| I did a lot of mathematics a while back when I was working on the subsystems of Obsidian, but for the whole thing I have used lots of computer simulations as it tends to be faster and can account for variances without a lot of complicated math. So I don't have a good "insert DC to produce win rate" formula for you.
However I can tell you that bumping the DC by 1 for the whole encounter tends to drop a party's win rate by 10%. So bumping it by 1 for one segment is about 3.3% or so. The number varies slightly if the player's know when the DC changes, as that might affect their decision making (aka I am more likely to spend an action point to reroll the skill check if I know the DC is low, since I have a better chance of getting it then if I reroll against a high DC). | 
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