When Will the Torch Go Out?

This article was previously published on Eposic but has been offline for a while.

Some people find the bookkeeping aspect of role playing games annoying. Some precise bookkeeping is inevitable, such as tracking how much damage your PC has taken. But such bookkeeping can become tedious and detract from the fun for some players and GMs, especially if several effects need tracking simultaneously. But there is a way to reduce the bookkeeping and at the same time add some suspense to the game.

Consider the need to determine when a lit torch goes out, and suppose that torches typically burn for 10 turns once lit, as in T&T edition 5.x. The PC lights a torch and the player or GM makes hash marks on a sheet of paper to track how many turns have passed since the torch was lit. When the 10th hash mark is recorded, the torch goes out. The player knows when the torch will go out as soon he lights it (barring, of course, any special circumstances, such as sudden gusts of wind, which I’m going to ignore). A fixed duration is unrealistic, in that not all torches are created equal; some should last longer than 10 turns and some less than 10 turns. Even though the average duration might be 10 turns, there should be some variation, some uncertainty as to how long a lit torch will burn before it goes out.

Anytime we want to introduce uncertainty, the obvious solution is to roll dice. So, what dice should we roll and what result should indicate the torch has gone out? The players will not be too thrilled with any solution that allows the torch to die as soon as it is lit. The GM won’t like a method that allows torches to burn forever. We need a solution that keeps the number of turns the torch stays lit close to that listed in the rulebook.

For this particular situation of a torch that normally burns for 10 turns, I’ve come up with a three-stage method, consisting of a guaranteed stage, a reliable stage, and a flickering stage, after which the torch burns out.

The torch is initially in the guaranteed stage, so called because the torch is guaranteed to burn for the full duration of the guaranteed stage. For this example, let’s use a guaranteed stage of 1 turn.

Then comes the reliable stage. At the end of each turn during the reliable stage, roll 1D6 to determine if the reliable stage has ended; the stage ends when the 1D6 rolls a 1. Since you’re rolling at the end of each turn, the reliable stage will last for at least 1 turn.

Last comes the flickering stage. During the flickering stage, roll 1D3 at the end of each turn; the flickering stage ends and the torch goes out when the 1D3 rolls a 1. As in the reliable stage, the torch will burn for a minimum of 1 turn in the flickering stage.

All together, the torch will burn for a minimum of three turns, one turn in each stage.

When we roll dice to determine the end of the reliable stage, there is a 1 in 6 chance of the stage ending, and the stage will last on the average for 6 turns. For you statistical types, the median is 4, but relatively large outliers pull the average up to 6. Likewise, the flickering stage will last 3 turns on average.

Since the guaranteed stage only lasts for 1 turn, the bookkeeping for that stage consists only of making a record that the torch is burning. You’d have to do this regardless of what method you were using to determine when the torch burns out. At the end of the first turn of burning, you record that the torch has entered the reliable stage. When the dice indicate that the reliable stage is over, you record that the torch has entered the flickering stage. Thus, instead of making 10 hash marks over a fixed period of 10 turns, you end up making 2 notations over a variable period of about 10 turns. That’s a nice reduction in bookkeeping, and you get to roll more dice!

I ran a computer simulation of this method, with one million tests. The minimum number of turns the torch stayed lit, as expected, was 3. The median was 8 turns, which means that in half of the tests, the torch burned for 8 turns or less, and in the other half of the tests, the torch burned for more than 8 turns. The average, as expected, was 10 turns. The average was higher than the median because of large outliers; in some tests, the torch stayed lit for more than 30 turns, and on rare occasions stayed lit in excess of 70 turns. However, the instances where the torch burned for longer than 30 turns amounted to about one-half of 1% of all tests.

On the average, the torch was in the reliable stage for 6 turns, and in the flickering stage for 3 turns. In general, if you roll a die with X sides for determining when a stage ends, with a roll of 1 on the die indicating the end of the stage, then the stage will last on the average for X turns.

If you roll a die with a large number of sides to determine the end of a stage, you will get more large outliers than if you roll a number of smaller dice over more stages. For instance, suppose you want a random duration of approximately 20 turns. You could have one stage that uses a 1D20 to determine the end of the stage. I ran a computer simulation using this method, and about one-half of 1% of the time, the effect lasted for over 100 turns. On a few occasions the effect lasted in excess of 250 turns. The median number of turns was 14.

I then ran a computer simulation with a guaranteed stage of 2 turns, followed by two reliable stages and a final flickering stage, each of which used 1D6 to determine the end of the stage. The average was 20 turns, as desired, and the median was 18, a number closer to the desired number of 20 than was the median of 14 for the 1D20 method. Moreover, the torch stayed lit longer than 100 turns in fewer than 10 instances out of one million tests.

So, to extend this method for use with longer durations, it’s better to increase the number of stages rather than the size of the die. Using 1D6 or a smaller die to determine the end of a stage is recommended.

To extend this method to durations of other effects, simply break up the expected number of turns into however many pieces you want so that you can map them to 1d2, 1d3, 1d4, and 1d6 rolls, plus some number of guaranteed turns.

For instance, take a lantern that is expected to stay lit for 50 turns. We could give the lantern a guaranteed stage of 4 turns, then 7 reliable stages where each stage ends when a 1 is rolled on 1d6, followed by a final flickering stage that ends when a 1 is rolled on 1d4. The average number of turns the lantern would stay lit is equal to 4 + (7*6) + 4 = 4 + 42 + 4 = 50. The minimum number of turns the lantern will stay lit is 4 + 7 + 1 = 12.

We could just as easily go with a guaranteed stage of 16 turns, five reliable stages using 1d6, and a flickering stage that uses 1d4. The average number of turns would then be 16 + (5 * 6) + 4 = 16 + 30 + 4 = 50. The minimum number of turns would be 16 + 5 + 1 = 22. This is a better minimum than for the example in the previous paragraph, but it also involves more bookkeeping with a longer guaranteed stage.

Let’s consider another example. Suppose you have a spell whose duration is listed as 4 combat turns. You coud give this a simple 1d4 to determine when the spell effect ends. Roll 1d4 at the end of each combat turn, and if a 1 is rolled, the spell effect ends. Or you could break this up into a guaranteed stage of 1 combat turn, and then a stage that uses 1d3. Or you could have two stages, both of which use 1d2. Or you could have a guaranteed stage of 2 combat turns, followed by a stage that uses 1d2. In all of these cases, the spell effect will last an average of 4 combat turns.

It’s not such a big deal to keep track of 4 combat turns, of course, but using dice to determine the end of an effect helps build suspense in the game. A GM might consider using this method simply for the sake of introducing an unpredictable factor.

If you understand the methods of my madness, you can easily convert any fixed duration to a variable one that requires less bookkeeping. Never knowing exactly when an effect will end is more realistic in some cases, and certainly adds a degree of suspense that a fixed duration does not. So give it a try in your games if you like. You can always go back to using fixed durations and your normal means of bookkeeping if the dice don’t render the sort of results you want.