aggsol
Wanderer
Bored...
Posts: 93
Favourite Gamebook Series: Lone Wolf
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Post by aggsol on Jul 25, 2022 13:17:08 GMT
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Post by scouserob on Jul 25, 2022 13:21:26 GMT
An exact match. Well that should give confidence in the repeated results. 😀👍🏻
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Post by misomiso on Jul 25, 2022 13:50:00 GMT
Perfect ty. This is all very very interesting for the math.
One thing, I think your +2 Skill calculation may be wrong = 66.4/(66.4+23.9) = 73.% to win? COuld be wrong though.
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Post by scouserob on Jul 25, 2022 13:59:52 GMT
You are bang on. 😀👍🏻 Not sure how I typed that calculation in wrong…. Hope there aren’t any other errors. 😬 I’ll go back and edit accordingly… All the three lists are now edited to correct for the error. Very well spotted, thank you.Sorry about that. I've double checked the other values in that table and they all check out. (Looks like I typed in 115/648 instead of 155/648 which yields an answer of 861/1091 instead of 861/1171.)
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Post by misomiso on Jul 26, 2022 13:34:34 GMT
scouserob No worries dude honestly ty for doing that math. Very helpful and very eye opening as well. In terms of game design it really makes it functionally impossible for a Hero to defeat somebody with 3 skill more than them. Even consistant enemies with a 1 point advantage would be hard. I defeated Deathtrap Dungeon once with an 11 skill hero but that was tough. This math should definately inform adventure design but I'm not sure quite how you would implement it. Maybe balance every adventure around a skill 10 stamina 20 hero? A bit above average stats but not by much.
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Post by scouserob on Jul 26, 2022 14:08:35 GMT
How about an experience point (XP) system? You gain XP when you defeat an opponent with skill greater than or equal to 1 less than yours. (Or complete a level N side quest when your skill is less than N, or something.)
If you get some amount of experience points then you add one to your initial skill and wipe out your XP.
Then lower skill adventurers would have to find paths to gain XP during the quest and buff themselves up.
Higher skilled adventurers won’t be able to get those XP benefits and will stay at their initial skill.
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CharlesX
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Post by CharlesX on Jul 26, 2022 16:34:23 GMT
How about an experience point (XP) system? You gain XP when you defeat an opponent with skill greater than or equal to 1 less than yours. (Or complete a level N side quest when your skill is less than N, or something.) If you get some amount of experience points then you add one to your initial skill and wipe out your XP. Then lower skill adventurers would have to find paths to gain XP during the quest and buff themselves up. Higher skilled adventurers won’t be able to get those XP benefits and will stay at their initial skill. I've sometimes had an idea in the back of my head an adventurer could complete an FF gamebook, possibly two or more, keeping the benefits before attempting a very hard FF (Crypt Of The Sorceror for being the one I've got in mind). I believe Fighting Fantasy Legends uses an XP-esque system, in their case I think Initial Stamina goes up as well as Initial Skill.
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Post by misomiso on Jul 28, 2022 15:15:28 GMT
@scourserob charles X I think these issues become very complex very quickly. It really depends on what you WANT from a gamebook, and what your design goals are. To my mind one of the big underrated strengths of the FF system was that is was so simple. If you start adding too much complexity you are going to turn a lot of people off. That doesn't mean the combat system couldn't be better - Luck needs a rework I think to be more impactful on combat, and I always like the idea of a separate 'Defence' stat that you needed to hit for each enemy, as that reduces rerolls and allows for a little nuance in monster design. But I guess everybody has different ideas. I think it would be better to maybe have 'achievements' or 'goals', so maybe there is achievement for defeating the book with certain set stat characters. But who knows.
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Post by johnbrawn1972 on Jul 28, 2022 15:20:04 GMT
How about an experience point (XP) system? You gain XP when you defeat an opponent with skill greater than or equal to 1 less than yours. (Or complete a level N side quest when your skill is less than N, or something.) If you get some amount of experience points then you add one to your initial skill and wipe out your XP. Then lower skill adventurers would have to find paths to gain XP during the quest and buff themselves up. Higher skilled adventurers won’t be able to get those XP benefits and will stay at their initial skill. I've sometimes had an idea in the back of my head an adventurer could complete an FF gamebook, possibly two or more, keeping the benefits before attempting a very hard FF (Crypt Of The Sorceror for being the one I've got in mind). I believe Fighting Fantasy Legends uses an XP-esque system, in their case I think Initial Stamina goes up as well as Initial Skill. I wonder how Raistlin or Fistandantilus would fare against Razaak.
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Post by scouserob on Oct 19, 2022 14:16:17 GMT
Can anybody explain this to me?
You: Skill 8 Stamina 14 Luck 7 Enemy: Skill 8 Stamina 8
Which of the two combat strategies would you guess is better?
1. Test your Luck if you win a round whilst your luck is 7 and the Enemy's Stamina is greater than 2. Also Test your Luck if you lose a round and your Stamina is 2.
2. Test your Luck if you lose a round and your Stamina is 2.Surely it must be the first strategy right? You have a greater than 50% chance of knocking two extra Stamina points off him for goodness' sake? You then reduce your chance of succeeding on a saving throw but surely you'll be less likely to need one...
Yet my matrix calculator outputs: 85.6% win rate with the first strategy. 86.2% win rate with the second strategy.
My first instinct was that the code was wrong but after picking through it there seemed to be no problem. So I effectively hand calculated a big probability tree in Excel for both strategies and the matrix output seems right!!!
