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I live in the Northern Territory, Australia where for the second year running the government and commercial entities have created a 1 million AUD fish competition to encourage tourism. One tagged and released barramundi if caught anywhere in the many waters within the NT will net the fisher $1 million. My question is given we are talking about a single fish with free reign to travel, are the odds of catching it increased by the number of times someone has a go? I'm inclined to think a person fishing for one day in a single spot has as much chance as a person who goes to a number of places even daily, as this fish is a moving target with a huge playing field. But I am not a statistician. Please enlighten me! PS I think for statistical purposes we would have to disregard the skill of the fisher and their knowledge of waters. Or does that come into play?

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My question is given we are talking about a single fish with free reign to travel, are the odds of catching it increased by the number of times someone has a go?

Almost certainly yes. Compare trying to catch the fish on $n$ days at a given spot compared to trying to catch it on $n - 1$ days. It seems possible to me that even if the fish happened to be present every time, you happened to miss it $n - 1$ days in a row and have a new chance to catch it on the $n$th.

I'm inclined to think a person fishing for one day in a single spot has as much chance as a person who goes to a number of places even daily

That seems to require the fish to be so mobile that its position on one day is totally unrelated to its position on the previous day, which seems very unlikely.

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