If there is a creek coming in, yeah 10' they should survive. but if no incoming water, I'd say 15'. I know its extra gear, but I would think that a under water viewer would be handy in actually seeing what is down there. Especially if not biting, meaning is it a 12" hammer handle or a 12" crappie. 2 guys are safer and you can haul more gear easier.
Speaking of creeks, we all know that fish migrate up creeks, so look down stream for lakes for what perhaps is in them, as likely that is what is in the smaller untested waters upstream. This is especially true if pike and walleyes are found downstream waters as they love to travel in the spring.
3 words of advice when exploring, have ice picks strung over your neck... And a ice chisel is very handy to have in your hand in testing the ice as you are walking out. Because from a current, beavers, to a spring, as all it takes is 1 bad step and SWOOSH! And you are in the middle of know where. And why a 50' safety line tied between 2 people is a smart idea - just for in case the unthinkable happens.
Or you could tell me where you are at and when you'll call in just for in case you go missing. That way I can call 911 to have them retrieve your body and someone knows your spot since you'll not be using it any more.
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God, help me be the man that my dog thinks that I am.