I have truly woeful luck with dice. To the extent that there was a point where, when playing Vampire, I wouldn't have my character take any action unless he had enough dice in his pool to claim an automatic success, because every time I rolled the dice I scored a botch. (Seriously)
And, indeed, there's also the "rolling hit points" fiasco - every single time I have rolled hit points for one of my characters in a post-3e d20 game, the die has come up a '1'. (Really - every single time. Though it's important to note that this only applies to 'real' PCs, only to my PCs, and also that I've only had to do so a handful of times, as I almost always DM the game.)
Now, when I'm running a game, I'm generally not too bothered by this. After all, I always have another monster to throw at the PCs, and anyway most of the fun of the game comes from the PCs doing awesome things, and bad dice rolls from the DM help with that. Although it is a little frustrating that any time I try to make allowance for my rotten luck, the dice 'turn' and that slightly-more-challenging encounter becomes a TPK.
However, when playing, it's a different matter altogether. It's horribly frustrating to be playing a character who simply can't hit his opponents. It's especially galling to see all of your Daily and Encounter powers eaten up by dice that simply refuse to come up with anything over a '6' - and yet that happens with distressing regularity.
(Incidentally, Blizzard, the makers of "World of Warcraft", have apparently done some significant work on the subject, and found that the game is most satisfying if characters have roughly a 70% chance of success when doing things they're good at. Which makes sense - you get the satisfaction of competence, without the game being too easy.)
And so, I've been thinking. A dangerous pasttime, I know. But, what if...
First version: Characters gain an escalation bonus to hit. This starts at +0. However, if their attack misses, the bonus increases by +2. Each time the character misses, the bonus increases by +2. However, when the character finally scores a hit, the bonus resets to +0. As always, a critical hit only occurs if the d20 roll comes up a natural '20'. If the system uses a confirmation roll, the escalation bonus does not apply to the confirmation roll.
Second version: Characters have an escalation die. This starts at nothing. However, if they miss, they gain a d4 escalation die. Each time they miss, this increases by one step: d4 to d6, to d8, to d12 (and then it stops). When they score a hit, this reverts back to nothing. When making an attack roll, roll the escalation die also, and add this as a bonus to the attack roll. (And, as above, a critical is scored only if the d20 comes up with a nat-20, and if using a confirmation roll, the escalation die does not apply to that.)
This is completely untested, of course. However, I believe the net effect of this should be that players who are unlucky should see the increased escalation bonus serve to level out their fortune - if they miss frequently on a first attack, they're more likely to hit on the second, and so on. On the other hand, 'lucky' players won't often have access to the escalation bonus/die, but they're hitting anyway so they're happy.
Meanwhile, the escalation bonus isn't so significant that it would encourage players to use rubbish attacks to build up a big bonus, then switch to a strong attack against the hard-to-hit monsters. At least, not usually - there is of course the corner case where the PCs require a '20' to hit the BBEG, and an escalation bonus would bring that much more easily in reach.
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