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As much as I'd love my characters to max out their hit points each level, d20 systems are based on the average roll. It really sucks, though, when your fighter rolls a 1 and the other guy's mage rolls a 4. You get to roll hit points so infrequently, that it sometimes seems like a big gamble to roll d10 each time.
For those that would prefer to mitigate that risk, I present an alternative method. The following chart lists adjusted rolls for each type of hit die. Each roll gives you the exact same average you would get with the standard roll but, as you move from left to right, you trend more and more towards the average. You sacrifice your chance to max out in order to avoid the killer low rolls.
DM's can optionally skew the results towards higher powered campaigns by increasing the die roll modifier by one or two points.
| Regular Hit Die | Adjusted Hit Die |
| d12 (1-12) | d10+1 (2-11) | d8+2 (3-10) | d6+3 (4-9) | d4+4 (5-8) | d2+5 (6-7) |
| d10 (1-10) | | d8+1 (2-9) | d6+2 (3-8) | d4+3 (4-7) | d2+4 (5-6) |
| d8 (1-8) | | | d6+1 (2-7) | d4+2 (3-6) | d2+3 (4-5) |
| d6 (1-6) | | | | d4+1 (2-5) | d2+2 (3-4) |
| d4 (1-4) | | | | | d2+1 (2-3) |
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