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Prophet

Fishing Math

Arrr, ahoy! This here be International Talk Like a Pirate Day, an' to celebrate, here be treasure! A handsome treasure of the mind, maties, and you may lay to that!

Piracy aside, this is the beginning of what I hope will become a resource for a lot of fishing related math or mathematically sound answers to difficult fishing questions. Questions like "how far should I cast when I'm powerfishing in Durem?" or "how much junk does the 2nd place Overall fisher have right now?" It is by no means complete, and I'm open to additions, suggestions, and questions from all corners! blaugh
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Prophet

Assumptions and Notes
The powerfishing tables assume that you always cast to exactly the listed distance, and that you catch everything you hook. The powerfiltering tables assume that you always cast to exactly the listed distance, and that you catch whatever you hook unless it is junk (or a yellow guppy) in which case you always filter it out.

The average casts column is the average number of casts you need to fill the bucket. For very short casts you will often not hook a fish, so the number of casts needed is very large.

The speed column is calculated as follows:
Speed = 1000 * Total Score of Buckets / Total Distance Reeled
This is the average score per foot reeled, times 1000 to make it look impressive. wink

Old cans are more likely to be hooked than other junk. The exact reason why was only recently discovered. Each chance to hook has a 1/200 chance of defaulting to an old can due to a poorly written line in the game - the exact effect on the value of junk you're catching therefore depends on the bait you are using. Because A bait has fewer junk available, the can default makes a bigger impact on what junk is hooked. On the other hand, when using F bait, the impact is less. The results of this finding have not yet been worked into the math here, but they will be as soon as I stop being all lazy.
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Prophet

Bass'ken Math

Bass'ken Perfect Bucket = 378pts

Bass'ken Powerfishing
F Bait
Optimal Cast Length: 75ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................48.764652....................121.367786....................13.73249814
035....................48.775824....................63.5937460....................22.83771458
040....................48.785898....................44.1733130....................29.09212886
045....................49.593020....................35.7080520....................32.69377423
050....................51.071246....................30.2824010....................35.86193355
055....................52.888362....................26.2536680....................39.06257459
060....................56.720510....................24.4688660....................41.15722080
065....................57.957400....................22.6656340....................41.89943552
070....................59.668130....................21.6671060....................41.82249849
075....................61.527364....................20.7384890....................41.98723022
080....................62.557108....................19.9430050....................41.55399622
085....................63.857526....................19.6461480....................40.41793886
090....................64.483688....................19.2225650....................39.31850379
095....................65.335546....................18.9936960....................38.10963918
100....................65.679754....................18.7620060....................37.25992583

D Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................67.822410....................131.38901....................17.60882871
035....................67.812648....................68.542382....................29.36937846
040....................67.827396....................47.520282....................37.45579024
045....................69.364060....................38.111599....................42.68515952
050....................72.153062....................32.032198....................47.73261579
055....................75.379070....................27.568048....................52.85160566
060....................81.754532....................25.339167....................57.15689720
065....................83.975360....................23.341641....................58.83966240
070....................87.007912....................22.168284....................59.52170904
075....................90.823050....................21.093067....................60.87420756
080....................93.505512....................20.221798....................61.20524123
085....................96.223022....................19.849512....................60.24461463
090....................97.879116....................19.384214....................59.15578212
095....................99.765252....................19.107890....................57.82700015
100....................100.20658....................18.852622....................56.55963538

A Bait
Optimal Cast Length: 85ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................80.997858....................158.10090....................17.40748282
035....................80.994480....................81.695033....................29.24697546
040....................81.001638....................56.420992....................37.38225817
045....................84.048746....................44.441569....................44.00853736
050....................89.419446....................36.604754....................51.38304638
055....................95.204946....................31.023424....................58.90478758
060....................105.02505....................27.721321....................66.75380753
065....................108.69201....................25.235078....................70.11180370
070....................114.44001....................23.622307....................73.19121375
075....................122.35535....................22.141636....................77.90317301
080....................129.78954....................21.020157....................81.54622806
085....................135.71586....................20.448194....................82.34660541
090....................139.61213....................19.845360....................82.31521591
095....................144.18040....................19.450637....................82.02300642
100....................144.57425....................19.130473....................80.35780332

Bass'ken Filtering (All Junk)
Filtering out junk is impossible in Bass'ken unless you also filter yellow guppies.

