Trying to keep a random number secret likely is less stressful than an actual lie. Even if lie detectors worked this wouldn’t be a great approach. My way is better, scrap them for parts and buy beer for whatever is left over.
Which begs the issue: If a lie detector is accurate only for answers that are stressful, then it sure looks like we need a detector to figure out if an answer is stressful or not.
Or to put it differently, now you have two problems: Lie detection and stressful-answer detection.
Nevertheless, I concede that your beer detection plan is superior.
Therefore I too must concede that the beer plan is flawless.