Tim Ott, Jack Moore,
Raghavender PN,
Sandeep Reddy
MS&E 220
Is there still bait
on my hook?
PROBLEM: Should the fisherman
reel in and check his hook?
Rechecking the bait on a hook too frequently lowers total
fishing time and number of fish caught
Not checking enough means you might be fishing with a hook
and no bait
SOLUTION: Dynamic Equations & Probability
In discrete time intervals, dynamic equations can help identify
a optimal time interval to re-check hook if no fish have been
hooked, as well as forecasted expected total catch
Solution varies by frequency of bites fish (p) and probability of
fishing being caught if it nibbles on bait (q)
E ( x, y) pq[1 E ( x 1, n)] p(1 q) E ( x y, n) (1 p) E ( x 1, y 1)
Result: More Fish,
Less Doubt
*Optimal interval:
In this scenario, 11 minutes
fish bite bait every
10 min on average, Expected catch
and 7 in 10 that
bite get hooked. 7
6
Expected Catch
Reeling in 5
optimally, which is 4
every 11 min if no 3
fish is hooked, can 2
double catch 1
compared to less 0
0 20 40 60 80 100 120 140
patient approach
Frequency of reel in time (in minutes)
Time Periods (t)
Model Extensions
Consideration of a “rookie factor” of losing bait
immediately upon cast
Calculation of expected catch and optimal patience if
some fish are too small to keep
E ( x , y ) bl [ p l q l (1 E ( x 1, n )) p l (1 q l ) E ( x y , n ) (1 p l ) E ( x 1, y 1)]
b (1 l )[ p s q s E ( x 1, n ) p s (1 q s ) E ( x y , n ) (1 p s ) E ( x 1, y 1)] (1 b ) E ( x y , n )