Trapping the Ultimate Success
Keyword(s):
We introduce a betting game where the gambler aims to guess the last success epoch in a series of inhomogeneous Bernoulli trials paced randomly in time. At a given stage, the gambler may bet on either the event that no further successes occur, or the event that exactly one success is yet to occur, or may choose any proper range of future times (a trap). When a trap is chosen, the gambler wins if the last success epoch is the only one that falls in the trap. The game is closely related to the sequential decision problem of maximising the probability of stopping on the last success. We use this connection to analyse the best-choice problem with random arrivals generated by a Pólya-Lundberg process.
Keyword(s):
2016 ◽
Vol 48
(3)
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pp. 726-743
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2015 ◽
Vol 243
(1)
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pp. 224-232
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2004 ◽
Vol 36
(2)
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pp. 398-416
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1973 ◽
Vol 17
(4)
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pp. 657-668
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