8 ways to substitute dice for block towers

Inspired by a post on Kaden Ramstack's blog with a list of towerless Wretched & Alone games.

A couple years ago I made a twitter thread (followed by an itch forum thread) about dice substitutes for Jenga-style block towers, which were the main mechanic in (among other games) The Wretched, which had an active SRD jam on itch at the time. The issue is basically that dice towers aren't necessarily easy to come by, and they're almost impossible to do digitally with the tools we have at the moment. There are 3D simulations of block towers, but I've never found one that's anywhere near as stable as the real thing. So, I turned to dice. I posted one mechanic, and some people on itch suggested some other dice mechanics.

Caveat: as I say in the twitter thread, these mechanics are always gonna have different feelings to pulling blocks out of a tower. They're completely random, for one. They just reflect the ideas of a safe start, dwindling resources or survival chances, and a long, tense, ending (usually). None of these have the feeling of deliberately choosing a block and trying to get it out without toppling the tower, the tension of knowing it's all on you. That said, none of them need you to have precise motor control or even actual physical game tools.

Like I said, these mechanics are handy if you're playing digitally. That means you don't have to, y'know, limit yourself by what's physically practical. It'd be a pain to roll e.g. 100d6 in real life, but it's super-simple with a discord dice bot or online roller like orokos or even google's dice-roller tool.

About probability

Nat Barmore, one of the developers of Dread, the 2005 block tower horror TTRPG, described their experience with Jenga game lengths:

FYI: our math when developing Dread was:
10 pulls: guaranteed
20: almost always
30: most groups
40: many groups
50: every pull after this is a gift of the Fates

Theoretical max is 105, but I don’t think I’ve ever seen 60.

This is for Dread, where you pull blocks and put them back on top of the tower. In Wretched & Alone games you don't (necessarily) do that.

About the mechanics

A couple of these are slightly changed from the way they're written in the sources, just to make them simpler. They work pretty much the same way.

Simulation details

The simulations I plotted for this post are a mix of average games (showing how an average game using each mechanic would go) and game lengths (showing how many games reach each number of rolls/pulls/etc.). Both plots are built from 10000 simulations each. No error bars on the average game plots because I can't be bothered.

These are done with MATLAB. I should probably switch to Numpy or Scipy or whatever.

The Mechanics

100d6

Source: me
What you need: 100d6
Block-pull…: Roll the dice you have and discard dice that show 1.
Tower-collapse…: The game ends when you run out of dice.

This is like radioactive decay. Your count drops fast at first, then slower and slower the fewer dice you've got (exponential decay). The tension rises with every roll later on, because you might be losing the one of the precious few dice you've got left. One neat feature of this mechanic is that because you have 100 things, and that count is always dropping, you've got always got a percentage number you can use in journalling. Percent of air left, or defensive walls un-breached, or distance to home, or whatever. You could also invert it, e.g. when you have 10 dice left, something in the story's 90% complete.

Here's the average game. Most of the dice drop out in the first 10 rolls or so, then the last 15 dice trickle out from the 11th roll onwards (even up to the 30th roll).

Here's how long the games are overall. Almost all games get past 20 rolls. The majority of games end between 20 and 30 rolls. About a third of games end between 30 and 40 rolls. The last 5% or so end after 40 or more rolls.

10d10 and only drop one die

Source: me
What you need: 10d10
Block-pull…: Roll the dice you have. If any show 1, discard a die.
Tower-collapse…: The game ends when you run out of dice.

d10s aren't as common as d6s, so you might be able to do this in real life more easily than the first one. That said, the rules are a little more complicated.

Here's the average game. Dice drop fast over the first 20 rolls or so, then slowly from the 21st roll to the 50th roll and beyond.

Here's how long the games are overall. Most games get past the 20th roll. About half get past the 30th roll. About another third get past the 40th roll. The rest end after roll 40.

1d6 vs tokens

Source: Chris Sims
What you need: 1d6 and 10 tokens
Block-pull…: Roll the die. If you roll equal to/greater than the number of tokens you have left, discard a token, except: you always lose a token on a roll of 6, and you never lose a token on a roll of 1.
Tower-collapse…: The game ends when you run out of tokens.

This one's a little different. It keeps the dwindling feeling, but not the tense, drawn-out ending. It also guarantees the game'll be at least 10 turns long (since you can only loes 1 token per turn at most), which could be handy.

Here's the average game. It's a bit linear at the start, then turns into exponential decay after about 15 rolls.

Here's how long the games are overall. Almost all games last at least 20 turns. Almost all games end between turn 20 and turn 50; a roughly consistent number end on every turn from turn 20 to turn 50.

1d6 vs countdown

Source: Chris Bissette
What you need: 1d6 and a counter (written or otherwise) starting at 30
Block-pull…: Reduce the counter by 1. Roll the die.
Tower-collapse…: The game ends when you roll higher than the counter.

Straightforward and easily-tweaked by changing the starting counter, but it has 0 tension until the last few rolls and also needs some book-keeping.

Here's how long the games are overall. No game can end before 25 rolls, and then the number of games that pass each roll from roll 25 to roll 30 drops sharply.

1d12 instead of 1d6

Suggested here, you could use a d12 instead of a d6, which'd add more rolls that could end the game.

Here's how long the games are overall. No game can end before 9 rolls, and then the number of games that pass each roll from roll 19 to roll 25 drops sharply. A small percent of games make it past roll 25, and all of them end by roll 30.

1d100 with advantage

Source: GalacticNomad
What you need: 1d100 (or 2d10 that you can tell apart from each other)
Block-pull…: Roll 1d100 twice.
Tower-collapse…: The game ends if both rolls are below the number of turns that've passed so far.

