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Two different situations exemplify the interest in maximizing the probability to stop on a last specific event.
# Suppose a car is advertised for sale to the highest bidder (best "offer"). Let <math>n</math> potential buyers respond and ask to see the car. Each insists upon an immediate decision from the seller to accept the bid, or not. Define a bid as ''interesting'', and coded 1 if it is better than all preceding bids, and coded 0 otherwise. The bids will form a [[random sequence]] of 0s and 1s. Only 1s interest the seller, who may fear that each successive 1 might be the last. It follows from the definition that the very last 1 is the highest bid. Maximizing the probability of selling on the last 1 therefore means maximizing the probability of selling ''best''.
# A physician, using a special treatment, may use the code 1 for a successful treatment, 0 otherwise. The physician treats a sequence of <math>n</math> patients the same way, and wants to minimize any suffering, and to treat every responsive patient in the sequence. Stopping on the last 1 in such a random sequence of 0s and 1s would achieve this objective. Since the physician is no prophet, the objective is to maximize the probability of stopping on the last 1. (See [[Compassionate use]].)
== Definitions ==
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