[mattkrause]

You can arrange a trial (either a clinical one or an A/B test) so that it stops early. However, the analysis plan needs to take that into account: you absolutely cannot just peek at the p-values willy-nilly and use that information to make go/no-go decisions; doing this makes them uninterpretable.

One of the simplest ways to end a trial early is through curtailment--you stop the trial when additional data won't change its outcome. Imagine you have a big box of 100 items, which can either be Item A or Item B. You want to test whether the box contains an equal proportion of As and Bs, so you pull an item from the box, unwrap it, and record what is inside. Naively, one might think that it is necessary to unwrap all 100 items, but you can actually stop after you find 58 of the same type because the 58:42 split--and all more extreme imbalances--allows you to reject the 50:50 hypothesis.

Curtailment is "exact" and fairly easy to compute if you have a finite sample size, each of which contributes a bounded amount to your result. This would certainly happen in your extreme examples. There are also more complicated approaches that allow you to stop even earlier if either a) you're willing to sometimes make a different decision than if you ran to completion and/or b) you're willing to stop earlier on average, even if it means running for longer in some cases.