🎯 Goal: Visualize "Absorbing States" (Victory vs. Ruin). Try this: Set Win Probability to 0.45 and run Auto. Notice how even a tiny disadvantage makes it almost impossible to win!
Ruins (State 0)
0
Current State
5
Wins (State 10)
0
Why does the House always win?
You might think dropping your win probability from 50% to 45% is just a small change. In reality, it is catastrophic.
1. The Tilted Floor (Gravity)
At 45%, the "floor" of the game is tilted to the left. You aren't just walking randomly; you are fighting gravity. Every step has a hidden pull toward Ruin.
2. The Waterfall Effect
To win, you need to go from State 5 to 10. But since you lose more often than you win, the math "erodes" your progress like a current swimming upstream. You take 2 steps forward, but probability forces you 3 steps back.
The Math of Ruin:
Starting at 50% odds = 50% chance of winning.
Starting at 45% odds = ~26% chance of winning.
Starting at 40% odds = ~12% chance of winning.