Board Thread:Game Discussion/@comment-59.61.168.173-20131108044038/@comment-9890645-20131112164726

Using straight binomial probability, the % chance that 1 of 10 pulls is your 10% success is 38.7%. The same formula gives Yankees' number of 34.9% (rounding!) when you assume 0 of 10 successes.

Given those two probabilities, your odds of being successful at least once are 100 - 34.9% = 65.1%.

The probability of failing on 20 tries is 12.16%. So there is a significant chance of failure here. If the success % is less than 10%, this percentage increases rapidly; if the success is 7%, 0 for 20 occurs 23.42% of the time.