Bass'ken Filtering (All Junk, One Small)
D Bait
Optimal Cast Length: 90ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................111.220590....................96.782026....................33.72167065
050....................116.614886....................79.535431....................40.40549523
055....................122.453068....................66.808043....................47.59763287
060....................132.799036....................58.836387....................55.37520557
065....................136.142542....................53.503220....................59.13786814
070....................140.698156....................49.968839....................62.14753226
075....................146.649604....................46.691871....................65.89917727
080....................151.338550....................44.342237....................68.19794502
085....................155.366946....................43.032333....................68.87892235
090....................157.837184....................41.771177....................68.95309599
095....................160.564880....................40.901435....................68.64820413
100....................161.082108....................40.264085....................67.88751155

A Bait
Optimal Cast Length: 95ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................113.466958....................91.752522....................33.69590217
050....................122.382220....................73.215809....................42.29602035
055....................131.178462....................60.100437....................51.53594177
060....................144.716136....................51.275714....................62.49176259
065....................149.725668....................45.985709....................67.77569545
070....................157.302826....................42.122040....................73.31550952
075....................168.161168....................38.537056....................80.88586691
080....................178.703944....................35.968636....................87.05033484
085....................186.152372....................34.412072....................89.91204511
090....................191.251918....................33.113108....................91.30711918
095....................196.723468....................32.107326....................92.29453976
100....................197.042608....................31.504526....................91.08181500
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Prophet

Gambino Math

Gambino Perfect Bucket = 522pts

Gambino Powerfishing
F Bait
Optimal Cast Length: 65ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................113.784188....................121.36779....................32.04249565
035....................113.810256....................63.593746....................53.28800068
040....................113.833762....................44.173313....................67.88163400
045....................114.889180....................35.708052....................75.73970919
050....................116.853734....................30.282401....................82.05401614
055....................119.273098....................26.253668....................88.09337464
060....................124.405790....................24.468866....................90.27063698
065....................126.010800....................22.665634....................91.09762325
070....................128.266490....................21.667106....................89.90436075
075....................130.640036....................20.738489....................89.15079260
080....................131.883652....................19.943005....................87.60463762
085....................133.542294....................19.646148....................84.52416828
090....................134.307472....................19.222565....................81.89309592
095....................135.355674....................18.993696....................78.95175311
100....................135.862986....................18.762006....................77.07466111

D Bait
Optimal Cast Length: 75ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................158.252290....................131.38901....................41.08726700
035....................158.229512....................68.542382....................68.52854973
040....................158.263924....................47.520282....................87.39684390
045....................160.144060....................38.111599....................98.54923063
050....................163.628198....................32.032198....................108.2476847
055....................167.642510....................27.568048....................117.5415912
060....................175.555668....................25.339167....................122.7359147
065....................178.316160....................23.341641....................124.9421575
070....................182.028168....................22.168284....................124.5246255
075....................186.583930....................21.093067....................125.0579988
080....................189.630568....................20.221798....................124.1251388
085....................192.841758....................19.849512....................120.7369833
090....................194.738044....................19.384214....................117.6949872
095....................196.950468....................19.107890....................114.1585323
100....................197.513962....................18.852622....................111.4828776

A Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................188.995002....................158.10090....................40.61745990
035....................188.987120....................81.695033....................68.24294274
040....................189.003822....................56.420992....................87.22526906
045....................192.560674....................44.441569....................100.8261755
050....................198.885494....................36.604754....................114.2854605
055....................205.682594....................31.023424....................127.2590345
060....................217.205930....................27.721321....................138.0558528
065....................221.443770....................25.235078....................142.8423500
070....................228.036646....................23.622307....................145.8430344
075....................236.935914....................22.141636....................150.8561751
080....................245.027598....................21.020157....................153.9498181
085....................251.628464....................20.448194....................152.6774427
090....................255.898006....................19.845360....................150.8772842
095....................260.965080....................19.450637....................148.4608201
100....................261.443552....................19.130473....................145.3165403

Gambino Filtering (All Junk)
D Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................254.159584....................64.998370....................106.2125431
050....................257.920776....................54.025429....................120.0028377
055....................262.141402....................45.884798....................133.5620322
060....................270.011866....................41.249221....................142.7441584
065....................272.633768....................37.723548....................147.7119842
070....................276.265794....................35.497086....................149.5170951
075....................280.910368....................33.443659....................152.0928586
080....................284.490386....................31.901737....................152.6477403
085....................287.767448....................31.106508....................150.0469555
090....................289.757920....................30.276840....................147.5272433
095....................292.021494....................29.735104....................144.1880759
100....................292.462048....................29.295611....................141.5875614

A Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................255.713998....................61.905469....................104.4128793
050....................262.013064....................50.324640....................120.5318808
055....................268.569592....................42.060734....................136.3124573
060....................279.228424....................36.835689....................149.9663754
065....................283.184098....................33.306413....................156.6345819
070....................289.418436....................30.879973....................161.4109094
075....................298.121740....................28.619977....................168.1998692
080....................306.556606....................26.973982....................172.5889132
085....................312.903652....................26.053108....................172.0733122
090....................317.222290....................25.173722....................170.8481997
095....................322.013950....................24.561842....................168.6489171
100....................322.368204....................24.126694....................165.5986115

Gambino Filtering (All Junk, One Small)
D Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................255.219030....................96.782026....................77.38146393
050....................260.613254....................79.535431....................90.29900000
055....................266.451452....................66.808043....................103.5699521
060....................276.797404....................58.836387....................115.4203646
065....................280.140998....................53.503220....................121.6882038
070....................284.696724....................49.968839....................125.7528836
075....................290.647996....................46.691871....................130.6069931
080....................295.336990....................44.342237....................133.0882039
085....................299.365274....................43.032333....................132.7177884
090....................301.835616....................41.771177....................131.8605646
095....................304.563360....................40.901435....................130.2135791
100....................305.080572....................40.264085....................128.5751789

A Bait
Optimal Cast Length: 90ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................257.465422....................91.752522....................76.45864333
050....................266.380700....................73.215809....................92.06274823
055....................275.176798....................60.100437....................108.1084137
060....................288.714584....................51.275714....................124.6736110
065....................293.724212....................45.985709....................132.9589175
070....................301.301234....................42.122040....................140.4301121
075....................312.159472....................38.537056....................150.1493466
080....................322.702376....................35.968636....................157.1949072
085....................330.150748....................34.412072....................159.4636084
090....................335.250302....................33.113108....................160.0545480
095....................340.721732....................32.107326....................159.8525878
100....................341.040992....................31.504526....................157.6442418
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Prophet

Durem Math

Durem Perfect Bucket = 666pts

Durem Powerfishing
F Bait
Optimal Cast Length: 65ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................178.803724....................121.36779....................50.35249317
035....................178.844688....................63.593746....................83.73828678
040....................178.881626....................44.173313....................106.6711391
045....................180.185340....................35.708052....................118.7856441
050....................182.636222....................30.282401....................128.2460987
055....................185.657834....................26.253668....................137.1241747
060....................192.091070....................24.468866....................139.3840532
065....................194.064200....................22.665634....................140.2958110
070....................196.864850....................21.667106....................137.9862230
075....................199.752708....................20.738489....................136.3143550
080....................201.210196....................19.943005....................133.6552790
085....................203.227062....................19.646148....................128.6303977
090....................204.131256....................19.222565....................124.4676880
095....................205.375802....................18.993696....................119.7938670
100....................206.046218....................18.762006....................116.8893964

D Bait
Optimal Cast Length: 65ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................248.682170....................131.38901....................64.56570528
035....................248.646376....................68.542382....................107.6877210
040....................248.700452....................47.520282....................137.3378976
045....................250.924060....................38.111599....................154.4133017
050....................255.103334....................32.032198....................168.7627537
055....................259.905950....................27.568048....................182.2315767
060....................269.356804....................25.339167....................188.3149323
065....................272.656960....................23.341641....................191.0446526
070....................277.048424....................22.168284....................189.5275419
075....................282.344810....................21.093067....................189.2417901
080....................285.755624....................20.221798....................187.0450364
085....................289.460494....................19.849512....................181.2293519
090....................291.596972....................19.384214....................176.2341922
095....................294.135684....................19.107890....................170.4900645
100....................294.821346....................18.852622....................166.4061199

A Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................296.992146....................158.10090....................63.82743699
035....................296.979760....................81.695033....................107.2389100
040....................297.006006....................56.420992....................137.0682800
045....................301.072602....................44.441569....................157.6438137
050....................308.351542....................36.604754....................177.1878746
055....................316.160242....................31.023424....................195.6132814
060....................329.386810....................27.721321....................209.3578981
065....................334.195530....................25.235078....................215.5728963
070....................341.633278....................23.622307....................218.4948551
075....................351.516482....................22.141636....................223.8091772
080....................360.265654....................21.020157....................226.3534082
085....................367.541072....................20.448194....................223.0082801
090....................372.183878....................19.845360....................219.4393524
095....................377.749760....................19.450637....................214.8986339
100....................378.312856....................19.130473....................210.2752772

