Examples
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"). n 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 n patients the same way, and wants to minimize any suffering, and to achieve success with every 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.
Read more about this topic: Odds Algorithm
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