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Post by misomiso on Jul 21, 2022 10:08:47 GMT
Could somebody explain the 'Odds' of the FF combat system?
What I'm specifically after is the odds of winning a single combat round for each difference in skill between the Hero and the opponent.
I've done some work on this myself but I think I've got it wrong because of the variance of the opponent's die roll - I have worked out the odds if the opponent always rolls a seven for example, but I know this is not statistically correct.
If I can see the odds of a hit, of being hit, or a reroll of each combat round, it could really help with balancing monsters.
Mny thks
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Post by johnbrawn1972 on Jul 21, 2022 11:42:40 GMT
My memory is so damaged by all the pills I cannot recall where it is but there was a wonderful matrix which showed the likely stamina loss given the difference between the relative skills and the initial stamina of the enemy.
I never realised a skill deficit of 2 was so brutal.
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Post by CharlesX on Jul 21, 2022 11:58:31 GMT
About a year ago I asked about the maths of fighting an opponent with a 3 stamina damage, -1 attack strength weapon, whether its advantageous or disadvantageous. I think its marginally advantageous if you both have the same skill and your opponent and you have high Stamina. The problem is doing more damage is of no help whatsoever if you cannot hit in the first place. However, a 4 stamina damage, -1 attack strength weapon tends to be effective (such as the battleaxe in Legend Of The Shadow Warriors). Not 100% relevant to this thread I know. Monsters often have special attacks of course.
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Post by a moderator on Jul 21, 2022 12:06:18 GMT
My memory is so damaged by all the pills I cannot recall where it is but there was a wonderful matrix which showed the likely stamina loss given the difference between the relative skills and the initial stamina of the enemy. I never realised a skill deficit of 2 was so brutal. |
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Post by johnbrawn1972 on Jul 21, 2022 12:14:37 GMT
My memory is so damaged by all the pills I cannot recall where it is but there was a wonderful matrix which showed the likely stamina loss given the difference between the relative skills and the initial stamina of the enemy. I never realised a skill deficit of 2 was so brutal. My GCSE mathematics ha ha does not know if this matrix is very good mathematics but I have used it a great deal in my ongoing project to update the solutions to make them more perspicuous. I now have a list of solutions to update if my computer ever starts working again. |
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Post by misomiso on Jul 21, 2022 12:40:08 GMT
What I'm after specifically are the odds of any one combat role.
So if I have ONE skill point higher than my opponent, if we fight one round of combat what the odds are of
a) I win
b) They win
c) We Draw
I have seen matrix like things before, but I'm after the raw data and odds.
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Post by scouserob on Jul 21, 2022 12:57:06 GMT
I’d imagine the raw odds for winning the attack round with a +1 skill advantage would be, where P(#) is the probability of rolling # on 2 dice.
P(2)*P(2) +
P(3)*(P(2)+P(3)) +
P(4)*(P(2)+P(3)+P(4)) +
…
… +
P(11)*(P(2)+P(3)+…+P(11))
P(12)*1
Which can be simplified but is probably easier to understand like this.
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Post by johnbrawn1972 on Jul 21, 2022 13:15:09 GMT
I’d imagine the raw odds for winning the attack round with a +1 skill advantage would be, where P(#) is the probability of rolling # on 2 dice. P(2)*P(2) + P(3)*(P(2)+P(3)) + P(4)*(P(2)+P(3)+P(4)) + … … + P(11)*(P(2)+P(3)+…+P(11)) P(12)*1 Which can be simplified but is probably easier to understand like this. It is times like this when I wish I had studied A-level mathematics. I think I will stick to the matrix as that is the front end whereas the question is about the mechanics rather than the results. If you can understand the mechanics you can answer different questions. I have to resort to looking at a matrix and then I try to find a plausible strategy. |
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Post by scouserob on Jul 21, 2022 16:38:56 GMT
What I'm after specifically are the odds of any one combat role. So if I have ONE skill point higher than my opponent, if we fight one round of combat what the odds are of a) I win b) They win c) We Draw I have seen matrix like things before, but I'm after the raw data and odds. So if I’ve calculated correctly the odds are: 55.6% (721/1296) for winning the round. 10.8% (35/324) for drawing. 33.6% (145/432) for losing. They add up to 1 exactly, which is promising. If you need me to explain any of the terms below then ask away. (For example the third term added in the first picture is the chance of you rolling 4 (3/36) multiplied by the probability of him rolling 4 or less (6/36)).    |
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Post by scouserob on Jul 21, 2022 20:34:48 GMT
Doing these calculations on my phone so fingers crossed…
Odds for winning a round with equal skill:
Win: 44.4% (575/1296)
Draw: 11.3% (73/648)
Loss: 44.4% (575/1296)
___________________________
Odds for winning a round with 2 more skill:
Win: 66.4% (287/432)
Draw: 9.6% (125/1296)
Loss: 23.9% (155/648)
___________________________
Odds for winning a round with 3 more skill:
Win: 76.1% (493/648)
Draw: 8.0% (13/162)
Loss: 15.9% (103/648)
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Post by misomiso on Jul 21, 2022 21:50:05 GMT
Hmmm ok.
