Category Archives: Game Mechanic

Taming the bell | … making probability bell curves more ‘swing-ish’

I only realized something about multi-dice probability bell curves recently … (if you’re a maths-wiz, click away now as the following will probably only offend your sensibilities!).

Bad intuition
Instinctively, I believed that for example 2D6 has the same probability profile as D8+D4. That is, they both give numbers from 2 to 12 and each number on each die is just as likely to turn up.

But, I was quite wrong.
:O|

It turns out the bigger the separation in the die size, the “flatter” the probability bell curve becomes. That is, the more unpredictable the probability spread becomes. In retrospect, this makes sense.

What am I talking about and why could this be useful?
Below is an example where the number range 2 to 12 is generated using two dice, i.e. 2D6, D5+D7, D4+D8, D2+D10 and D1+D11:

2 to 12 ranges

In the Range 2 to 12 using two dice (made via anydice.com); the penultimate graph should have been labelled D2+D10 of course!

2 to 12 graph

As above, but presented graphically

So, it can be seen from the above that as the difference in the die size increases, the flatter the probability bell curve becomes (this means the probability curves is becoming more “swingish”).

This is another way to represent the ‘flattening’ of the bell curve; a D4+D8 has a much bigger flat top section (range 5-9) section than 2D6 (just for 7).

Range 2 to 12

Broader plateau seen in top D4+D8 vs bottom 2D6 covering the range 2-12 with two dice

Of course 2D6 systems are widespread in RPGs, for example see a recent post by Larry Hamilton concerning this: https://followmeanddie.com/2019/09/21/newfound-appreciation-of-the-2d6-table/

Here’s another example but for the range 3-18 using three dice (e.g. as used for PC stats, or the damage of a two-handed sword in AD&D).

3 to 18 range

In the Range 3 to 18 using three dice (made via anydice.com)

3 to 18 graph

As above, but presented graphically

So the message here is, when summing two (or more) dice, you can make the outcome more “random” (less constrained by the bell-shaped curve) by using a big spread in dice size. Edit: it has been pointed out to me that the term “random” as used here is better described mathematically as “variance”.

I think you mentioned useful?
In the main, this observation is not going to change your game. But, this phenomena is worth remembering for the old DM tool kit.  Below are some theoretical examples where this could come into play:

• Perhaps the fighter is drunk (and she is fighting with a two-handed sword; normally doing 3D6 damage), being drunk she is less in control of the weapon, and so is more unpredictable with it. Or, perhaps she is on her last hit-point and wants to try a ‘do-or-die’ attack. In either of the above cases, maybe the damage she does could be more unpredictable, more likely to be a flop or a whopper. So, to simulate either of the above, perhaps replace the normal (more predicable) 3D6 (3-18) with the more ‘swing-ish’ D10+2D4 (3-18) …

• 3D6 is also synonymous with rolling up PC stats e.g. STR, DEX, CON etc. But, if in your game you wanted more ‘swingy’ stats, then perhaps again consider using D10+2D4. Again, maybe let the player decide if they want to roll one or more ‘swingy stats’?

• 3D6 or 4D6 attribute tests – some gamers make ability checks using nD6 instead of a D20 (incidentally I compare the two systems here); if you wanted to make the nD6 test less predicable, use pairs of D4+D8 to replace pairs of 2D6s etc.

• Falling damage. Maybe falling down a large tree should be more unpredictable that falling off a cliff. Perhaps the branches might cushion the PC’s fall, or give the PC an extra thrashing on the way down?

• Perhaps you think fireball magic should be more unpredictable than is governed by standard bell curve generated by nD6. Again, mix it up.

• Recently, I’ve found a D6+D8 gives a better probability spread (for a Hex Flower I’m working on) than 2D7 would (which is lucky as I don’t own any D7s).

etc …

Take-home message
This observation is unlikely to change your game much, but ….

… if you get into the situation where a bunch of dice are being rolled and added, and you decide that you want that outcome to be less constrained by the bell, i.e. more “random”, then see if you can substitute the homogeneous dice with dice with bigger gaps between the dice size.

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InHotS the cover imageMe on DriveThruDriveThru; at the moment I’m mainly pimping my procedural High Seas ‘Hex Crawl’ – In the Heart of the Sea.

Tuesday Toot!! | ‘God Call’ an Excel Widget

Tuesday TootG+ is closing closed. When it was alive things happened. Things unexpected. Great things. Whilst my creative output is only modest, I thought I’d hold something up into the living light, something that came about purely because G+ existed … This is a toot to G+. (published a day early this time …)

This Widget was put up on G+ and automates the process I submitted to ‘& Magazine’.