Durem Filtering (All Junk)
D Bait
Optimal Cast Length: 75ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................398.157872....................64.998370....................166.3890044
050....................401.919368....................54.025429....................187.0010839
055....................406.139666....................45.884798....................206.9296903
060....................414.010138....................41.249221....................218.8701171
065....................416.632144....................37.723548....................225.7297807
070....................420.264202....................35.497086....................227.4501007
075....................424.908744....................33.443659....................230.0576728
080....................428.488778....................31.901737....................229.9123167
085....................431.765744....................31.106508....................225.1301731
090....................433.756360....................30.276840....................220.8425573
095....................436.019742....................29.735104....................215.2884254
100....................436.460584....................29.295611....................211.3005436

A Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................399.712334....................61.905469....................163.2101332
050....................406.011512....................50.324640....................186.7743936
055....................412.568136....................42.060734....................209.3988973
060....................423.227032....................36.835689....................227.3043090
065....................427.182514....................33.306413....................236.2828809
070....................433.416828....................30.879973....................241.7199310
075....................442.120300....................28.619977....................249.4436555
080....................450.554838....................26.973982....................253.6587641
085....................456.902076....................26.053108....................251.2615403
090....................461.220730....................25.173722....................248.4022525
095....................466.012270....................24.561842....................244.0654037
100....................466.366532....................24.126694....................239.5696883

Durem Filtering (All Junk, One Small)
D Bait
Optimal Cast Length: 80ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................399.217470....................96.782026....................121.0412572
050....................404.611622....................79.535431....................140.1925048
055....................410.449836....................66.808043....................159.5422714
060....................420.795772....................58.836387....................175.4655235
065....................424.139454....................53.503220....................184.2385395
070....................428.695292....................49.968839....................189.3582350
075....................434.646388....................46.691871....................195.3148089
080....................439.335430....................44.342237....................197.9784629
085....................443.363602....................43.032333....................196.5566544
090....................445.834048....................41.771177....................194.7680333
095....................448.561840....................40.901435....................191.7789541
100....................449.079036....................40.264085....................189.2628463

A Bait
Optimal Cast Length: 85ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................401.463886....................91.752522....................119.2213845
050....................410.379180....................73.215809....................141.8294761
055....................419.175134....................60.100437....................164.6808856
060....................432.713032....................51.275714....................186.8554593
065....................437.722756....................45.985709....................198.1421395
070....................445.299642....................42.122040....................207.5447147
075....................456.157776....................38.537056....................219.4128264
080....................466.700808....................35.968636....................227.3394795
085....................474.149124....................34.412072....................229.0151716
090....................479.248686....................33.113108....................228.8019767
095....................484.719996....................32.107326....................227.4106358
100....................485.039376....................31.504526....................224.2066686
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Prophet

Junk Math

Junk Powerfishing
D Bait
Optimal Cast Length: 55ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................26.30476300....................131.38901....................6.829543008
035....................26.31105234....................68.542382....................11.39520837
040....................26.30152601....................47.520282....................14.52428516
045....................26.13280592....................38.111599....................16.08157004
050....................25.79137056....................32.032198....................17.06219456
055....................25.40433061....................27.568048....................17.81210173
060....................24.64925229....................25.339167....................17.23298691
065....................24.38424362....................23.341641....................17.08549582
070....................24.05058253....................22.168284....................16.45289196
075....................23.68693609....................21.093067....................15.87618412
080....................23.50797077....................20.221798....................15.38744606
085....................23.26575850....................19.849512....................14.56654162
090....................23.14767132....................19.384214....................13.98989547
095....................22.98757403....................19.107890....................13.32430300
100....................22.92755620....................18.852622....................12.94100891

F Bait
Optimal Cast Length: 55ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
030....................38.78318336....................121.36779....................10.92164040
035....................38.77586871....................63.593746....................18.15555637
040....................38.76927295....................44.173313....................23.11898993
045....................38.64734775....................35.708052....................25.47793343
050....................38.40853745....................30.282401....................26.97025285
055....................38.11280490....................26.253668....................28.14956312
060....................37.47417562....................24.468866....................27.19180276
065....................37.29341110....................22.665634....................26.96071380
070....................37.02580969....................21.667106....................25.95207643
075....................36.77325792....................20.738489....................25.09464319
080....................36.66823654....................19.943005....................24.35713241
085....................36.49233143....................19.646148....................23.09743131
090....................36.42406793....................19.222565....................22.20933537
095....................36.32765364....................18.993696....................21.18959521
100....................36.24756178....................18.762006....................20.56313219

