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Post by pip on Oct 26, 2022 19:25:36 GMT
Shadow of the Giants - The Rune Sword Path
As usual always use Luck in Battle if you lose an Attack Round on 2 Stamina.
I did not take using Luck during fights into account for my stats, as that could get very complicated if you want to be thorough about all the possible options, but this rule makes perfect sense and I see that it also improves the odds for my own solution (especially for low skill characters). I'll be comparing my stats to yours for this other solution as well.
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Post by pip on Oct 26, 2022 19:54:43 GMT
Comparing the two solutions, I see that our stats don't agree, but either way the Rune Sword option improves the odds for low skill characters. If, however, you have a high skill but low stamina character, the odds are slightly worse (with a stamina 14 character, the stats start getting worse if your skill is >= 9). Overall, the Rune Sword option seems safer unless you rolled that aforementioned high skill / low stamina hero. If you have high skill / high stamina, the odds are basically the same for both solutions. skill 7 stamina 14 luck 7
survival rate: 23%
skill 8 stamina 14 luck 7
survival rate: 48,4%
skill 9 stamina 14 luck 7
survival rate: 71,1%
skill 10 stamina 14 luck 7
survival rate: 83,9%
skill 11 stamina 14 luck 7
survival rate: 90,7%
skill 12 stamina 14 luck 7
survival rate: 93,5%
--------------------
skill 7 stamina 14 luck 8
survival rate: 24,6%
skill 8 stamina 14 luck 8
survival rate: 50,7%
skill 9 stamina 14 luck 8
survival rate: 73,2%
skill 10 stamina 14 luck 8
survival rate: 85,9%
skill 11 stamina 14 luck 8
survival rate: 92,8%
skill 12 stamina 14 luck 8
survival rate: 95,7%
--------------------
skill 7 stamina 14 luck 9
survival rate: 26,1%
skill 8 stamina 14 luck 9
survival rate: 52,4%
skill 9 stamina 14 luck 9
survival rate: 75,1%
skill 10 stamina 14 luck 9
survival rate: 87,5%
skill 11 stamina 14 luck 9
survival rate: 94,4%
skill 12 stamina 14 luck 9
survival rate: 97,4%
--------------------
skill 7 stamina 14 luck 10
survival rate: 27,1%
skill 8 stamina 14 luck 10
survival rate: 54%
skill 9 stamina 14 luck 10
survival rate: 76,4%
skill 10 stamina 14 luck 10
survival rate: 88,7%
skill 11 stamina 14 luck 10
survival rate: 95,5%
skill 12 stamina 14 luck 10
survival rate: 98,7%
--------------------
skill 7 stamina 14 luck 11
survival rate: 27,8%
skill 8 stamina 14 luck 11
survival rate: 54,9%
skill 9 stamina 14 luck 11
survival rate: 77,4%
skill 10 stamina 14 luck 11
survival rate: 89,5%
skill 11 stamina 14 luck 11
survival rate: 96,4%
skill 12 stamina 14 luck 11
survival rate: 99,6%
--------------------
skill 7 stamina 14 luck 12
survival rate: 28,2%
skill 8 stamina 14 luck 12
survival rate: 55,4%
skill 9 stamina 14 luck 12
survival rate: 77,9%
skill 10 stamina 14 luck 12
survival rate: 90%
skill 11 stamina 14 luck 12
survival rate: 96,8%
skill 12 stamina 14 luck 12
survival rate: 100%
--------------------
skill 7 stamina 24 luck 7
survival rate: 46,7%
skill 8 stamina 24 luck 7
survival rate: 66,5%
skill 9 stamina 24 luck 7
survival rate: 82,2%
skill 10 stamina 24 luck 7
survival rate: 91%
skill 11 stamina 24 luck 7
survival rate: 97%
skill 12 stamina 24 luck 7
survival rate: 100%
--------------------
skill 7 stamina 24 luck 8
survival rate: 46,6%
skill 8 stamina 24 luck 8
survival rate: 66,6%
skill 9 stamina 24 luck 8
survival rate: 82,2%
skill 10 stamina 24 luck 8
survival rate: 91,1%
skill 11 stamina 24 luck 8
survival rate: 97%
skill 12 stamina 24 luck 8
survival rate: 100%
--------------------
skill 7 stamina 24 luck 9
survival rate: 46,8%
skill 8 stamina 24 luck 9
survival rate: 66,6%
skill 9 stamina 24 luck 9
