Andrew Drage

Published Gamebooks I've worked on:

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Conversion of the Gamebook Adventures system to a 2D6 system

Fitness checks can made during any particular round to add 1 to your roll or deduct 1 from your opponent’s roll (and having the reverse effect if you fail the roll).




This article is even more esoteric than yesterday’s topic on probabilities in the Gamebook Adventures system, but it’s related and to those that are designing and writing gamebooks of their own, this may prove useful for their own designs…

Or at least give them ideas. There’s a few things happening in the “gamebook world” at the moment that could benefit from this, and so having done this conversion for a new project I’m working on, I thought I’d share my work, and to kinda follow on from my article yesterday.

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Probabilities in the Gamebook Adventures system

Probability Meme
Odds Meme
Chance of Success (not including FIT checks)
Average Damage when hit (not including FIT checks)
Average Damage per Round (not including FIT checks)
Chance of success for consecutive FIT checks
Chance of Success (including FIT checks)
Average Damage per Round (including FIT checks)
Impact of Fitness Checks on Chance to hit and Average Damage per Round
Adjusted Average Damage per Round (factoring in consecutive FIT checks)

Today’s article is all about probabilities in the Gamebook Adventures system (with some limited comparison to other systems, particularly Fighting Fantasy). Statistics can be a bit of a dry topic haha, so I’ll try to reduce it to the important elements for you… Well important that is if you’re writing for such a system or are interested to know what the game odds are… Beware though, there’s a lot of tables and charts incoming :)

                 

 

Calculating probabilities for a system such as Fighting Fantasy is reasonably straight forward: (In a typical battle) you roll two six-sided dice for each combatant and add a given Skill score to each combatant’s roll, with the highest score dealing 2 Stamina damage to the other combatant. Use of Luck rolls makes it a little more complicated but not by much. You can “Test your Luck”; by attempting to roll two dice equal to or under your current Luck; in order to do one more Stamina damage, but failing this roll means you do one less Stamina. Skill and Luck scores vary, resulting in an exponential scale where even a few points of Skill difference make it unlikely for one side to win, even with far more Stamina.

For example, if your Skill is 3 lower than your opponent’s, then your opponent is roughly five times more likely than you are, to be the one making a hit in a given combat round, not including the Luck factor. In other words, if your hero has Skill 9 Stamina 24 and your opponent Skill 12 Stamina 5, then you both have about the same chance of winning…

                               

 

The Gamebook Adventures system is considerably more complicated to calculate probabilities for (even though the rules themselves are of a similar level of complexity) and shares a similar but less extreme exponential scale, such that the outcome of a combat is not as much of a sure thing. Combatants roll between one and six six-sided dice to attack (as determined by their Offence rating) and between one and six six-sided dice to defend (as determined by their Defence rating). If the attacker’s highest roll is higher than the defender’s highest roll, then they do damage equal to the sum of all their dice. (And in the case of tied rolls, the two tied dice are removed and the next two highest rolls are compared, until no dice are left). In addition, the hero can make a “Fitness check” on any given combat round by rolling two dice under their current Fitness. This is similar to “Testing your Luck” in the Fighting Fantasy system, except that the advantage given is to add 1 to their highest roll, significantly increasing the chance of hitting or defending.

In the extreme case of 6 dice in Offence against an opponent with 6 dice in Defence, and including the two additional dice rolled for a Fitness check, there are 6^14 possible dice combinations for any given round (that’s 78,364,164,096 combinations). And to calculate the highest roll and damage inflicted for each of these combinations, is quite a task… But I’ve done this (well kind of; I had to take some short cuts, but the end conclusions are about the same) and this is what I present below.

