Sometimes the dice abandon us. This doesn't pose a huge problem to GMs - we can conjure more creatures or challenges into the story to make sure it remains an adventure rather than a cakewalk. No, the problem with improbability that I'm tackling today is those few cursed ones utterly bereft of fortune. Those players that constantly roll 1s, that never break the 10 on a d20 in three consecutive games and for whatever reason, simply defy the nature of probability.
Nearly every game I've played in enjoys a house rule to compensate for these situations in some form or another (something I've had to do away with for playtest balance). The options being digested here are as follows: objects of fate, depleting powers and the Luck attribute.
Objects of Fate
The first of these are things that players can get easily within the core rules and are a good solution for the luckless member of a group, but should be granted carefully - some are extremely valuable and if the PC passes away in a situation where their equipment is not compromised, it can become problematic. Stick to the lower level roll manipulation magic items and don't get overzealous about it. This also, of course, can be very frustrating for other players and the last thing a GM needs to be handed is a group with multiple rerolls for each and every member; its tedious and your game is going to ultimately suffer for having such a wide breadth of consequence evasion. While I love the Deck of Many Things, the fact of the matter is that it's a really good time because the randomness inherent can be vastly unbalancing (with joyous, dramatic, stunned and horrified expressions, as well as everything inbetween). I'm a perfect example of the kind of player that really enjoys those kinds of game tools because they never seem to sour on me - I walk away with 5 wishes or some other unbalancing element that aggravates all my companions, who more often than not have suffered a grievous loss.
The second option is something I've referred to before and is definitely a dangerous terrain to cross. If you choose to go this route, I recommend using either the rules given (for Pathfinder, just make them play a halfling with the adaptable luck racial trait) or to model your own off of them. If you're using 3.5, I can tell you from personal experience as a player who enjoyed the Auspician class - it is to be avoided by all but the truly cursed (or at the very least, watered down). That class can be a game changer in a very serious way and if you're not any good for quick improvisation or seamlessly weaving unexpected elements into your story, consider banning it.
Luck as an Attribute
Luck, as a seventh attribute, is my preferred and favorite way to bring some 'entropy' into the mix for die rolls. In the days of yore, before I had to adhere to Pathfinder Core Rules for everything, this was what I used for my home games. Everybody gets one (I preferred them to be at 12 or above) and this replaces The 2 Rule. "You're about to lose your grip, but the plate guarding your arm snags the rope, giving you the instant of relief needed to regain your resolve and hang on for dear life!"
If it's getting really god awful, allow the PC to make a saving throw (determined by how generally improbable their request is, but usually a DC 10) that will grant them a reroll on the original check. Sometimes (for those truly lucky players that net an attribute score of 18) this is going to get out of hand, but there's a solution for that as well: either give major NPCs a Luck attribute of their own, or keep a "Karma" or "Fate" track and make sure that eventually, the PCs achieve balance with all their rerolls (having to make saves to avoid rerolling the checks you really want to hit them with).
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