survival rate: 82,2%
skill 10 stamina 24 luck 9
survival rate: 91%
skill 11 stamina 24 luck 9
survival rate: 97%
skill 12 stamina 24 luck 9
survival rate: 100%
--------------------
skill 7 stamina 24 luck 10
survival rate: 46,9%
skill 8 stamina 24 luck 10
survival rate: 66,7%
skill 9 stamina 24 luck 10
survival rate: 82,2%
skill 10 stamina 24 luck 10
survival rate: 91%
skill 11 stamina 24 luck 10
survival rate: 97%
skill 12 stamina 24 luck 10
survival rate: 100%
--------------------
skill 7 stamina 24 luck 11
survival rate: 46,9%
skill 8 stamina 24 luck 11
survival rate: 66,6%
skill 9 stamina 24 luck 11
survival rate: 82,2%
skill 10 stamina 24 luck 11
survival rate: 91,1%
skill 11 stamina 24 luck 11
survival rate: 97%
skill 12 stamina 24 luck 11
survival rate: 100%
--------------------
skill 7 stamina 24 luck 12
survival rate: 46,9%
skill 8 stamina 24 luck 12
survival rate: 66,8%
skill 9 stamina 24 luck 12
survival rate: 82,2%
skill 10 stamina 24 luck 12
survival rate: 91%
skill 11 stamina 24 luck 12
survival rate: 97%
skill 12 stamina 24 luck 12
survival rate: 100%
--------------------
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Post by scouserob on Oct 26, 2022 23:19:33 GMT
If, however, you have a high skill but low stamina character, the odds are slightly worse (with a stamina 14 character, the stats start getting worse if your skill is >= 9). Overall, the Rune Sword option seems safer unless you rolled that aforementioned high skill / low stamina hero. If you have high skill / high stamina, the odds are basically the same for both solutions. Yeah for high stamina, luck and skill the probabilities are pretty much the probabilities of surviving the final battle. (Which is why the Serpent Sword strategies are dominated by the Dragon/Rune Swords in these cases.) I always get the Rune Sword better though. I’ll try and replicate your probabilities without using aggressive luck in battle when I get back to my laptop next week. I’ve probably made an error in the code somewhere but if we could track that down, perhaps over PMs then it would be helpful.
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Post by johnbrawn1972 on Oct 27, 2022 17:11:12 GMT
Done some manual number crunching to investigate why the Rune Sword path may be the best choice.
The Spider Hag is effectively Skill 6 Stamina 6 (with the Helmet’s Attack Strength bonus) and even a Skill 7 Adventurer, who will be at Initial Stamina for the fight, will have little problem emerging victorious, 1 Stamina Rune Sword penalty or not.
The Gorgon is only two Attack Rounds so even a Skill 7 Adventurer can only lose 4 Stamina. (5 Stamina with the Rune Sword.)
The only things we have to worry about are the Wraith and Cobrax.
The Wraith fight seems to be most difficult fight on the Vampire Sword/Dragon Sword path at least in terms of expected Stamina loss for low Initial Skill adventurers.
(Ignoring Using Luck.)
Skill 7 Adventurer
Wraith Fight (Vampire Sword Dragon Sword Path) Adventurer (+2 Attack Strength): Expected Stamina Loss Per Round ≈ 2*0.5563 ≈ 1.113 Wraith Skill 10: Expected Stamina Loss Per Round ≈ 2*0.3356≈ 0.671
Cobrax Fight (Both Paths) Adventurer (+1 Attack Strength): Expected Stamina Loss Per Round ≈ 2*0.6644 ≈ 1.328 Cobrax Skill 10: Expected Stamina Loss Per Round ≈ 1*0.6644 + 1*0.0965 + 3*0.2392 ≈ 1.478
Expected Stamina loss to fully deplete the Wraith's 8 Stamina ≈ 13.260 Expected Stamina loss to fully deplete Cobrax's 10 Stamina ≈ 8.987 Expected Stamina loss to fully deplete Cobrax's 10 Stamina with Rune Sword Penalty ≈ 9.987
Skill 8 Adventurer
Wraith Fight (Vampire Sword Dragon Sword Path) Don't even have to work it out. You have the same effective Skill so you expect to lose the same amount.