This isn’t meant to be a rigorous statistics paper, so I’ll spare you comprehensive details of how I came up with these numbers… But basically I listed every dice combination out on a spreadsheet, so that I could be sure I was calculating correct averages etc, until the number of possible combinations became too unwieldy. I listed all combinations up to seven dice, which is 6^7 or 279,936 combinations. The numbers for the remaining eight to fourteen dice combinations I estimated using a “best fit” exponential regression equation. In other words, I took the half-finished set of values I had manually calculated and used them to apply a formula to estimate the rest…

First of all, we’ll ignore the impact of Fitness checks, and just focus on the chance of success (success being an attack that hits the defender) for each Offence / Defence combination:

                 

 

So to interpret what these numbers mean, it’s saying that if your Offence value was 6, and your opponent had a Defence value of 1, then (not including Fitness checks) your chance of success (i.e. hitting) is 76.00%, and if their Defence was 2, your chance is *about* 57.77% and so on…

The yellow cells in the above table are where I had to cut corners as the number of combinations was too large to individually analyse. These are the values I extrapolated based on the trend already shown. This trend (as you can see in the above graph) is an exponential decline, where the degree to which your chances drop lessens as Defence values increase.

Here are some interesting conclusions from these numbers:

  • Even at maximum Offence (6) versus minimum Defence (1), you have at best a 76% chance of hitting. This compares to a 100% chance for a similarly extreme matchup in the Fighting Fantasy system, and to many other dice-based game systems where the best odds tend to be 95% (anything but a roll of one on a twenty-sided dice), 97% (anything but double-one or double-six on two six-sided dice) or 99% in percentile-based systems.
  • Conversely though, even at minimum Offence (1) versus maximum Defence (6), you still have a 7.33% chance of hitting (more once you consider Fitness checks), which typically compares to between 0% and 5% in other systems.
  • Typically your chance of hitting; without including Fitness checks; is lower in the Gamebook Adventures system than that for other systems such as Fighting Fantasy, Lone Wolf, Dungeons and Dragons and the Basic Role Playing system. (However when you do hit, your damage is typically higher than what occurs in these systems).
  • Increasing Offence or Defence has an increasingly smaller impact. For instance, you’ll see that Offence 6 is only slightly better than Offence 5, particularly against high Defence values. (Although I suspect it’s not quite a close as shown, since the values in the yellow cells were those obtained from extrapolation).


Now let’s look at the average damage inflicted when you hit:

              

It’s actually difficult to draw much from these numbers since you need to factor in the chance of hitting to say how much damage is done on average each round… The amount of damage done for any given Offence rating only increases slightly with increasing Defence (based on the fact that the higher the Defence value you’re trying to hit, the more likely that a successful hit was based on a high roll).

By multiplying the chance to hit, by the average damage done when hit, we come to this table (which is very useful from a design / game-balancing point of view):

                

 

So now we can start to see exactly how hard any given combat is. For instance, if you have an Offence of 4 and a Defence of 2, and are fighting an enemy with an Offence and Defence value of 3, then you inflict an average of 6.08 damage per attack, whilst your opponent inflicts an average of 5.44 damage per attack… Pretty useful huh?

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Guest — Evan Read
Wow man, that's some deep stats goin' on!! Well done brewin' - the hard work is paying off!
Tuesday, 19 June 2012 09:45
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Post-mortem of a Book Launch

The latest covers for my three published works

On Saturday the 28th of April 2012, I held my “triple book launch” at the Royal Hotel in Clifton Hill. The video of my speech (which included me reading an extract of The Dark Horde that contains swearing and graphic content) can be seen here:


Attendance and sales for the day was broadly comparable to the “book launch gigs” I held (for the then-released versions of my Evermore novel) in 2001 and 2003. Well when I say broadly comparable, it was actually less. Here’s a reasonably accurate breakdown and comparison of my three book launches:

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Guest — Nevermore
Whilst I understand the frustration of your career path, you miss or gloss over a few key points. Namely, that a majority of peopl... Read More
Wednesday, 02 May 2012 12:02
Brewin
Thank you for your contribution Nevermore. I think I get what you are trying to say, but I have to correct you on your perception ... Read More
Wednesday, 02 May 2012 16:43
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AN INCOMPLETE HISTORY OF BREWIN’ – PART TWO











(Click here for Part One)

So where was I? Ah yes I was telling you about who I am, well at least in terms of my history. Why am I doing this? Well aside from it helping you to understand my works I’m promoting through this site (and hopefully being an entertaining read!) it also helps you understand who I am. Which is in short, a freak haha…

 

A “limited” edition version of the cover for one of my books; limited to one copy!

