Probabilistic Live-Bait Fishing: Executive Summary
Problem
Fishing can leave many fishermen feeling uncertain as they wait and wonder whether they should check whether any fish have stolen the live bait off of their hook. Faced with this uncertainty, impatient people reel in too frequently and spend much of their time reeling and re-casting, while others are overly patient and sit for an hour with a hook with no bait in the water because a fish has stolen their worm.
Probability Model
Our probability model uses dynamic equations and discrete time intervals to addresses this uncertain challenge by calculating an optimal interval which the fisherman should reel to check the line in if he hasn’t hooked a fish, as well as the expected total catch for the fisherman. The solution varies based on two uncertainties: (a) the frequency with which fish at the location bite at the bait, and (b) the probability that a fish steals the bait without the fisherman knowing it.
Essentially, in every minute that the fisherman has a line in the water, there is a certain probability that a fish will bite at the line. The higher cumulative minutes in the interval that fisherman decides to keep his line out, the higher the probability that a fish will bite at the bate sometime in the that time. However, there is a risk that a fish bites and steals the bait without getting hooked and without the fisherman knowing it. If this uncertain risk occurs, the fisherman does not get any added probability of catching a fish until he rebaits his hook. By employing dynamic equations to evaluate the entire time of the fishing outing, our model’s calculation estimates the interval (in minutes) that h should check his line.
Sensitivity Analysis and Extensions
We analyze this model with different frequency of fish biting, as well as different levels of likelihood of the fish taking the bait off the hook without getting caught. Model extensions include situations where one can only keep (and seeks to catch) fish of a certain length, as well as a “rookie factor” to account for the possibility that the bait falls off the hook immediately during the cast.
Conclusions
For a fisherman who frequently tracks his catch and bait used at a particular location, this model could be used to increase his total catch as well as to reduce that feeling of self doubt about when to check the line. More generally, for most ranges of values, it is apparent that risk of checking one’s hook too often has a much more sensitive impact on the estimated total catch than does waiting too long. Patience truly is useful in fishing. Also, losing bait immediately upon casting is a habit a “rookie” should work very hard to break.