Randomised response is a research method used in structured survey interview.
For example, social scientists have used it to ask people whether they use drugs, whether they have illegally installed telephones, or whether they have evaded paying taxes.
Plausible deniability allows the subject to credibly say that they did not make a statement, while the randomized response technique allows the subject to credibly say that they had not been truthful when making a statement.
Only they know whether their answer reflects the toss of the coin or their true experience.
It is very important to assume that people who get heads will answer truthfully, otherwise the surveyor is not able to speculate.
So whatever proportion of the group said "no", the true number who did not have sex with a prostitute is double that, based on the assumption that the two halves are probably close to the same as it is a large randomized sampling.
The subject takes one card, turns it over, and answers the question on it truthfully with either "yes" or "no".
Warner's original version (1965) is slightly different: The sensitive question is worded in two dichotomous alternatives, and chance decides, unknown to the interviewer, which one is to be answered honestly.
Inserted into the formula you get If all interviewed have answered honestly then their true proportion of consumers is 1/8 (= 12.5%).