The normal odds of a 2d6 roll versus the default target of 8+ in Traveller are well known by players as being just under half, or 42% to be exact. The use of dice modifiers (DM), such as +1/-1, etc, are commonly used to reflect ability and conditions related to the task. On the surface it would appear a DM of +1 adds an equal benefit as is taken away by a DM of -1. As can be seen below, this is not quite true.
Due to the use of two dice, the choice of 8 as a target and the inability to roll a 1, the odds are actually shifted slightly towards favoring the positive DMs over the negative DMs. A +1 grants an extra 17% to the chance of success while a -1 lowers the chance by only 14%. This trend continues all the way to a 50% increase for a DM of +4 with only a 39% decrease for a DM of -4. The returns diminish with each further step, a DM of +2 is not twice as good as +1 and so on.
The end result of all this gives the players a bigger bump up when they have an advantage but doesn’t cut them down as much when they have a disadvantage. This tarnishes the games’ reputation for ruthlessly punishing players but is an acceptable result when you consider that failure is frustrating and good gaming often gives the players a ‘heroic edge’.
In 2nd Edition Mongoose Traveller a mechanic was added called Boons and Banes that allowed another type of modifier, a third d6. The Boon condition allows players to keep the best two of the three d6 rolled while the Bane does the exact opposite and forces keeping the lowest two. So what does this do to the odds in the end? As can be seen in the above image, it is similar to adding a DM of +1.5 or -1.5 to the baseline 2d6 roll. So is best used when a DM of +1/-1 is not enough to represent what the referee wants and a DM of +/-2 is just a bit too much. A similar result would occur when using both the Boon/Bane system with another normal DM such as +1/-1. The result would shift up in the middle of the next range.
The takeaway? Don’t be afraid of negative DM’s, they might sting a little but they are really just moving the needle back towards neutral more than inflicting serious punishment when viewed across the number of rolls in a typical game.