But why is fighting that way better? Any ideas?
Rows below in each group are: Your Stamina, Enemy Stamina, Probability. The yellow cells are groupings from the boxes below.
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CharlesX
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Post by CharlesX on Oct 19, 2022 15:26:23 GMT
Two 6-sided dice gives wide probability differences. The odds of getting one in six is 16 2\3%, odds of one in twelve is 8 1\3%. Odds of winning with the same Skill but different Stamina seems again to give a wide probability matrix with such similar numbers. If there are seven rounds, your opponent has to win all seven while you have to win only four. Obviously, the second strategy beats doing nothing. My vague guesswork grasp is that counting eleven rounds, winning four the odds aren't at all terrible. Using the first strategy is therefore advisable to beat those odds - but why you may ask is it less advisable than the second strategy?
There are two pieces of the key why strategy two is more advisable than strategy one using the above information: Primary one - Work out those numbers, four in eleven, versus the odds of getting 6 or less on 2 dice, which is more favourable. Like betting on a winner in snakes-and-ladders with not 2 or 3 players but maybe 10 players. The fact the numbers\factors used vary enormously (the number of players, the size of the board) are very, very much key.
Also - No account is made of the possibility of getting a 6 with 2 dice, which might be unconsciously biased against because human beings tend to think odds of less than 50% means something almost certainly won't happen. Sometimes, they do.
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Post by scouserob on Oct 19, 2022 17:24:23 GMT
Thanks CharlesX, I think you just made a penny drop. 👍🏼
Thinking about it in terms of rounds won/lost from a maximum, like you say, gives:
For Strategy 2: P(Win at least 4 rounds from 11)*P(Lucky) + P(Win at least 4 rounds from 10)*P(Unlucky)
= (227/256)*(21/36)+(53/64)*(15/36)
= 86.230%
For Strategy 1: P(Win at least 3 rounds from 9)*P(Lucky)*P(Unlucky6) + P(Win at least 3 rounds from 10)*P(Lucky)*P(Lucky6) + P(Win at least 5 rounds from 11)*P(Unlucky)*P(Unlucky6) + P(Win at least 5 rounds from 12)*P(Unlucky)*P(Lucky6)
= (233/256)*(21/36)*(21/36)+(121/128)*(21/36)*(15/36)+(743/1024)*(15/36)*(21/36)+(1651/2048)*(15/36)*(15/36)
= 85.578%
It worked! At least approximately. Now that would have saved me a long time in Excel!
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CharlesX
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Post by CharlesX on Oct 19, 2022 18:07:40 GMT
Glad I helped scouserob - I did my normal dyspraxic BS of mixing up the words in my reply but I got it in the end!
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Post by a moderator on Oct 19, 2022 21:21:00 GMT
I'd expect the probabilities to vary slightly depending on whether the opponent's Stamina is an odd or even number. If it's even and you Test your Luck to try and increase damage but are Unlucky, you increase the number of rounds you have to win by 1, but if it's odd, being Unlucky makes no difference to how often you need to hit your opponent.
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Post by scouserob on Oct 19, 2022 21:53:42 GMT
I'd expect the probabilities to vary slightly depending on whether the opponent's Stamina is an odd or even number. If it's even and you Test your Luck to try and increase damage but are Unlucky, you increase the number of rounds you have to win by 1, but if it's odd, being Unlucky makes no difference to how often you need to hit your opponent. I've run the numbers and you are spot on. 😀👍🏼 (An intuitive result from good reasoning. Thank goodness. That makes a change when using Luck in battle.)
Yeah, the advantage of using luck when winning rounds against an enemy with an odd number of Stamina points is clear. In fact that strategy is never worse in that case.
So that strongly infers that the counterintuitive (at least to me) disadvantage of using a better than 50% chance of doubling damage is due to it sometimes being outweighed by the possibility of requiring an extra round for victory.
[Note that below Strategy 1 is extended so that you always use it after winning an attack round if your Luck is greater than 6.]
Here is the advantage in percentage of winning for Strategy 1 over Strategy 2 when the enemy has Skill equal to yours (8) and Stamina 8: (Note that if you have Luck 7 you shouldn't use Luck after a won attack round, err, except with Stamina 15. 😮 Probably something to do with both my strategies not incorporating saving throws when you lose rounds on odd stamina points.)
And here is the advantage of Strategy 1 over Strategy 2 when the enemy has Skill equal to yours (8) and Stamina 9: (As you say the advantage for using Luck after winning attack rounds is much more pronounced as there is no real penalty for failing at it, at least on the first occasion. 😎) Thanks, both of you, I am reassured that the results weren't just a coding error. 😀
PS: Here is the encounter which caused me such panic when seeing Strategy 2 was not always better. I'm looking forward to completing the book and fully exploring the options. (Attempt 3 ended ...
at a locked door without a key or picklock after fighting 9 Zombies.)
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Post by johnbrawn1972 on Oct 20, 2022 15:46:54 GMT
I'd expect the probabilities to vary slightly depending on whether the opponent's Stamina is an odd or even number. If it's even and you Test your Luck to try and increase damage but are Unlucky, you increase the number of rounds you have to win by 1, but if it's odd, being Unlucky makes no difference to how often you need to hit your opponent. To quote Jon Virgo it is a shot to nothing.
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Post by misomiso on Oct 20, 2022 20:07:13 GMT
Ah Jon Virgo...
...I remember the days of late Snooker getting 10 million viewers!
Peter Ebdon for the win! Mark Williams on a roll!
Those were the glory days...
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