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I have a desired percentage, 33%, and a 100-sided dice. I also have the number of times the dice has been rolled, and the number of times the dice roll has been successfully under the desired percentage.

How would I go about changing the desired percentage to match the real results? Such that when the dice has been rolled 3 times and succeeded 1 time, the target is the default of 33. Yet when the dice has been rolled 4 times and succeeded 1 time, the target increases (and so becomes easier), and when the dice has been rolled 3 times and succeeded 2 times, the target decreases (and becomes more difficult) by going down to around 16. It's also important that the target never reaches 100% or 0%, ideally capping out at 99% or 1% for a really long string of lucky/unlucky rolls.

If you could post an example with the actual numbers plugged in that would be super helpful, too.

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    Basically the target for each dice roll is changed each roll, based on the number of tries vs successes to attempt to return towards the base, which is 33%. So 3 tries 1 success would be 33 for the next roll (normal), 4 tries 1 success would be around 41 (too many tries), 3 tries 2 success would be around 22 (too many successes).2012-11-30

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If I understand you, you want to roll a d100 numerous times, changing the success threshold to try to keep the number of successes close to 33%. This is not enough information to formulate an answer. One simple approach would be whenever the fraction of success is less than 33%, make the threshold 99 so you almost always succeed. When it is greater than 33%, make the threshold 1 so you almost always fail. It sounds like you want something smoother than that. You could do something like threshold=33-2(current-33)=99-2current, applying your cap to 1 or 99 at the end. You could change the multiplier from 2 to suit you. This one is continuous, but has corners, which could be smoothed. There are many more.

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    That's unfortunate, as I'm mainly looking for something that will scale between 1 and 99. The formula works great for below $5$0%, but that's just half the problem. This is mainly intended for smaller amounts of tries since just a raw 33% will trend towards that given a long enough time.2012-12-01