In AI evaluation, pass@k measures capability: given k attempts, what is the probability that at least one output is correct? For example, imagine an AI generating prior authorization summaries. If the model produces five variations and at least one meets the desired result, that counts as a success. If this happens in 92 out of 100 cases, the system has a pass@5 of 92%. 

This metric is useful during development when people or downstream systems can choose the best result. However, in healthcare operations where a system often produces one live response to a payor, provider, or patient, pass@k can create a false sense of safety. It measures the model’s or application’s potential, not its operational reliability.

Highly regulated environments require a stronger guarantee – in healthcare, you cannot stop at Pass@k. At Infinitus we go further and rely on what you can think of as pass^k: the probability that the system produces the correct result consistently across k independent runs, conditions, or variations. 

For instance, if the same prior authorization request referenced above is processed five times (or under prompt, temperature, or context variations) and the output must be correct every time, the case only passes if all five are accurate. 

This distinction matters because healthcare systems don’t get retries. A model that is “usually right” but occasionally wrong may appear safe under pass@k, yet still create unacceptable operational and regulatory risk when deployed. Pass^k surfaces whether correctness is repeatable and robust, not just possible, which is the difference between a promising prototype and a production-ready system in a high-stakes environment like healthcare.

Think of it like this: If a model has a single-run accuracy of 95%, its pass@5 is very high (~99.999%), but its pass^5 drops to ~77%, revealing instability that matters in production. Moving from pass@k to pass^k requires disciplined evaluation practices such as error analysis, open coding to identify emergent failure patterns, and axial coding to link errors to root causes (policy ambiguity, context gaps, prompt sensitivity). This shift reframes evaluation from “Can the model get it right?” to the more important healthcare question: “Will it get it right every time?”

Operationalizing pass^k also changes how teams design and test AI systems. Evaluation datasets must reflect real-world edge cases, ambiguous documentation, policy conflicts, and longitudinal scenarios. Failure patterns uncovered through qualitative methods should feed directly into system improvements such as tighter constraints, structured outputs, retrieval validation, deterministic workflows, and human-in-the-loop thresholds for high-risk cases. 

In one of our most interesting experiments, we evaluated the system with n = 12 samples per task and looked at performance through the familiar pass@k lens with k = 3. The result? A perfect pass@3 = 100%. In other words, for every task in the batch, at least one of the three attempts produced a correct solution. By conventional reporting standards, that’s a headline number, the kind that suggests the system solves everything.

But we didn’t stop there.

Instead of focusing only on whether the model could get it right within three tries, we asked a tougher question: how reliably does it behave within those attempts? That’s where pass^k comes in. In this same experiment, pass^3 was 94.14% , meaning that in 94.14% of cases, the model reached success in a way consistent with strong, dependable behavior across attempts, not just a lucky hit among several samples.

This distinction matters.

pass@k measures capability: can the system produce a correct answer if given multiple shots?
pass^k measures reliability dynamics: how consistently does it succeed without depending on fallback attempts?

For offline evaluation or research benchmarks, pass@k is often enough. But in customer-facing agents, users don’t experience one of several hidden attempts. They experience a single interaction and expect it to work. Every time.

A system that achieves 100% pass@3 but only 94.14% pass^3 reveals an important truth: success exists, but consistency still has room to improve. And in real-world deployments, especially where trust, safety, and user satisfaction are on the line, consistency is the product.

That’s why we look beyond pass@k. Because reliability isn’t about whether the system can succeed, it’s about whether it does so predictably, transparently, and every single time it matters.

Over time, organizations can track pass^k by workflow, risk tier, and regulatory impact, creating an auditable reliability profile rather than a single headline metric. In healthcare, where consistency is synonymous with safety and compliance, this evolution turns evaluation from a model performance exercise into a production readiness and risk management discipline.