Predict: what is the end to end success rate of a 10-step agent task if each step succeeds with 90% probability?

The trick here is that the ten steps are independent and every one of them must succeed for the whole task to succeed. When independent events all have to happen together, you multiply their probabilities. You do not average them. So the answer is not 0.9. It is 0.9 multiplied by itself ten times, written as **0.9 to the power of 10**. Punch that into a calculator and you get about 0.349, or roughly 35%. That number surprises most people. Each step looks reliable at 90%, yet the full chain succeeds only about a third of the time. The reason is that the small 10% failure chance gets a fresh roll of the dice at every step, and those chances stack up. The wider lesson is that error compounds across steps. The more steps an agent takes, the lower the odds that all of them go right. This is why long agent loops degrade, and why engineers obsess over per step accuracy and recovery mechanisms.

Each step succeeds independently with probability 0.9, and all ten steps must succeed. For independent events that must all occur, you multiply the probabilities. Reliability over N steps is: $$\text{reliability} = p^{N}$$ Plugging in the numbers gives `0.9^10`, which equals about 0.349. So the end to end success rate is roughly 35%. The headline insight is that per step error compounds multiplicatively. A 10% failure per step does not stay 10% over the whole task. It grows because the chain survives only if every link holds. This is why long agent loops degrade. Doubling the steps to twenty drops success to about 12%. To hit 90% end to end across ten steps, each step would need roughly 98.9% reliability, since `0.9^(1/10)` is about 0.989. That is a brutal bar, and it explains the push toward fewer steps, retries, and verification.