An agent model has 95% per-step accuracy. A 5-step plan succeeds with probability 0.77. If you improve per-step accuracy to 97%, what is the success probability for a 10-step plan?
- About 85%, because the 97% accuracy compounds less aggressively than 95% and most of the error budget is consumed by the first 5 steps of the plan
- About 74%, computed as 0.97 raised to the 10th power, demonstrating that even a 2% accuracy improvement significantly extends the viable plan length
- About 60%, because 10-step plans always have roughly the same success rate regardless of per-step accuracy once the plan exceeds a critical length threshold
- About 90%, because improving accuracy by 2 percentage points roughly doubles the effective plan length that can be executed at any given success probability target
Why
The success probability for a multi-step agent plan where each step succeeds independently with probability p is p raised to the N power. At 97% accuracy with 10 steps, this is 0.97 to the 10th power, which equals approximately 0.737 or about 74%. Compare this to 95% accuracy at 10 steps: 0.95 to the 10th equals 0.60, or 60%. The 2-percentage-point improvement in per-step accuracy raises the 10-step success rate from 60% to 74%, a 14-percentage-point improvement. This demonstrates that small improvements in per-step reliability have outsized impact on multi-step plans because the improvement compounds at each step. The 85% estimate incorrectly assumes non-uniform error distribution across steps. The 60% estimate uses the old 95% accuracy rate, not the improved 97%. The 90% estimate overstates the improvement. The practical implication is that investing in better tool descriptions, structured outputs, and observation validation to push per-step accuracy from 95% to 97% can nearly double the viable plan length from 5 steps to 10 steps while maintaining acceptable success rates.