As I modify the rules of what I'll continue to call my OD&D game, I've decided to change the hit dice progressions away from what is found in the LBBs and Supp 1.
Here is how the new hit dice progressions look:
As a character moves up a level, he will roll the total number of dice shown... and if the number rolled is higher than his current total hit points, he'll use the new total. For example, a 3rd level thief with 11 hit points makes it to 4th level. The player rolls 4d6, as shown. If he rolls higher than an 11, he gets the new total; otherwise he keeps the 11.
For Mages, a d5 will be simulated as follows: roll a d6, rerolling if a 6 appears.
In addition, characters with a 15 or better constitution can add a +1 per level to their score; and Fighters and Adventurers with an 18 constitution can add +2 per level to their score.
*From this point forward, a character's constitution bonus is frozen, and a cumulative addition as shown is added to the roll of the dice. For example, a player with a Cleric attaining 12th level with a 16 constitution would roll 10d6 (tenth level) +10 (Cumulative but frozen constitution bonus) +2 (11th level) +2 (12th level). If this sum were higher than the current hit point total, the cleric would use the new, higher total; otherwise would remain at the previous hit point total.
As with all modifications I attempt; we'll see how this plays out in the game...