So the thing I find interesting in Fighting Fantasy terms is that a draw is in effect nullified as nobody takes any damage, so the actual odds with a one skill advantage is 55.5/(55.5+33.6) which is 62.1%. quite high, and 73.4% for two higher skill.
So if you are fighting an opponent with two less skill you can say on average you will 2 stamina for every 6 lost of theirs.
I actually DID get similar maths to yours on one of my calulations but used a different method so that's interesting.
I feel the FF writers should use this math for their adventure design!
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Post by scouserob on Jul 21, 2022 22:24:06 GMT
For completeness:
Odds for winning a round with 4 more skill:
Win: 84.1% (545/648)
Draw: 6.2% (5/81)
Loss: 9.7% (7/72)
___________________________
Odds for winning a round with 5 more skill:
Win: 90.3% (65/72)
Draw: 4.3% (7/162)
Loss: 5.4% (35/648)
___________________________
Odds for winning a round with 6 more skill:
Win: 94.6% (613/648)
Draw: 2.7% (35/1296)
Loss: 2.7% (35/1296)
___________________________
Odds for winning a round with 7 more skill:
Win: 97.6% (1261/1296)
Draw: 1.5% (5/324)
Loss: 1.2% (5/432)
___________________________
Odds for winning a round with 8 more skill:
Win: 98.8% (427/432)
Draw: 1.5% (5/648)
Loss: 0.3% (5/1296)
___________________________
Odds for winning a round with 9 more skill:
Win: 99.6% (1291/1296)
Draw: 1.5% (1/324)
Loss: 0.08% (1/1296)
___________________________
Odds for winning a round with 10 more skill:
Win: 99.9% (1295/1296)
Draw: 0.08% (1/1296)
Loss: 0% (0)
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Post by thealmightymudworm on Jul 22, 2022 1:36:38 GMT
Odds for winning a round with 10 more skill: Win: 99.9% (1295/1296) Draw: 0.08% (1/1296) Loss: 0% (0) SKILL 2 hero in The Crimson Tide battles a mudworm, thinking "I'm sure I killed one of these things once." |
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Post by slloyd14 on Jul 22, 2022 11:19:54 GMT
I've come to the conclusion that a skill 7 character can't beat any book if they have to fight a skill 10 opponent (Warlock if you want the treasure or Battle Blade Warrior). The biggest difference in skill should be 2 for a fight where either side could win, which makes balancing a book for characters with a skill of 7-12 very difficult. It's like skill 7 characters need their own special items to overcome opponents or special items that raise skill to a certain level.
Demons of the Deep has a good one - you have a swordfighting lesson which is a combat. If you win, your initial skill goes up by 1, but if you lose, it goes up by 2, indicating that worse skill values get a bigger boose.