Background:
The idea is that maybe a PC wants to make a plea for divine intervention … when desperate. This widget is meant to enable that process.

But, in this system, for there to be even a chance for a deity to hear you, the PCs are really going to have to make a sacrifice, a level sacrifice (so it’s going to hurt). Also, there is a chance that if the PC goes ‘chips all in’, the deity could take the PC soul as payment. What can I say, trifle with the Gods at your peril.

And, even if your deity hears you, are they going to act, and act in your favour?

Well, in this system that depends on the nature of the deity (a chaotic good deity might be a helpful sort, but what of Chaotic Neutral or even true Neutral deity?) and what you want from them.  Is your request inline with their ‘legal ethos’ (i.e. lawful, neutral, chaotic) and their spiritual ethos (i.e. good, neutral, evil). If inline with those ethoses, the chance of success is greater.

The Excel widget does the maths … and gives a verdict.

Screen capture:

God call 101e

& Magazine
This widget is based on ‘& magazine’ issued 14; pages 35-40;  “Making the ‘God Call’”. Link: http://www.and-mag.com/wp-content/uploads/2018/02/and-mag-i14-p2.pdf

Widget
The Excel widget can be found here: xls Download

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InHotS the cover imageMe on DriveThruDriveThru; at the moment I’m mainly pimping my procedural High Seas ‘Hex Crawl’ – In the Heart of the Sea.

Session Zero – ‘Consequences-Style’ Background Builder

Download a (readable)  image_preview .pdf version

Idea 
I had this idea about making a Consequences-style ‘session-zero’ background builder.

cons

Visual version of the ‘Consequences’ game

You must have played the “Consequences” game at some point. A group of people take turns to answer a series of questions on a sheet of paper, without seeing the previous answers, and so a random narrative is generated as a result (for more see here).

I’ve come up with my RPG version of this (link above). The idea is that each PC gets a randomly generated background by using the ‘Consequences’ type mechanic at the table. I suppose it’s not necessary for everyone to have their PC’s background generated this way (but that would be more fun), as long as everyone doesn’t mind chipping in to help fill out the questions.

In my version, people get to read the answer (only) directly above the box they are filling in, just to aid with the consistency of the narrative.

The idea is that the answers to the questions can be used to ‘seed’ a background, or used as is (maybe needing a bit of a narrative to weave things together – i.e. to join up the dots).

Here’s a screen-capture of my Consequences back-ground builder:

Session Zero - ‘Consequences-Style’ Background Builder - cover

image_preview .pdf version

There are lots of creative people out there who could run with this idea, and I’m sure could make up some (more?) interesting questions, and/or questions that fit their campaign better. Indeed, I’d be surprised if this idea has not been proposed by someone before.  

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PC Death is Power Creep … failing forwards in D&D

Edit: I’ve move this sentence to the top: –> If you bust the PC down to 1st level with only basic equipment (and I’m not against that), then there is no need to read on …

I’ve often wondered if PC death leads to party advancement …

Dead PC is Loot

Borrgat’s eulogy was brief  …

dead pc is looted

:: Often when a PC dies this happens

  1. PC dies

  2. Party (maybe) sheds a tear

  3. Party loot the body of gold, armour and magic items, and leave the body for carrion crawlers

  4. Dead PC’s player gets new PC; usually at around-ish party level and equipped with new magic items

  5. Net result, the party’s position has improved

:: Suggested ritual disposal mechanic

  1. (as above)

  2. (as above)

  3. Party need to ritually dispose of the body

  4. All gold and/or XP spent ritually disposing of the dead PC goes into the new PCs XP/GP pot spend. For example, a lavish burial inclusive of burying the PC with all their in life possessions and laid to rest on a bed of  gold and +1 swords

  5. The total GP/XP pot for the new PC should probably not surpass the dead PC’s XP total at death (‘power gamers’ would be on this loophole like a whippet)

  6. Net result party position is not improved by the PC’s death

Pros:

  • Dead PCs are treated more than as a meat-popsicle loaded with loot
  • Reduces power creep based on PC death
  • Good way to consume excess gold (PCs could even save for a lavish send off)
  • Good way to remove all those excess but redundant magic items the players hoard, e.g. the proverbial +1 sword of just-in-case

Cons:

  • Players might think you (the DM) are being an arse
  • Dead PC’s player might be resentful if the other players don’t give up the loot to bring the PC up to spec …
  • Not so easy to generate a ‘decent’ replacement PC in the middle of the dungeon (but then again, maybe the PCs should be thinking of properly disposing of their dead comrade, not pressing on for more dungeon loot … )

Example 1:

7th Level Fighter JUBELO (taken from AD&D’s Tomb of the Lizard King)
dies and is is buried will all his possessions:

  • shield +2 (500 XP;  5,000 GP)
  • long sword +1, Nine Lives Stealer (1,600 XP; 8,000 GP)
  • potion of super heroism (450 XP; 750 GP)
  • horn of Valhalla (bronze) (2,000 XP; 30,000 GP)

Totals = 4550 XP + 43750 GP = 48300 XP/GP

So from the above, a DM has three choices to give GP/XP to the player to spend  on the new PC (depending on how ‘hard’ the DM feels about PC death):

i.e.: 4.5K, 44K or 48K XP/GP pot.

For reference, the 1e PHB XP table is reproduced below for fighters:

Fighter XP table 1e PHB

Example 2:

7th Level Cleric AZURE (also taken from AD&D’s Tomb of the Lizard King)
dies and is buried will all her possessions:

  • staff of curing (6,000 XP, 25,000 GP)
  • plate mail +2 (1,750 XP; 10,500 GP)
  • scroll with:
    • divination (800 XP, 2,400 GP)
    • remove curse (800 XP, 2,400 GP)
    • find traps (800 XP, 2,400 GP)

Totals = 10150 XP + 42700 GP = 52850 XP/GP

Again, from the above, a DM has three choices to give XP to the player to spend on the new PC (depending on how ‘hard’ the DM feels about PC death):

i.e.: 10K, 43K or 53K XP/GP pot.

For reference, the 1e PHB XP table is reproduced below for clerics:

Cleric XP table 1e PHB

Examples – conclusions

First up there is no need to be quite so formal. A DM might simply take account of the ‘ritual burial’ and think “yes the rights have been well observed, I’ll give a new 5th level PC + some modest magic items etc.

But, let’s work through some of the ‘crunch’ mentioned above:

So, in the two above examples (taking the middle XP/GP pot option; i.e . the bolded option), the new PC would have about 50K to spend between (i) XP for levelling and (ii) gold for magic items (assuming the party buried the dead PC with all their possessions).

But, the party might decide to keep back some choice magic items (lowering the total spend to below 50K).

Or, if the DM is only using the XP value of the magic items (i.e. and not also it’s GP value of the item), the party might spend big on the funeral (e.g. 40K GP, assuming they have it), erecting a statue in the PC’s home town (adding to the total pot spend).

Overall –> the way I’d probably do it would be to tell the player they have about 2/3 of the XP/GP pot to use as XP on the new class. Once the class is settled, I as the DM would probably pick out some appropriate class-related magic items (i.e. using the remainder of the XP/GP pot). Of course, there’s no fun as a player in picking your own magic items.

Like less ‘crunch’ –> give the player a new PC which is about 3/4 the level of the rest of the party (or one or two levels lower). Give the PC no magic items, or 1 item per 2 (or 3) levels of new PC experience.  My guess is that many DM’s instinctively use this method, but without requiring a ritual burial and/or the loss of any ‘party owned magic items’.

However, by contrast, if the DM had simply gifted the party a replacement PC at 7th level with equivalent magic items, the party would have gained probably about  5-10,000 XP and 20-40,000 GP worth of magic items alone. This, just for dying. In some cases, arguably, this would be a better haul of loot than the loot in many a dungeon …

Nonetheless, no matter what I say above, may be the ‘economy of PC death’ in your game works fine, and death is not a shortcut to net party improvement … or perhaps a natural check to a too hard scenario … in which case, of course, ignore all of the above.

– – –

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Combat Morale Tracker | … a simple Hex Flower morale tracker/AI

Edit: A higher quality .pdf version can be found here: Link
and a template Hex Flower Engine can be found here: Template

Combat is more interesting and faster when the morale of Monsters and Henchmen are taken into consideration. This (hopefully) light-weight morale tracker using a Hex Flower Engine should not bog down combat  but also allow moral to be tracked easily.

Combat Morale Tracker - cover image 2019

Background

If you’ve got no idea what this post is about, the below links give some context:

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Me on DriveThruDriveThru; at the moment I’m mainly pimping my procedural High Seas ‘Hex Crawl’ – In the Heart of the Sea.

