Thursday, October 14, 2010

A table of probabilities

Hi all!

Just a quick post to give the percentage probabilities of winning, drawing or losing an attack round depending on the difference between your skill and the skill of your opponents.

If you want more info on how I calculated this, look at the explanation under the table.

The headings mean:

Skill difference: If you subtracted your opponent's skill from your skill, this is the skill difference. I have done it from +6 to -6. any bigger than that and I wouldn't bother rolling dice.

% chance to win, draw or lose: Self explanatory.

If the probabilities do not add up to 100, it is because of rounding.

Of course, these values do not take into account special combat rules.

For example, in Slaves of the Abyss, you automatically kill an opponent if you roll a double 6 (you have a 1/36 chance of winning automatically).

In Creature of Havoc, you automatically kill your opponent if you roll a double (that equivalent of a 1/6 chance of killing your opponent. It is interesting that although Creature of Havoc is one of the hardest FF books, it has the easiest combats)

I also haven't calculated the probabilities of rolling 3 dice and taking the best 2 which occurs in Legend of Zagor.

It appears that if you face an opponent with a skill 3 or more higher than yours, then you are stuffed. You could just about survive an opponent with a skill 3 higher than yours if you are very lucky, but it seems that if my gamebook has an opponent whose skill is 3 higher than the possible initial skill of the hero and the hero has not had a chance to make a choice to avoid the combat or find a way to increase his or her attack strength, then my gamebook has ended there probably with a lot of frustration.

Hope this helps in some way. In the next few days, I'll post about the good points of having dice in gamebooks.

Have a look at Fighting Fantazine ( Issue 4 is coming out soon and I am writing an essay for issue 5 on a particular Fighting Fantasy book on why it is so great. However, I acn't say which one. You will have to wait until issue 5!

How did I work it out?

The way I calculated the % chance to win was to take the sum of the probabilites of rolling a number on 2 six sided dice that has a chance of winning you the attack round and multiplying by the probability of your opponent rolling a number on 2 six sided dice which would mean their attack strength would be lower than yours.

Quick maths lesson - to express something as a probabiliy, you put it in square brackets. For example, the probability of rolling a 2 can be written as [rolling 2]

For example, if your skill difference is 0, the sum is:

([rolling 3] x [rolling 2]) + ([rolling 4] x [rolling 2 or 3]) + ([rolling 5] x [rolling 2-4]) + ([rolling 6] x [rolling 2-5]) + ([rolling 7] x [rolling 2-6]) + ([rolling 8] x [rolling 2-7]) + ([rolling 9] x [rolling 2-8]) + ([rolling 10] x [rolling 2-9]) + ([rolling 11] x [rolling 2-10]) + ([rolling 12] x [rolling 2-11])

If your skill difference is -6, the sum is:

([rolling 9] x [rolling 2]) + ([rolling 10] x [rolling 2 or 3]) + ([rolling 11] x [rolling 2-4]) + ([rolling 12] x [rolling 2-5])

To get a draw I took the sum of the probabilities of rolling numbers where the attack strength was equal.

Once I had calculated the % probabilities of getting a win or a draw, I did the sum 100-[win or draw] to get the probability of losing in %.

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