Junk Reverse Filtering
F Bait
Optimal Cast Length: 75ft
Cast Length.........Average Score..............Average Casts.....................Speed.........
045....................72.000000....................62.044378....................25.78799323
050....................72.000000....................48.025555....................29.98403662
055....................72.000000....................44.591020....................29.35772514
060....................72.000000....................40.441910....................29.67218907
065....................72.000000....................35.370747....................31.31662183
070....................72.000000....................33.262907....................30.92247555
075....................72.000000....................29.574964....................32.45988736
080....................72.000000....................29.144809....................30.88028472
085....................72.000000....................28.200494....................30.03702075
090....................72.000000....................26.065028....................30.69246655
095....................72.000000....................25.503124....................29.71772152
100....................72.000000....................23.851502....................30.18677817

Average Value of Junk
Current Estimate: 3.928382427

Soucres:
Red HOOD Warrior 11911 12042 13170
Holy Knight57 15381 15310 17109
Domain Name 28 36 73
The_last_alchemist 16490 16608 18127
Zanam Djinn 9350 9529 10392
K Prime 3889 3922 4405
Bria_Teragram 17230 17027 19090
Gaidin 13396 13498 14981
tiranaki 7719 7653 8684

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Prophet

Overall Math
STILL HEAVILY UNDER CONSTRUCTION!

Equations to Qualify By
You qualify if and only if
4*B>B+G+D+J
and
4*G>B+G+D+J

If you have many Bass'ken fish and Gambino fish, the maximum number of Durem fish you can have and still qualify is:
D<B+G-2*|B-G|-J

If you have many Bass'ken fish and Durem fish, the number of Gambino fish you need to qualify is
G>(B+D+J)/3

If you have many Gambino fish and Durem fish, the number of Bass'ken fish you need to qualify is
B>(G+D+J)/3

If you have many Durem fish and few Bass'ken and Gambino fish, the number of Bass'ken and Gambino fish you'll need to qualify is
B>(D+J)/2
and
G>(D+J)/2

Equations to Score By
Basic Definitions
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Basic definitions. Lake Score and # Fish Caught can be determined from the stats page, but anything involving junk is harder to determine from a casual glance.

Performance Index
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The first equation is useful only for the people who are on Channels and the person in first place. The middle two are for personal use, since you can keep track of your own junk fish and score easily. The last is what Extended Stats uses, together with an estimate of the junk fish.

Final Score
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Final Score is always visible for everyone on the Overall list, as well as in your personal stats. These are included for completeness, and because the third equation can be solved for a junk estimate.

Equations for Comparing Fishers
Junk Estimate
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Junk Estimate - image too big to include here.

Normalized Score
Normalized Final Score = (Raw Score-8*Gambino Fish-16*Durem Fish)^2/(20*Total Fish)

Normalized score is useful for comparing fishers towards the beginning of the month when they have many fish from one lake. For example, if Alice is fishing for Overall but is sticking to Bass'ken for the first week and Bob is also fishing for Overall but fishing in Gambino, then it can be difficult to compare the two. It is not generally useful, but could also be used for inter-lake competitions of other sorts.

Potential Score
Potential Final Score = (Bassken Average Value*Bassken Potential Fish+Gambino Average Value*Gambino Potential Fish+Durem Average Value*Durem Potential Fish+Junk Score)^2/(20*(Bassken Potential Fish+Gambino Potential Fish+Durem Potential Fish+Junk Fish))

Bassken Average Value = Bassken Score/Bassken Fish
Gambino Average Value = Gambino Score/Gambino Fish
Durem Average Value = Durem Score/Durem Fish

If D+J>2*B and D+J>2*G
Bassken Potential Fish = (Durem Fish+Junk Fish)/2+1
Gambino Potential Fish = (Durem Fish+Junk Fish)/2+1
Durem Potential Fish = Durem Fish

If D+J>2*B and D+J<=2*G or D+J<=2*B and D+J<=2*G and G>=B
Bassken Potential Fish = Gambino Fish
Gambino Potential Fish = Gambino Fish
Durem Potential Fish = 2*Gambino Fish-Junk Fish-1

If D+J<=2*B and D+J>2*G or D+J<=2*B and D+J<=2*G and B>=G
Bassken Potential Fish = Bassken Fish
Gambino Potential Fish = Bassken Fish
Durem Potential Fish = 2*Bassken Fish-Junk Fish-1

So what does all this involved calculation do? It tells you much much score you'd have if you fished out to your full potential. That is, if you fished to the point where you had the maximum Durem fish while still qualifying for Overall. However, this relies on a couple assumptions: first, that you won't catch any more junk than you already have, and second, that you continue to fish at approximately the same score per fish in a particular lake. Overall fishers tend to take one of two routes in fishing - either they build up a lot of potential during the first half of the month and then fulfill it during the second, or they continually hop between lakes and keep themselves at potential. In the second case it is easy to tell where they are and where they'll end up, but in the first case, something like this can help to determine how far they've gotten.
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