This one's maybe even less demanding than number 3, but it does need polyhedral dice and not just regular d6s. It also needs you to keep track of the number of turns that've passed, and it doesn't have any feeling of decay/dwindling. However, it does give you 2 numbers you could use somehow in your journalling (the two different d100 rolls).

Here's how long the games are overall. It's a neat and tidy S-curve: most games make it past 10 rolls, then most games end between 10 and 40 rolls, then a few games make it past 40 rolls.

Domino doubles

Source: JVC Parry
What you need: a full set of 28 European-style dominoes with 0–6 pips on each side, an opaque bag or something
Block-pull…: Pull a domino from the bag. If it's a double (same number on both sides), keep it in front of you, otherwise discard it.
Tower-collapse…: The game ends when you have every double domino in front of you (double-0/blank, double-1, etc. through to double-6).

Dominoes aren't super-common but this is a neat alternate and gives you a bunch of numbers (or shapes of pip patterns) that you can use while journalling if you like. This one does always end within 28 turns, though, and it's also super-unlikely it'll end before turn 20 (most games'll end on turns 26–28, even).

Here's how the average game goes. The number of double dominoes left drops at a constant rate.

Here's how long the games are overall. Almost all games last for at least 20 domino pulls. After 20 pulls, the number of games left drops faster and faster. No game makes it past 28 pulls (since there are only 28 dominoes in the set).

One neat thematic thing you can do with this: 28 dominoes in a set, about 28 days in a moon cycle, or 28 Days/Weeks Later…

d6 dice pool

Source: Tales by Bob
What you need: 10d6
Block-pull…: Roll the dice.
Tower-collapse…: The game ends when the total result of rolling the dice pool is less than the number of turns that've passed so far.

This one has a kinda creeping feeling of difficulty and it's pretty easy to tune by changing the number of d6s. The only downside is (like some of the others) there's no sense of dwindling resources, or falling chances of survival. Like yeah you have a lower and lower chance of succeeding with every turn, but there's no visual for that (e.g. discarding tokens or dice or dominoes).

Here's how long the games are overall. Almost all games last at least 24 rolls. Most games end after 25–36 rolls.

1d6 vs lists

Source: egw
What you need: 1d6 and two lists of the numbers 1–6
Block-pull…: Roll the die. Cross out that number on the first of the two lists, if it hasn't been crossed out already. If all the numbers on the first list are crossed out, cross out that number on the second list instead (unless it's crossed out there as well).
Tower-collapse…: The game ends when every number on both lists are crossed out.

A neat mechanic with a dwindling feeling. It's a little bit complex, but you can use that complexity in journalling. Something's clearly either stacking up or being lost here, something you're actively keeping track of in the same medium you're writing your journal entries.

Here's how the average game goes. The number of list items left to cross off drops almost exponentially. However, this is the *average*; in reality there are *two* exponential decays in each game, one for the first list, another for the second list. They blend together in the average data here. One of those cases where summary stats can be misleading.

Here's how long the games are overall. Most games make it past the 20th roll; most of the games end between 20 and 40 rolls, and a few last for more than 40 (even more than 50) rolls.

Comparing the mechanics

Average games

N/A

N/A

Game lengths

Conclusions?

Well, basically they're (almost) all pretty similar. Most of them pretty much guarantee you'll get 15–20 turns before there's any real chance of the game ending, and on average they all end after 25–35 turns. Most of the average game graphs show exponential decay (including d6 vs tokens, which starts its decay after turn 15 or so).

The main things are:

whether a game's got a really hard limit (like the dominoes or 1d6 vs countdown) or can go on seemingly forever. I'm counting stuff like 1d100 with advantage as “going on forever”, since it's got a high cap you almost certainly won't reach.
whether the game's binary or not. By “binary” I mean each turn you do pretty much the same roll and if it fails the game ends. The mechanics where I don't have an “average game” graph are binary, cause there isn't really anything to plot. The others measure your progress, like losing dice or tokens or crossing things off lists.
the exact stats, e.g. when you use the 100d6 mechanic, about half of the games end before roll 30, but when you use 1d6 vs tokens, three quarters of games are still going by then.

That leaves other stuff like aesthetics, tools, tune-ability. I've talked about these under each mechanic—things like how easy or hard it is to tweak, and how you could use some of the numbers each mechanic gives you. Here are the ones I think're are easier to meaningfully tweak:

100d6: just add more dice (or take them away) or change the die size
10d10 and only drop one: again, change the die size or how many you start with (you could also change the number of dice you can lose per turn, but dropping up to 2 or something like that feels arbitrary)
1d6 vs tokens: change the die size or the number of tokens
1d6/1d12 vs countdown: changing the die size directly sets how many turns you're actually in danger near the end of the game
d6 dice pool: change the number of dice or the die size

And here're the ones I think are harder to meaningfully tweak:

1d100 with advantage: it relies a lot on the d100 and there isn't a similar, simple roll you could change it to
domino doubles: the easier changes have drastic effects (e.g. needing the doubles to be drawn in a certain order) or tiny effects (e.g. needing to draw all doubles plus all dominoes with one 6 barely changes things)
1d6 vs lists: like above, all the changes you easily could make (changing the die size, adding/removing lists) are pretty drastic

That doesn't mean these mechanics are bad, just that they're kinda rigid unless you're making big changes.

So, I guess, in conclusion, any of these is fine, just check out the graphs to make sure it's exactly what you want, and if you wanna tweak it, you might be better off with one of the five more-easily-tweaked mechanics.

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