The Gambler | a ‘bolt on’ class for the daring-do classes; a class heavily influenced by Luck & Superstitions

Edit: A .pdf version can be found here: Link
and a template Hex Flower Engine can be found here: Template

 

Lucky 1.pngThe Gambler 
The Gambler is a person ruled by fates, omens and fortunes. They perceive everything through the lens of luck and chance. For a Gambler, everything happens for a reason. For a Gambler Luck: is as real as a baked potato; is cat-fickle and has a mood; is flattered by rituals and appeased by signs; is consistently unpredictable; is offended and implacable; is passionately for or against you; is never fair; is dangerous to define; is like your best friend’s lover.

 

Class restrictions
This bolt-on class is open to persons of physical dare-do, i.e. fighters or thieves.

Current Luck State
Every session roll 2D6 using the navigation Hex (see below) to determine the Gambler’s current Luck State (LS). The new LS Hex is determined by moving from the current LS Hex to the new LS Hex in the 2D6 navigation direction. LS is also determined if the player rolls a ‘crit’ or ‘fumble’; there’s a gamble, or if anything unusual/significant happens in the game (i.e. there is a shift in the fates).

Hex Flower Engine:

Gambler HFGambler HF Key

Luck Points
When the Gambler levels up, they: gain ‘Luck Points’ (LPs) equivalent to the PC’s level (so 5 LPs a gained upon attaining 5th level); any previously hoarded LPs are lost; and they may exchange their current LS Hex for Hex 10.

LPs are used to help change the outcome of the 2D6 navigation roll, hence the current Luck State. That is, after the 2D6 navigation roll is made, the player must decide if they are going to spend any LPs, to lock in the current Luck State. Spending LPs moves the 2D6 navigation direction by 1 face per LP spent. So, spending 3 LPs would in effect reverse the navigation direction. Halflings get +1 LP per level, but must take on an extra superstition at first level.

Superstitions
Each level the Gambler acquires a new superstition, e.g. three at 3rd level. Preferably, the superstition should be based on an event that happened during the levelling up period. Each superstition should be significant and indexed to character level, and hence should be more onerous than the last. DM input may be required here.
Breaking a superstition – all LPs are lost. If LPs are already at zero, then move to Hex 1.

Background
If you’ve got no idea what this post is about, the below links give some context:

InHotS the cover imageMe on DriveThruDriveThru; at the moment I’m mainly pimping my procedural High Seas ‘Hex Crawl’ – In the Heart of the Sea.

‘You sank my BattleDungeon’ … | Procedural Grid-Crawl Dungeon using the Battleships game as a template

An idea for making a quick dungeon using Battleships as a template for a Grid-Crawl.

image_preview  A more readable pdf version can be found here: Link

Battleships Dungeon
Using the Battleships game as a template to procedurally generate a
20 room, 2 level (Grid Crawl) dungeon

Method
This is a method and explanation of how to use the Battleships game as a template to make a procedural dungeon map in about 5 minutes. Of course, this could be any kind of point crawl, not just a ‘dungeon’. A simple one page method (without the explanations) is given at the end of this document for easy use.

:: Step 1
Start with two blank ‘Battleships Maps’ (probably best to renumber the top line ‘1 to 10’ rather than ‘A to J’), e.g.:

1

Left Grid                                                                        Right Grid

This can be done with the physical game i.e. with the plastic pieces etc., or by simply using paper grids. The Left Grid is the entry level and the Right Grid is the second level of the dungeon.

:: Step 2
Place the ‘ships’ on the grids (as if you were playing the Battleships game). If doing this on paper grids, just shade the squares, e.g.:

2

Left Grid                                                                       Right Grid

:: Step 3
In each of the Grids put a Red Peg in the diagonal positions, except for the top leftmost cell (i.e. put these in positions 2;2, 3;3, and 4;4 etc.), e.g.:

3

Left Grid                                                                      Right Grid

These Red Pegs are simply a visual reminder that these rooms do not connect to themselves.

The START location is on the Left Grid in cell 1;1 (marked with an S). The BOSS encounter (or adventure goal, quest item etc.) is located on the Right Grid in cell 1;1 (marked on with a B).

The battleships are being used in this method to introduce an element of chaos, and to force the DM out of any unconscious bias in later peg placement.

