[tshort]

Faced with a finite series of independent decisions with a favorable or unfavorable outcome after which number of trials in which you receive a favorable outcome should you stop repeating the event?

The simple example he gives is a dice rolling example. You are going to roll a die up to 12 times. It is favorable to roll a 6 and unfavorable to roll anything else. Your goal is to stop rolling the last time you roll a six (keeping in my mind you're going to roll it up to 12 times). After what number of rolls should you stop if you roll a 6?

The odds-algorithm he specifies gives you the answer which is after 7 rolls you should stop as soon as you get a 6.

He applies this algorithm to other events which may have unknown or maybe unequal probabilities. He eventually uses the example of clinical trials. You have 50 patients, after which success should you stop administering further trials?

The math in the article can't be explained much simpler.