Sunday, October 10, 2010

Dice in game books part 3 - Blocking Victory

Ok, this will be the last time I'll be down on the dice. They do have their good points too.

This post links in with part 1 about how dice could foil your last attempt for victory despite you doing everything right. It is the fact that using dice makes a gamebook completely unfair if you do not work out your probabilities.

Someone was telling me yesterday that he had to cheat at some gamebooks by not rolling dice and just assuming that he won all combats. I told him that with some books, it was the only way to win.

Some of the most unfair books in terms of unfairness were some Fighting Fantasy books.

The biggest source of unfair die rolls is probably your first one - your skill score.

Your skill represents your fighting prowess. Every round, you roll two dice and add the result to your opponent's skill, then roll two dice and add the result to your skill. The combatat with the highest score wins and inflicts damage the loser.

This is a fine method of combat, but the problem lies in the range of skill you can have. In most books, your skill is determined by rolling one six sided die and adding 6. This gives a skill score of 7-12. This is a massive range when you consider the statistics involved with rolling dice.

If maths doesn't thrill you, skip over the probability part.


For an introduction to probability, try this:

There are 36 possible permutations when you roll 2 dice:

So when you roll 2 dice, there is only a 1 in 36 chance of rolling a 12. There is a 6 in 36 chance of rolling a 7.

This means that a skill 7 hero fighting a skill 12 boss monster needs to roll 8 or more to even have the remotest chance to win an attack round. The odds of that is 15/36. That is not even taking into accound what your opponent needs to roll. To wound an opponent if you roll an 8, your opponent needs to roll a 2.

The probability of this is 5/36 x 1/36 = 5/1296.

Hmm. Not looking good is it?

Ok, so that's just if you roll an 8. You *might* win the round if you roll an 8-12, but your opponent needs to roll low scores so you can win. If you roll a 12, your opponent needs to roll a 6 or less.

After doing some calculations on excel, I calculated that the probability of winning an attack round if your skill is 5 less than your opponent's is 5.4%. And you have to do this several times to win a combat.

You're stuffed.

If you fight an opponent with the same skill, you have 44% chance of winning a round with 44% chance of losing and 12% chance of drawing.

If you fight an opponent with a skill 1 above yours, you chances of winning are now 34%. Fighting an opponent with a skill 2 higher than yours and your chance of winning a round has now dropped to 24%.

Even a small change in skill rapidly decreases your chances.


So fighting somone with the same skill gives you a 44% chance of winning a round.

If their skill is above yours by 1, your chance of winning becomes 34% and if it is above yours by 2, your chances fall to 24%.

What appears to be a difference in 1 gives a huge difference in probability. This means that it is very difficult to give any character who has a skill between 7 and 12 a challenging yet do-able game. A skill 7 character will probably find weak opponents quite deadly, whereas a skill 12 character would find all the combats tedious as they just win them.

There are a few ways around it such as:

  • Having other skills or spells (Citidel of Chaos and Sorcery! are good examples).
  • Not having mandatory combats or few mandatory combats (Spectral Stalkers and Space Assasin are good examples).
  • Being able to find items in the book which mean that you can avoid difficult combats (Warlock of Firetop Mountain has items which allow you to avoid combat with both the warlock and the dragon. It's a shame you have to still fight a skill 10 opponent. Beneath Nightmare Castle is a good example of not having to fight difficult opponents if you get the right items).

I quickly realised this so almost all Fighting Fantasy books I have written involve the character having a skill picked from 2 or 3 possible values. This makes combats fairer.

I'm sure when these books were first written was that there was a progression in strength of monsters, but you cannot have their skills increase too much as your character will soon be out of their depth. Soon, if you work out the probabilities, it would become apparent that you have more chance of winning the lottery than some FF books.

Some later ones got worse in terms of unfairness.


Black Vein Prophecy (which is one of my favourites despite its flaw) requires you to fail your first test for luck to win. So if your luck is 12, you're stuffed. Who said it is better to be lucky than to be good?

Knights of Doom, Magehunter and Spellbreaker just have a huge number of dice rolls and combats, Magehunter while you are in the body of a feeble old man. I love the stories in these books, they were just let down by their dice rolling.

I endeaver to make sure that there are no unavoidable unfair combats or rolls in my books as it is basically like having a gamebook you can't win. No gamebook should have victory decided by a die roll. You have to play the odds in order to win (but of course, as mentioned in post 1, there will be one time where you do everything right and the dice are against you which means you lose)

Oh yes, there's also stamina and luck too, but they are fair and you could get through most books with a minimum stamina and luck.

I guess it's all about the skill in Fighting Fantasy.

Other books ahve other stats and these seem quite fair, apart from fear in House of Hell. You can't win if it is below a certain value.

If I can't put fair dice rolls in a book, I won't use them at all.

Speaking of which, I did that with my Windhammer entry. It is a diceless gamebook, but when I started it, I decided to have dice. They just became less and less relevant. Read all of them and vote! Voting closes on October 31st!


  1. That's some interesting maths calculations!

    I must admit that I always automatically won dice combats too. But, after seeing the probability that you've mentioned, it almost seems like a no-brainer to "cheat" :)

    I also wanted to mention, that my friend and I have been writing a Sci-Fi gamebook for the iPhone by trying to make combats more gamer friendly. Since, it's an iPhone gamebook, we're replacing dice combat with real-time mini game based combat. We're using these mini-games to determine an encounter's outcome, so there is no random loss or 'luck' involved. Just thought you would like to check it out:

  2. Looks interesting, Suresh. I think that most gamebooks would be much better without a random element - it has to be done very well to get it right. The last thing you want is people thinking your gamebook as unfair. I look forward to experiencing it.

  3. Totally agree on the random being unfair bit. It's equally unfair when some gamebooks make random death choices. "You open the door and fall into a deep pit and die". okaaaay, how was I supposed to know that?

    In fact, by completely replacing random encounters with mini-games, we've found that people who are new to the gamebook genre are also able to play Star Breed a lot more easily. Hopefully, we can do our bit in getting more people to experience gamebooks. We're like the Wii of gamebooks :)

    BTW, we've just submitted to Apple, so I'll let you know once we launch...

  4. Lloyd, just wanted to let you know that our game's out now on the App Store, in case you want to check it out:

  5. The most unfair fight in all of FF is of coarse the laughable Razaak in the awful Crypt of the Sorcerer. I'd like you to do the odds of winning *that* fight.