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Post by nathanh on Jul 22, 2022 11:35:39 GMT
I've come to the conclusion that a skill 7 character can't beat any book if they have to fight a skill 10 opponent (Warlock if you want the treasure or Battle Blade Warrior). The biggest difference in skill should be 2 for a fight where either side could win, which makes balancing a book for characters with a skill of 7-12 very difficult. It's like skill 7 characters need their own special items to overcome opponents or special items that raise skill to a certain level. Demons of the Deep has a good one - you have a swordfighting lesson which is a combat. If you win, your initial skill goes up by 1, but if you lose, it goes up by 2, indicating that worse skill values get a bigger boose. A 7/24/12 character has about a 50% chance to beat a 10/10 enemy with judicious use of Luck. In contrast, a 7/14/7 character has a mere 8% chance of winning such a fight (I haven't accounted for the Shield or a potion of Strength here). Another way to balance books for the skill range is a choice of two routes, one of which has the 10/10 fight and the other has say a Luck test or just a 50-50 dice roll for example. Then you choose the route according to your Skill. |
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Post by johnbrawn1972 on Jul 22, 2022 12:19:18 GMT
I've come to the conclusion that a skill 7 character can't beat any book if they have to fight a skill 10 opponent (Warlock if you want the treasure or Battle Blade Warrior). The biggest difference in skill should be 2 for a fight where either side could win, which makes balancing a book for characters with a skill of 7-12 very difficult. It's like skill 7 characters need their own special items to overcome opponents or special items that raise skill to a certain level. Demons of the Deep has a good one - you have a swordfighting lesson which is a combat. If you win, your initial skill goes up by 1, but if you lose, it goes up by 2, indicating that worse skill values get a bigger boose. A 7/24/12 character has about a 50% chance to beat a 10/10 enemy with judicious use of Luck. In contrast, a 7/14/7 character has a mere 8% chance of winning such a fight (I haven't accounted for the Shield or a potion of Strength here). Another way to balance books for the skill range is a choice of two routes, one of which has the 10/10 fight and the other has say a Luck test or just a 50-50 dice roll for example. Then you choose the route according to your Skill. This is what I am driving at in my solution for Warlock. Roughly speaking you have 7/28/7 to beat the Cyclops and the matrix says you need 28 stamina to beat a 10 skill stamina 6 enemy so use 2 rounds of luck and then 1 luck when you have 2 stamina points left. Also you have a 58% chance of acquiring the shield which should just give you the edge to defeat the Cyclops with 1 or 2 stamina point remaining. The use of luck is by no means a given but I am hoping this gives you about a 25% chance of winning here. |
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Post by CharlesX on Jul 22, 2022 12:42:13 GMT
I've come to the conclusion that a skill 7 character can't beat any book if they have to fight a skill 10 opponent (Warlock if you want the treasure or Battle Blade Warrior). The biggest difference in skill should be 2 for a fight where either side could win, which makes balancing a book for characters with a skill of 7-12 very difficult. It's like skill 7 characters need their own special items to overcome opponents or special items that raise skill to a certain level. Demons of the Deep has a good one - you have a swordfighting lesson which is a combat. If you win, your initial skill goes up by 1, but if you lose, it goes up by 2, indicating that worse skill values get a bigger boose. Well, Demons Of The Deep also has the special bath sauna where you reroll all your values of course. |
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Post by philsadler on Jul 22, 2022 17:34:29 GMT
I've come to the conclusion that a skill 7 character can't beat any book if they have to fight a skill 10 opponent (Warlock if you want the treasure or Battle Blade Warrior). The biggest difference in skill should be 2 for a fight where either side could win, which makes balancing a book for characters with a skill of 7-12 very difficult. It's like skill 7 characters need their own special items to overcome opponents or special items that raise skill to a certain level. Demons of the Deep has a good one - you have a swordfighting lesson which is a combat. If you win, your initial skill goes up by 1, but if you lose, it goes up by 2, indicating that worse skill values get a bigger boose. Well, Demons Of The Deep also has the special bath sauna where you reroll all your values of course.
Sounds interesting. Can you give the reference number please?
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Post by CharlesX on Jul 22, 2022 17:56:39 GMT
Well, Demons Of The Deep also has the special bath sauna where you reroll all your values of course.
Sounds interesting. Can you give the reference number please?
I don't have the book wi me anymore so hopefully another fellow fan can.. You are told the sauna will "make you feel like a new person", and if you pay gold and go for the sauna, you reroll your initial skill, stamina and luck. I don't remember whether the sauna restores your current level to its initial level or whether it specifies either way. |
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Post by a moderator on Jul 22, 2022 18:25:57 GMT
Sounds interesting. Can you give the reference number please?
I don't have the book wi me anymore so hopefully another fellow fan can.. You are told the sauna will "make you feel like a new person", and if you pay gold and go for the sauna, you reroll your initial skill, stamina and luck. I don't remember whether the sauna restores your current level to its initial level or whether it specifies either way. Section 266. It says 'Change all your current scores to these new Initial scores, so if you're in bad shape when you arrive, even getting a lower score on the reroll could leave you better off. |
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Post by dragonwarrior8 on Jul 22, 2022 18:50:58 GMT
My Skill-10 Stamina-14 (going into the fight) adventurer who was just killed by a Skill-7 Stamina-9 Troll would like two minutes for rebuttal. Or at least he would if he wasn't dead.
