That sounds more like what I was experiencing in the game, which is why I was looking to increase those numbers. I see the key is to look at the odds of not being noticed instead. I guess it's because being noticed is a single event per multiple steps and not being noticed is a single event per one step, but I still find that difference pretty elusive.
You can think of it like flipping a coin twice, where flipping tails is "being noticed".
If you flip tails on the first flip, you're done. That will happen half the time.
The only way to get noticed on your second flip is to flip "heads - tails". That happens 1/4 of the time (half times half).
The only way not to get noticed at all is to flip "heads - heads". If you think about it, the only way to avoid being detected in x turns is to flip heads x times. The odds of that happening are (1/2)**x (one-half to the xth power). The odds of being noticed, then, are one minus that number.
It takes a bit more care in keeping track of things when the odds of "being detected" are not equal to the odds of "slipping by successfully" for each turn, but the logic is identical.