies (its power falls behind monster health). Permanent progression (Memories, never reset): - Workshop: 4 main stats, +1% per level and ×1.038 every 25 levels; price = 2 × (level+1)^0.99 × 1.0058^level. The max level starts at 250 and rises by 60 per "Limit research" in the Lab (40 research levels, duration 30 min × (level+1)^1.8, real time). - Lab: 2 research slots, real-time research; base research ×1.13 per level, duration doubles each level up to level 8, max 30 days. - Each permanent system has a power cap: Workshop ×1450, Lab ×11, Pets ×11, Gear ×11. Worlds: - World 2 multiplies monster health and rewards ×20, world 3 ×3, worlds 4–8 ×2 each, then ×3 each. - The next world unlocks after beating the World Boss on floor 300 (odd worlds: boss health ×3; even worlds: boss damage ×3). - The player always plays the world that gives the most Memories per hour. Simulate 120 days and show: 1. On which day each world unlocks, and whether worlds come evenly or in bursts. 2. Memories per day and where they are spent (Workshop vs Lab). 3. On which day the Workshop reaches its power cap. 4. Whether progress stalls for more than 7 days at any point. 5. Which world and how deep the player farms best on day 30, 60, 90 and 120.
