This is where mathematics meets psychology. The system must not only function correctly, it must function in a manner perceived as fair by the player. Although it is theoretically possible to have 10 or 20 consecutive failures, the vast majority of players will not tolerate more than 4 or 5. In those cases perhaps we need to modify the algorithm. For example if a player has had 4 consecutive failures, then guarantee a success on the next try. To compensate for the slight increase in total percentage of successes, drop the percentage chance of success slightly. Result: same overall success percentage over a sample of all players, but no more unhappy players complaining about 7 consecutive failures at 70% probability of success.