>Extensive play-testing revealed that a player who was told that he had a 33 percent chance of success in a battle but then failed to defeat their opponent three times in a row would become irate and incredulous...So Meier altered the game to more closely match human cognitive biases; if your odds of winning a battle were 1 in 3, the game guaranteed that you’d win on the third attempt...
Fire Emblem (another strategy game series) solves this problem by taking the average of two random numbers. If the average is lower than the "to miss" value, an action succeeds [0]. This skews the probabilities at the low and high ends so that an 80% chance becomes 92%, 90% becomes 98%, etc, to minimize the occurrence of "spearman defeats tank" scenarios where players assume a 1/10 chance of failure will never happen.