It's what makes the combat in FF tense and exciting, but still I'd like to know how other players mentally handle those frustrating unlikely defeats as I know we have all been there. For me it often ends with slamming the book down and shouting "OH C'MON!!!"
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Post by a moderator on Jul 22, 2022 19:40:01 GMT
I'd like to know how other players mentally handle those frustrating unlikely defeats as I know we have all been there. For me it often ends with slamming the book down and shouting "OH C'MON!!!" I think of it as counterbalancing the time my Skill 7 adventurer slew the Skill 12 Birdman in Dungeon of Justice without sustaining a single injury. Then I shake my fist at the adventure's author, because even with such a low Skill I still succeeded at the roll which it is essential to fail in order to have any chance of winning, and thus wound up executed shortly after my glorious victory against an opponent who outclassed me to such an extent. |
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Post by dragonwarrior8 on Jul 22, 2022 20:23:32 GMT
I'd like to know how other players mentally handle those frustrating unlikely defeats as I know we have all been there. For me it often ends with slamming the book down and shouting "OH C'MON!!!" I think of it as counterbalancing the time my Skill 7 adventurer slew the Skill 12 Birdman in Dungeon of Justice without sustaining a single injury. Then I shake my fist at the adventure's author, because even with such a low Skill I still succeeded at the roll which it is essential to fail in order to have any chance of winning, and thus wound up executed shortly after my glorious victory against an opponent who outclassed me to such an extent. I have to admit, I was infuriated when I learned what you needed to do to beat Dungeon of Justice. I'm actually getting hot again just thinking about it. I can only imagine the triumphant feeling of beating that Birdman in such a David vs Goliath manner only to then be brought low in such a way. This also reminds me of something from Caverns of the Snow Witch that you mention in your blog. Imagine making it through almost to the end of that extremely tough book (including the ridiculous Skill 12 Birdman there as well), down to your very last Stamina point, only to lose it at the watering hole, which would have immediately been restored had you not been on your last point. (Really Ian Livingstone? Was this solely included to kill off, and piss off, an adventurer who had exactly 1 Stamina point left and no other reason?) |
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Post by misomiso on Jul 23, 2022 16:21:40 GMT
What I'm after specifically are the odds of any one combat role. So if I have ONE skill point higher than my opponent, if we fight one round of combat what the odds are of a) I win b) They win c) We Draw I have seen matrix like things before, but I'm after the raw data and odds. So if I’ve calculated correctly the odds are: 55.6% (721/1296) for winning the round. 10.8% (35/324) for drawing. 33.6% (145/432) for losing. They add up to 1 exactly, which is promising. If you need me to explain any of the terms below then ask away. (For example the third term added in the first picture is the chance of you rolling 4 (3/36) multiplied by the probability of him rolling 4 or less (6/36)). View AttachmentView AttachmentView AttachmentCould you go through the math for this? I'm sure you are right, as I said I got something simialr in one of my calculations, but I would just like to have the reasoning very clearly spelled out.
The reason I ask is that the odds seem a lot more reasonable than I was thinking. In my own Gamebook design I have a fixed ' defence' stat that I though had much better math, but the FF skill system actually seems quite good.
Mny thks
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Post by misomiso on Jul 23, 2022 16:48:59 GMT
Just want to say I concur with your math now.
If you want to put it all out in a table, taking out the draw odds (and compensating for them with the Math!) then that would be helpful, but only if you have the time!
ty!