 

I can actually recall thinking at the age of eight that I wasn’t remotely like anyone else and that what’s more, I didn’t want to be. Being “normal” or “like others” seemed so boring, the internal universe I predominantly lived in creating stories and games in my head, was so much more interesting… And in many ways, I haven’t really changed; I’m still the kid wrapped up in his world creating stuff, it’s just that I’m starting to release some of it now.

But rather than attempting to qualify the above statements much for now (that can come later maybe if there’s sufficient interest), I’ll just tell you about some of the cool stuff I’ve created over the years and post some interesting pictures:

This is a review of one of the more popular games I made (in the style of the Zzap 64 magazine) from 1989… It featured robot ninjas!

 

My childhood, like my life, was anything but normal. By the time I was eight, I was devouring gamebooks and role playing games and had started to write my own. Before I turned eleven at the end of 1985, I was running RPG, gamebook and “creepy-crawly” clubs, had written many stories (some over a hundred pages long albeit smaller pages than a typical book), gamebooks, games, club magazines and was selling and distributing them.

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Guest — Nikos
So when do we get to read about Chuck Billy and The Royal? Nah dude...ahh y'know....Good effort in doing this. Very enjoyable rea... Read More
Wednesday, 21 March 2012 11:05
Brewin
Don't spoil Part 3 Nikos! You'll give the punch line away!
Wednesday, 21 March 2012 11:13
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AN INCOMPLETE HISTORY OF BREWIN’ – PART ONE






Well telling you a bit about me seems as good a place as any to start for my blog. Some of the things mentioned here I’ll elaborate on over subsequent posts, but for now, here’s (the start of!) an overview of who I am and how I came to be here writing this post that you’re now reading:

Most people I guess, take a while to find their calling and some never do. This wasn’t my experience however, in fact I was only seven when I decided I wanted to be a writer, and this ambition has shaped my life ever since…

 

The face of genius? ...Nup, it's just the brewin :)

I was born December 1974 into a large family of Brewins but my childhood was more like that of an only child, as I was the only child of my mother’s second marriage (hence why I am Andrew Drage rather than Andrew Brewin) and most of my five older siblings had already left the nest by the time I was born. This environment lent itself to spending a lot of time on my own creating stories and games from about the age of six. My mother was awarded first class honours in psychology the day I was born (a story that was featured on the front page of The Age newspaper at the time but I’m damned if I can find this article now) and her love of knowledge and reading was fostered in me from as far back as I can remember.

I’m quite proud of the fact that the first story I wrote at the age of six was a horror story called The Dangerous World where everyone died, and it didn’t take long for my older brothers to notice my fascination with “imaginary worlds”; be that fantasy, science-fiction or horror; and they gave me this for my seventh birthday:

From the era when “role playing games” had nothing to do with computers and were supposed to teach you about the occult and make you want to kill yourself or other people haha

 

However it was all a bit much for me to understand at that point (that would come a couple of years later) but it contained a TSR catalog called Gateway to Adventure that I still remember fondly to this day. You know how you have those pivotal moments in your life where everything was different from that point onwards? Well this was one of those… And by the glory of the modern internet, I’ve not only found the catalog cover, but the entire document in pdf format as well:

I can remember looking at this catalog for the first time and thinking “Wow, there’s a whole world of stuff out there for me to get into!”

 

A trip down memory lane with all the awesome games and accessories that were in this catalog is now just a click away!

Sometime in the following year (1982) saw the next pivotal moment in my reading/writing/playing life. I was in a bookstore (as I often was in those days) and a new book had turned up that immediately caught my attention:

You mean it’s a book where I get to be the hero, fight monsters and collect treasure? I’m so in!

 

Suddenly “normal” books had lost their charm. This was a type of book where I was the one fighting monsters and exploring fantastic worlds… And best of all it was only number one in a brand new series!

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