:: Step 4
Put a White Peg in each Column somewhere, i.e. where there is a gap (shown as light shaded Blue Pegs below), e.g.:

4

Left Grid                                                                      Right Grid

:: Step 5
Look across each Row, if a Row does not have a White Peg in it somewhere, then add one (shown below as light Green Pegs), e.g.:

5

Left Grid                                                                   Right Grid

In the example above, this would be in Rows 6, 8 and 10 on the Left Grid; and on the Right Grid that would be Rows 4, 7, 9 and 10. If doing this on paper the Green Dots could represent secret doors. However, doing this might make the dungeon appear more linear looking to the players. To increase interconnectivity, hence ‘jaquaying-the-dungeon’, simply add a few more pegs (e.g. 3) at random.

:: Step 6
Finally, remove one Red Peg from each Grid. Optionally, consider replacing this with a White Peg (to be visually distinct). Below this is shown as a red X, e.g.:

6

Left Grid                                                           Right Grid

Please note: the map looks busy in this example because I’m using colours to aid explanation. In reality, you’d just have Red and White Pegs. The red X represents the point where the two levels interconnect. So in the above example, this could be stairs going from Room 4, Left Grid to Room 7, Right Grid. Of course, there is nothing stopping you adding more level interconnections. Again, this will help in ‘jaquaying-the-dungeon’. For simple bookkeeping, remove the pegs from matching positions e.g. 4;4 Left Grid leads to 4;4 Right Grid, and 7;7 Grid Left leads to 7;7 Right Grid. The connections do not need to be stairs, they could be tunnels etc. If doing this on paper, a mega dungeon can be made easily by simply using multiple paper grids and interconnecting them in this way.

What is this gibberish?
Here’s a link to my initial post about Grid-Crawls, hopefully that helps, else see the below example: Link

Below is a brief example of how to navigate a Grid-Crawl map:
The example does not consider any encounters in the rooms etc.

• The PCS start in Room 1 on the Left Grid, i.e. corresponding to Colum 1; Row 1. This position is marked with an S on the map.

• The DM Looks across Row 1 and down Column 1. There is a Non Red Peg in the 5 and 9 positions (see arrows), i.e.:

7

Left Grid

This means Room 1 connects to Rooms 5 and 9.

• The PCs decide to go to Room 5. In Room 5 the DM Looks across Row 5 and down Column 5. It can be seen that there are Non Red Pegs in the 1, 3, and 4 positions, i.e.:

8

Left Grid

From this it can be seen that Room 5 connects to Rooms 1, 3, and 4.

• The PCs then go to Room 4. The DM Looks across Row 4 and down Column 4. There is a Non Red Peg in the 5 and 7 positions, and a red X at the 4 position, i.e.:

9

Left Grid                                                    Right Grid

From this it can be seen that Room 4 connects to Rooms 5 and 7. Also, Room 4 Left Grid connects to Room 7 Right Grid, e.g. as marked by the red X on each grid.

• The PCs therefore can now move from the Left Grid (upper level) to the Right Grid (lower level) if they choose to …

• And so on.

Map
For the sake of completeness, I’ve gone to the effort of drawing out the Grid-Crawl above as a Point Crawl (please see maps below). I’ve done this just to show what kind of map this method generates. To be fair, part of the point of this system is for the DM not to have to draw a map (unless of course that brings you joy). The players are free to map as they will, and the DM might enjoy seeing their work :O|


The second map uses the option for secret passages as mentioned in Step 5 (i.e. for the Green Dots)

These point-crawl maps were made using: https://csacademy.com/app/graph_editor

Quick Method – Battleships Dungeon
Step 1
Start with two blank ‘Battleships Maps’ (probably best to renumber the top line ‘1 to 10’ rather than ‘A to J’).

Step 2
Place the ‘ships’ on each grid (as if you were playing the Battleships game). If doing this on paper grids, just shade in the squares.

Step 3
In each of the grids put a Red Peg in the diagonal positions, except for the top leftmost cells; i.e. at positions 2;2, 3;3, and 4;4 etc. In the paper method use a solid ‘dot’ in place of the peg.

Step 4
Put a White Peg in each Column somewhere, i.e. where there is a gap. In the paper method use an open (unshaded) ‘dot’ in place of the peg.

Step 5
Look across each Row, if a Row does not have a White Peg in it somewhere, then add one (these might represent secret passages).

Optionally, add a few extra White Pegs at random to increase same level interconnectivity.

Step 6
Finally, remove one Red Peg from each Grid. Optionally, consider replacing this with a White Peg (to be visually distinct). In the paper method you might put this down as an X.

Optionally, add an extra interconnectivity pathway between the grids (i.e. dungeon levels) in the same fashion.

– – –

Me on DriveThruDriveThru; at the moment I’m mainly pimping my procedural High Seas ‘Hex Crawl’ – In the Heart of the Sea.