Is This Offer Too Good to Be True?" - Little Leather Library (Mid-Week Pictorial, April 20 1922)
The pattern
This still is filed under If-then promise.
Define
A conditional contract: if you do this, you get that. The sentence can be tested against the reader's own case.
Mechanism
Specificity does the persuading. The if names the action. The then names the outcome. Hedging kills it.
Verdict
We can name both the action and the result without adjectives
Why it works
The headline states the reader's own objection before the reader can, which is the oldest way to neutralise it - once the advertiser has said it first, the thought stops feeling like the reader's private scepticism and starts feeling like a shared problem the two of them are solving. The body then does something unusual: it tells on itself, narrating a failed mailing and a successful one, and the admission that people only believed when they could touch a sample makes every subsequent claim more credible by association. Because the advertiser cannot put a sample in the page, it borrows the publication's credibility explicitly and then substitutes the entire set on approval for the sample it cannot send - the guarantee is engineered to replace the missing physical proof. The refund language is deliberately absolute, for any reason or for NO reason, which removes the last exit the sceptic has.
Steal this when
Your offer is genuinely strong and the dominant response is suspicion rather than indifference. Put the suspicion in the headline verbatim, narrate the evidence of your own failures and tests, and make the guarantee absolute enough to stand in for the sample you cannot hand over.