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Post by scouserob on Jul 23, 2022 17:44:40 GMT
Just want to say I concur with your math now. If you want to put it all out in a table, taking out the draw odds (and compensating for them with the Math!) then that would be helpful, but only if you have the time! ty! Sure. I’ll put something together. (Hopefully tomorrow, if nobody beats me to it.) |
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Post by scouserob on Jul 24, 2022 11:22:20 GMT
So the thing I find interesting in Fighting Fantasy terms is that a draw is in effect nullified as nobody takes any damage, so the actual odds with a one skill advantage is 55.5/(55.5+33.6) which is 62.1%. quite high, and 73.4% for two higher skill. As requested and using your own formula (Hopefully, I haven't made a typo somewhere): +1 Skill: Win Next: 721/1156 ≈ 62.37%, Lose Next: 435/1156 ≈ 37.63% +2 Skill: Win Next: 861/1171 ≈ 73.53%, Lose Next: 310/1171 ≈ 26.47% +3 Skill: Win Next: 493/596 ≈ 82.72%, Lose Next: 103/596 ≈ 17.28% +4 Skill: Win Next: 545/608 ≈ 89.64%, Lose Next: 63/608 ≈ 10.36% +5 Skill: Win Next: 117/124 ≈ 94.35%, Lose Next: 7/124≈ 5.65% +6 Skill: Win Next: 1226/1261 ≈ 97.22%, Lose Next: 35/1261 ≈ 2.78% +7 Skill: Win Next: 1261/1276 ≈ 98.82%, Lose Next: 15/1276 ≈ 1.18% +8 Skill: Win Next: 1281/1286 ≈ 99.61%, Lose Next: 5/1286 ≈ 0.39% +9 Skill: Win Next: 1291/1292 ≈ 99.92%, Lose Next: 1/1292 ≈ 0.08% Below is the calculation for winning the next round with +1 Skill.  Attachments:
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Post by sleepyscholar on Jul 25, 2022 4:45:05 GMT
Odds for winning a round with 10 more skill: Win: 99.9% (1295/1296) Draw: 0.08% (1/1296) Loss: 0% (0) SKILL 2 hero in The Crimson Tide battles a mudworm, thinking "I'm sure I killed one of these things once." "But oh, that was a tenth the size of this one: maybe this is its mother?" Incidentally, can I also just say: "maths". |
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Post by scouserob on Jul 25, 2022 6:23:39 GMT
This may also be useful.
Expected stamina points lost per next non-drawn round:
(Ignoring the use of luck in battle, and not simultaneously fighting multiple opponents.)
Equal Skill: 1
-1 Skill: 1.247 (721/578)
+1 Skill: 0.753 (425/578)
-2 Skill: 1.467 (861/587)
+2 Skill: 0.528 (310/587)
-3 Skill: 1.654 (493/298)
+3 Skill: 0.346 (103/298)
-4 Skill: 1.793 (545/304)
+4 Skill: 0.207 (63/304)
-5 Skill: 1.887 (117/62)
+5 Skill: 0.113 (7/62)
-6 Skill: 1.944 (2452/1261)
+6 Skill: 0.056 (70/1261)
-7 Skill: 1.976 (1261/638)
+7 Skill: 0.024 (15/638)
-8 Skill: 1.992 (1281/643)
+8 Skill: 0.008 (5/643)
-9 Skill: 1.998 (1291/646)
+9 Skill: 0.002 (1/646)
-10 Skill: 2
+10 Skill: 0
These can be used to calculate how many non-drawn rounds each combatant can be expected to survive.
(Divide current stamina by expected stamina loss per non-drawn round.)
The minimum of these values for the two combatants will be the expected length of the battle in non-drawn rounds.
Multiplying this expected length of the battle by the expected winner's expected stamina loss per non-drawn round will give you their expected stamina loss in the battle.
Subtracting this from their current stamina will give you their expected stamina after the battle.
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Post by scouserob on Jul 25, 2022 8:53:01 GMT
(Hopefully the maths is sound and ignoring using luck in battle.)
This is possibly even more useful.
The multiple of your opponent’s stamina required to last the same expected number of rounds:
Equal Skill: 1
-1 Skill: 1.696 (721/425)
-2 Skill: 2.778 (861/310)
-3 Skill: 4.786 (493/103)
-4 Skill: 8.651 (545/63)
-5 Skill: 16.714 (117/7)
-6 Skill: 35.029 (1226/35)
-7 Skill: 84.067 (1261/15)
-8 Skill: 256.2 (1281/5)
-9 Skill: 1291
So if you have a Skill of 9 and battle through to the Cave Troll (Skill 10 Stamina 11) then, ignoring luck, you would need 19 stamina to be the favourite to emerge triumphant from that battle.
11*(721/425) ≈ 18.661
A stamina of 18 would make you a slight underdog with the most likely outcome then being that Throm would have to finish off your wounded vanquisher before journeying on alone.
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