Well, 3d6 for PC stat generation in 1e AD&D isn't really viable/desirable, according to it's primary author. There are quite a few OD&D & classic D&D gamers that play 1e AD&D with those/their game's assumptions, but the 1e DMG gives 4 methods for character stat generation, the first being 4d6 drop lowest, arrange to taste.
Method 2 is "All scores are recorded and arranged as in Method I. 3d6 are rolled 12 times and the highest 6 scores are retained."
Method 3 is "Scores rolled are according to each ability category, in order, STRENGTH, INTELLIGENCE, WISDOM, DEXTERITY, CONSTITUTION, CHARISMA. 3d6 are rolled 6 times for each ability, and the highest score in each category is retained for that category."
Method 4: "3d6 are rolled sufficient times to generate the 6 ability scores, in order, for 12 characters, The player then selects the single set of scores which he or she finds most desirable and these scores are noted on the character record sheet." (see 1e DMG pg 11 for all)
Furthermore, right at the start of describing ability scores in the player's handbook, Gygax wrote: "The premise of the game is that each player character is above average - at least in some respects - and has superior potential. Furthermore, it is usually essential to the character's survival to be exceptional (with a rating of 15 or above) in no fewer than two ability characteristics. Each ability score is determined by random number generation. The referee has several methods of how this random number generation should be accomplished suggested to him or her in the DUNGEON MASTERS GUIDE. The Dungeon Master will inform you as to which method you may use to determine your character's abilities." 1e PH pg 9, underline mine
So while it is true that one has to be lucky to play a few classes or combos (paladin, monk, bard, dual class humans), generally the only actual limitation is when one is very UNLUCKY, as defined by rolling a stat of 5 or less.
