"A coin you can both see spinning works fine for that - you can use a random source of 0s and 1s to generate an arbitrary-precision fraction uniformly between 0 and 1."
"Let's say that Text is 0 and Queen is 1, on a spinning coin. The first time you spin it, add 1/2 to the total if it comes up Queen. The next time you spin it, add 1/4 to the total if it comes up Queen. Third time, 1/2 to the third power or 1/8."
"Suppose you spin three times and the results are Queen, Text, Queen, Text. The current running total is 1/2 + 0/4 + 1/8 = 5/8 or 0.625, can't get any lower than that, and can never go above 6/8ths or 0.725 even if every future spin comes up Queen. So if you were trying to generate a 60/100 chance of something, you could stop at that point and declare that the event hadn't happened."
"Uh, assuming there's no magic way to control how coinspins land. If there is, you'd have an arms race between that and Detect Magic and whatever counters Detect Magic etcetera, if the coinspins were important."