Timeline is an idea I came up with while waiting for the bus.  The fluff is that your character was abducted by aliens and injected with a powerful virus.  This virus gives you a very limited array of powers as well as drawbacks, the biggest of which is that your character has only a year to live.  The game involves the hunt and conception of a cure while interacting with the alien abduction community as well as evading government boogeymen.

As far as task resolution goes, you'll do the standard "roll dice and beat a certain number", but with one catch: fail the roll, and time speeds up.  Instead of going day-to-day, the game starts going week-to-week or even month-to-month.  Succeed at a roll, and time slows down.  (note that this isn't an actual warp in time, in game, it's just heavy downtime inbetween scenes.  In-game reasons for the downtime so far are that the characters are sick due to the virus, or have to hide out for some time to avoid the government.)

There's different types of rolls: Interaction rolls deal with general interaction with the environment (search the internet for someone's address; climb a brick wall; hold your breath underwater).  You need to fail four times in order to speed up time, and likewise, you need to succeed four times with these rolls to slow down time.  Such failures and successes are noted on your character sheet, and whenever four are obtained, all other successes or failures regarding that type of roll are gone (for example, I have two successes and three failures on my Interaction rolls.  When I get that fourth failure, time shifts, and I lose those four failures and those two successes.  Start over with the next Interaction roll).

Virus rolls are rolls that deal directly with learning about and curing your virus.  It only takes a single success or failure in this area to change time, as it is the most important thing to the characters and will set the pace of the game.

Power rolls relate to using your powers that the virus grants you.  It takes two successes or failures to change time, as usage of these powers mutates the virus itself.

Lastly, Community rolls represent your interaction and standing in the alien abduction community.  Getting information from them, getting help from them, anything involving them counts as a Community roll.  These guys are nutjobs, and only so many of them were actually abducted, and you need four successes or failures to change time regarding them.

The game starts at day-to-day, then fluctuates from weeks to months to days and all over the place as the characters try to cure their virus before the end of the year.  The GM keeps track of time, and indeed, when the year ends, those who have a cure survive, and those who do not will die.  The reason the time limit exists is an experiment in pacing, which I've always had problems with, and to create a sense of dread and urgency as that due date looms ever closer.

The situation I'm in now is that my task res. mechanic was to roll 2d6 and try to get an 8 or higher.  Points spent in various stats (Interaction, Virus, Community, and other such stats) provide a bonus to the roll.  These bonuses are always low, around 1 or 2, and I found myself wondering: maybe instead of adding to the roll, they'd let you re-roll a certain dice.  a +1 mod lets you reroll (optionally) a low-numbered dice, whereas a -1 mod has you reroll your highest numbered dice.  It's an issue of probability - success and failure is integral to the game, as it takes us closer or farther from the resolution of the story, so I want there to be an equal chance of changing time in either direction.  I'm wondering if I should alter the target number, or simply devise a different system alltogether.  Any probability gurus around to help?  Thanks in advance!

Howdy, Keith.

I've worked out the stats for just applying a single bonus.  Without going into how these bonuses and penalties might interact with each other, here's the deal:

Your base target number is 8, meaning that a roll with no modifiers has a 15 in 36 (= 5/12 ~ 42%) chance of success. 

With a +1 bonus to the roll, the dice only have to make a 7, so we have a 21 in 36 (= 7/12 ~ 58%) chance of success. 

If you reroll the lower die, we still get about a 58%.  What you have to think about when doing this math is what the chances are of each result on the higher die, ignore the lower.  So we have an 11 in 36 chance of the high die being a 6, a 9 in 36 chance of the high die being a 5 and so on.  For the 6, since the rerolled die just has to be a 2 or better now, we multiply our 11/36 by 5/6 (chance of getting a 2 or better), and do similar math for each of the digits on down.  Sum all these chances of success in different ways up, and you get about .5787 or roughly 58%.

With a -1 penalty to the roll, the dice have to make a 9, so we have a 10 in 36 (= 5/18 ~ 28%) chance of success.  (actually .27 with a horizontal line over the 7).

If you reroll the higher die, we still get about a 25%.  Using similar math to the reroll lower die, except basically the chances of the remaining die being each value are flipped, we actually get about .2546; roughly 25%.

So yeah, if we ignore what might happen if you give multiple bonuses, multiple penalties, or a combination of any of the four types of modifiers above, then giving a +1 or -1 does just about the same thing to their chances as rerolling the lower or higher die, respectively.

You can certainly use the same math for more complex situations, but fair warning, it'll get complicated quick.  For instance, using this method, and only two reroll-type modifiers, you'll end up summing a couple dozen fractions in the end.  I recommend using OpenOffice Calc or MS Excel to chart things out if you're going to go that far.

However, it might just be more fun to use the reroll mechanic.  If that's the case, it's probably well worth the math busywork you could put in to make sure your system is balanced to where you want it.  Hope this helps!

-JT

The re-roll mechanic is a little more dynamic - you're doing something besides counting.  So what I think I'll do is add more dice to the roll and make it so that certain numbers are successes, and certain rolls require a certain amount of successes.

Immediately what comes to mind is this: all virus rolls require 3+ successes, all interaction rolls require 1+ success, etc.  This would require more dice, obviously.  And I'd give the ability to re-roll to achieve those successes.  Which, now, opens up a whole new foray into rules and stats (which is bad for me, as I'm trying to make this as rules-light as possible)

Thank you for that impressive wall of statistics, though.  It's helping me tweak what I need to tweak.

This is an interesting concept, Keith, but I'm having trouble putting it together because one important piece seems to be missing from your description: when do scenes happen and how long do they take? That is, how do we know they are "over" so that we can jump to the next day/week/month in the sequence? What are the criteria for something being a scene and coming to some conclusion?

Good question - since time is of importance and not just a standard of measurement here, it gets its own system:

Time Period (days, weeks, or months).
Time Shift (succeeding or failing, resulting in the measurement of time to switch between days, weeks, or months)

Days
- the group determines how awake they are by way of their Preservation stat, which governs stamina.  All players subtract their stat from 12 (usually resulting in a score of 1-10).  The highest of these stats equals how many scenes the characters can go through (scenes last, in-game, either when the conflict of the scene is resolved or when an hour has passed in-game, whichever comes first).  Players can roll their Pres. stat to buy additional scenes, but at the cost of failing and shifting time.  Sleep fatigue and insomnia roleplay are encouraged, as the Virus takes its toll physically.

Weeks
- every three scenes is one day.  Thus, the characters get 21 scenes minus their Pres. stat.  They have more time before the next period of time (as opposed to day-to-day), but the trade-off is how close they get to the end of the year.

Months
- at this point, characters are considered violently ill or incapacitated, so each scene is one day.  They can barely function at this point.  Instead of their Pres. score taking scenes, they are stuck at a static 28, but suffer penalties to rolls instead.

What I may do is up the number of rolls needed to shift time.

Another rule is that of Conflict Rolls - any rolls made have to relate to the current scene's conflict, which should prevent rolling for mundane things simply to shift time.  As well, ALL scenes in a given time period must be used up before a shift in time can occur.  This means the rules for shifting must be re-worked: must roll for every scene, and you tally up successes and failures at the end of the time period.

The task res. system needs something more strategic (to fit with the new rules), bigger and more epic (to compensate for all the rolling required), and more related to running out of time / a dwindling supply (to reflect the theme.)