Trout up high can’t be too picky when it comes to deciding if they are eating a fly or not, so they are often taken with general purpose flies that don’t exactly match anything - they strike if it’s roughly the correct size and shape.
I generally tell someone new to western fishing to at least bring the flys below. Some of the saddest moments of young adulthood were getting on a hot stream or lake and running out of the fly catching all the fish.
The black wooly bugger about 2” long imitates a type of leach found throughout the west - it stands out, swims nicely and big trout love them. I keep one rigged up about 4’ behind a small water filled casting bubble on an ultra light spinning outfit with 4 lb or 2 lb line (2 lb line actually breaks at 3 lb). If there is a big rock in a river or inaccessible part of a lake - this reaches out nicely and often gets a big strike on the first cast. Strip it in 6” to 12” at a time and it swims well.
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Also for use with a casting bubble or fly outfit is a blue or olive dun as well as the same in black. Sizes 16, 14, and 12 are pretty standard, but I also bring some really small ones that resemble the many small mosquitos and similar looking flying things. It can be fished as a floating fly or waterlogged as a wet. Rainbow stockers love this behind a casting bubble when stripped in fast.
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If you only bring one dry fly I’d go with the elk hair cadis in brown as well as black in multiple sizes clear up to a #10. 90% of the time I’ll be using this on small streams in a size 14 because it floats well and is easy to see. Don’t forget fly floatant with these.
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A subsurface fly like the prince nymph or ears hair nymph should be in every fly fishing box. Size 18 & 16 ish. A smaller one without a bead head makes a good dropper fly, or a bead head under the very floaty Chernobyl Ant.
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Finally, I’m never without the clunky Chernobyl ant in yellow over black about an inch long or so. When fish are striking at anything that falls in the water, these are twice as tough as an elk hair caddis, easy to see and often effective until most of it has been eaten away. I’ve come into a hot lake full of rainbows and brookies and hooked a dozen fish an hour all around the edges with these.
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Every region has it’s own special flies and if someone is into matching the hatches more closely there’s nothing wrong with that, but these should be in every Boy Scout’s bag.