This has to be the last time I reply to this....
Rubik, I looked at your spreadsheet example and found a big problem, at least in my Excel, the random number function produces an 'evenly distributed' set of random numbers (it says so in the formula description), so this cannot represent the independent craft events that occur in game. Also at 50% odds either way, like the flip of a coin, it will at times appear as if the average/overall probability is 50% but it does not have to stay that way.
Gidget, sample size is irrelevant. These are independent events, so their population is 1. There is an equation for determining the correct sample size of a population, but it requires the population size, standard deviation, and the z-scores that correspond to the desired confidence interval. You can't do that with independent events, no matter how much data you collect. And we don't need to because the population of an independent event is 1 and we already are given the probability for one action, it is displayed in the craft window.
Bittty, going back to my roulette example (which I have to correct since we have 38 spaces on an American roulette wheel) no matter how many observations you make and calculate the probability from, these are just curious observations. They have no analytical or predictive value. There is no overall or average success rate for a group of independent events since they are in fact independent of each other. The closest we can get would be to ask questions like: What is the probability of hitting number 7 four times in a row? We can easily calculate this by doing (1/38)^4=0.00000048 or less than 5 in a million. Applying this to an Armilo tool situation: What is the probability of no boosts in ten crafts? (9/10)^10=.03486. So even with ten crafts the probability of all failing is still almost 35%, nearly 25% more than your success rate of an individual action. It takes 22 crafts for the chance of failure to fall below the chance of success (9/10)^22=0.0984. But even multiplying the probabilities of independent events is still just an estimation, they are independent and each action is still as probable as its own success rate.
Rubik, I looked at your spreadsheet example and found a big problem, at least in my Excel, the random number function produces an 'evenly distributed' set of random numbers (it says so in the formula description), so this cannot represent the independent craft events that occur in game. Also at 50% odds either way, like the flip of a coin, it will at times appear as if the average/overall probability is 50% but it does not have to stay that way.
Gidget, sample size is irrelevant. These are independent events, so their population is 1. There is an equation for determining the correct sample size of a population, but it requires the population size, standard deviation, and the z-scores that correspond to the desired confidence interval. You can't do that with independent events, no matter how much data you collect. And we don't need to because the population of an independent event is 1 and we already are given the probability for one action, it is displayed in the craft window.
Bittty, going back to my roulette example (which I have to correct since we have 38 spaces on an American roulette wheel) no matter how many observations you make and calculate the probability from, these are just curious observations. They have no analytical or predictive value. There is no overall or average success rate for a group of independent events since they are in fact independent of each other. The closest we can get would be to ask questions like: What is the probability of hitting number 7 four times in a row? We can easily calculate this by doing (1/38)^4=0.00000048 or less than 5 in a million. Applying this to an Armilo tool situation: What is the probability of no boosts in ten crafts? (9/10)^10=.03486. So even with ten crafts the probability of all failing is still almost 35%, nearly 25% more than your success rate of an individual action. It takes 22 crafts for the chance of failure to fall below the chance of success (9/10)^22=0.0984. But even multiplying the probabilities of independent events is still just an estimation, they are independent and each action is still as probable as its own success rate.