Playing Dread over G+ Hangouts

Dread is a great game.  It's a horror/suspense/slasher movie simulator, and one of the few horror role-playing games that really works.  Part of the reason is because it uses a Jenga tower, which gets ricketier as play goes on. In order to do almost anything, players have to make pulls from the tower, and when the tower falls, the player's character dies.  The tension created by the tower adds to the atmosphere of the game and creates a real sense of threat and impending doom that is hard to come by in similar games.

Issues with Dread on Hangouts

Dread would be an ideal game for late-night G+ Hangout play, except that there's only one way to play Jenga: in person, sitting around a table, with a bunch of able-bodied people. This doesn't work for all play groups!  The Dread book does suggest alternatives to Jenga, but they all have a similar physical component.

We'd like to find a solution that will work for people playing remotely, or for people who lack fine motor control.  Any alternative mechanic should fulfill at least the following requirements:

  1. It should use readily-available materials.
  2. It should build tension - the lethality should start near zero and ramp up over time.
  3. It should be obvious to all the players how "rickety" the tower is - how dangerous a "pull" will be for them - at any given time.
  4. It should kill players in about the same number of "pulls" - 35-55 according to the authors - that the Jenga tower in Dread does.

I believe I have a Hangouts-friendly alternative that meets all of the above requirements - I call it "D20 Dread".

D20 Dread

D20 Dread only requires two items: a 20-sided die or die roller and a shared sheet of paper.  That's it - all you need!  Here's how it works:

  1. Write the numbers 1-20 in the left column of the document
  2. Every time a player would make a pull, they roll a d20.
  3. For each result, make a mark next to the number that was rolled.
  4. When the fifth mark is placed next to any number, the player who rolled that number dies, as if they had knocked over the Jenga tower.
  5. A player may elect to "knock over the tower" at any time, with the same rules as in the normal game.
  6. Any time the rules refer to resetting the tower, instead erase all the marks.

This system fulfills all the requirements set out above. DiceStream is always available in G+, and failing that, most gamers have a d20 lying around.  The only other object needed is a piece of paper, physical or digital, which can be provided by Google Docs on G+.  The tension also ramps up over time as the checks next to each number fill up.  As I'll show later, for the first twenty rolls or so, there will be almost no danger of death.  Once the number goes north of 30, however, the danger ramps up significantly.  And based on the number of rows with four check marks, it's pretty obvious to players exactly how dangerous a roll is going to be.

Statistical Analysis

The Dread authors strongly recommend that any alternative to Jenga kill a player in roughly every 35-55 pulls.  Now, there can be some flexibility with the optimal number of pulls between deaths depending on the length of game and the aggressiveness of the GM, so an alternate resolution mechanic need not mimic the Jenga probability distribution exactly (and in fact, it is highly unlikely that any alternate mechanic even could).  But we'd like to know that D20 Dread at least arrives in the same neighborhood as Jenga.  So let's break down the odds of a player dying on each roll...

Defining the Problem

Say you have an N-sided die, and death occurs when exactly M of the same number of results has been rolled.  Say we're rolling the die for the nth time. What is chance that this roll will result in death?  Let's ignore what exactly the player rolls. Whatever they rolled, what's important is that exactly M-1 of the same result have been rolled in the previous (n - 1) results.

In general, the chance that there are exactly x results of a particular value on an N-sided die in y rolls is <number of ways to choose x things> times <odds of those things being the specified value> times <odds of the other things not being that value>.  Or to put it mathematically:

\large E\normalsize ^N(x,\;y) = {y\choose x}\cdot\left({1\over N}\right)^x\cdot\left({N-1\over N}\right)^{y-x}

Therefore, if we fix the count required for failure as M, the probability of a failure on roll x is:

\large F\normalsize\buildrel{N}\over{_M}(x) = \large E\normalsize ^N(M-1,\;x-1) = {x-1\choose M-1}\cdot\left({1\over N}\right)^{M-1}\cdot\left({N-1\over N}\right)^{(x-1)-(M-1)}

This makes the total probability of failure on rolls 1 through x equal to either zero (if x is less than M), or <the probability of failure on rolls 1 through x - 1> plus <the probability of no failure on those rolls> times <the probability of failure on roll x>. Mathematically:

\large P\normalsize\buildrel{N}\over{_M}(x) = \begin{cases}\large P\normalsize\buildrel{N}\over{_M}(x-1) + (1 - \large P\normalsize\buildrel{N}\over{_M}(x-1))\cdot\large F\normalsize\buildrel{N}\over{_M}(x)& \text{if } x \ge M\\0& \text{otherwise}\end{cases}

By The Numbers

Now that we have a formal way to compute the probabilities, what are the odds that a single roll will result in death? What are the odds that a character will be dead by the time the nth roll is made?  I've created an Excel workbook that can calculate both \large F\normalsize\buildrel{N}\over{_M}(x) and \large P\normalsize\buildrel{N}\over{_M}(x) for arbitrary N, M, and x.

Dread D20 (Excel .xlsm workbook)

However, if you can't (or don't want to) load an Excel workbook, I've added the table for d20 and M=5 at the end of this post.  Note that this can't be used to determine the probability of death on a roll in any specific game, since the actual probabilities depend on how many numbers have reached exactly four marks.  But it does give an idea of how likely on average a death will happen at any point in a typical game.

For a More or Less Lethal Game

If you want to change the lethality, increase or decrease M (the number of marks next to any single die result that kills a player) by one.  Don't set it any lower than 4 or higher than 6; that will seriously unbalance the game.  But if you find that 5 doesn't give you the pacing you want, change it.  The average number of rolls before the first death will be:

M = 4:  26 rolls
M = 5:  37 rolls
M = 6:  50 rolls

The Table (d20, M=5)

RollCumulative Chance
of Death
Die This Roll
Pull 1
Die This Roll
Pull 2
Die This Roll
Pull 3
60%0%0%0%
70%0%0%0%
80%0%0%0%
90%0%0%0%
100%0%0%0%
110%0%0%0%
120%0%0%1%
131%0%0%1%
141%0%1%1%
151%0%1%1%
162%0%1%2%
172%1%1%2%
183%1%2%3%
194%1%2%3%
205%1%2%4%
216%1%3%5%
228%2%3%5%
239%2%4%6%
2411%2%4%7%
2513%2%5%8%
2616%3%6%9%
2718%3%6%10%
2821%3%7%11%
2924%4%8%12%
3027%4%8%13%
3130%5%9%14%
3234%5%10%15%
3337%5%11%16%
3441%6%12%18%
3545%6%12%19%
3648%7%13%20%
3752%7%14%21%
3856%8%15%22%
3959%8%16%23%
4063%9%17%25%
4166%9%18%26%
4269%9%19%27%
4372%10%19%28%
4475%10%20%29%
4578%11%21%30%
4680%11%22%31%
4783%12%23%33%
4885%12%23%34%
4987%13%24%35%
5089%13%25%35%
5190%14%26%36%
5291%14%26%37%
5393%14%27%38%
5494%15%28%39%
5595%15%28%40%
5696%16%29%41%
5796%16%30%41%
5897%16%30%42%
5997%17%31%
6098%17%

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