Cobrax Fight (Both Paths) Adventurer (+1 Attack Strength): Expected Stamina Loss Per Round ≈ 2*0.5563 ≈ 1.113 Cobrax Skill 10: Expected Stamina Loss Per Round ≈ 1*0.5563+ 1*0.1080+ 3*0.3356 ≈ 1.671
Expected Stamina loss to deplete the Wraith's 8 Stamina ≈ 8 Expected Stamina loss to fully deplete Cobrax's 10 Stamina ≈ 6.656 Expected Stamina loss to fully deplete Cobrax's 10 Stamina with Rune Sword Penalty ≈ 7.657
Skill 9 Adventurer
Wraith Fight (Vampire Sword Dragon Sword Path) Adventurer (+2 Attack Strength): Expected Stamina Loss Per Round ≈ 2*0.3356 ≈ 0.671 Wraith Skill 10: Expected Stamina Loss Per Round ≈ 2*0.5563 ≈ 1.113
Cobrax Fight (Both Paths) Adventurer (+1 Attack Strength): Expected Stamina Loss Per Round ≈ 2*0.4437 ≈ 0.887 Cobrax Skill 10: Expected Stamina Loss Per Round ≈ 1*0.4437+ 1*0.1127 + 3*0.4437 ≈ 1.887
Expected Stamina loss to deplete the Wraith's 8 Stamina ≈ 4.827 Expected Stamina loss to fully deplete Cobrax's 10 Stamina ≈ 4.702 Expected Stamina loss to fully deplete Cobrax's 10 Stamina with Rune Sword Penalty ≈ 5.702
And I've just realised that I didn't reduce the Spider Hag’s effective skill for the Rune Sword above when I reduced it for the Dragon Sword path... Recalculation time! 🤦🏻♂️ Can I be my autistic self and ask about the 7 skill calculations for fighting the Cobrax? Are you sure your mathematics is correct? Many moons ago Sylas rather grumpily yet rightly said a -2 skill disadvantage is usually lethal never mind a possible -3 skill disadvantage. The wonderful matrix(not Neo) that I found so helpful, from memory, showed a -12 stamina loss when you are at -1 skill disadvantage. This drove my reasoning of a reasonable chance of 7/14/7 boosted to 7(+2) skill to overcome the Cobrax. After that I was willing to accept slightly reduced chances but at least you still had good chances. Hence my use of the lucky button. Prima facie, and I do not have mathematics only intuition, it seems like your chances for 7/14/7 in your solution would be relatively low a bit like Poomchukker being around 15%. Straight off the bat you are starting at 13 stamina. You do have the significant boost of a -1 damage per round advantage. You can only take 7 hits at most. So is the mathematics correct?
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Post by scouserob on Oct 28, 2022 0:56:06 GMT
Hi JohnBrawn
For a Skill 7(+1 Attack Strength) opponent against Cobrax’s Skill 10 the odds for each round are: Loss: 66.4% (287/432) [You lose 2 it loses 1] Draw: 9.6% (125/1296) [It loses 1] Win: 23.9% (155/648) [It loses 3]
Your average stamina loss per round is 2*66.4% about 1.328. Cobrax’s average loss per round is 66.4%+9.6%+3*23.9% about 1.478.
So Cobrax loses more Stamina per round on average, despite being more than twice as likely to win the round, and you are a decent favourite to win the fight even without using luck for saving throws and to do 5 damage.
Without the arrows his expected Stamina loss per round is only about 0.478 so you’d expect to lose 28.8 Stamina in the fight, with the Rune Sword penalty, rather than just 10.0. (As Sylas said you’d be doomed by the 2 Skill deficit.)
Those arrows of Goose’s make a huge difference.
That much I’m pretty certain on and is hand calculated maths separate from my code.
For the rest it is possible I made an error in the code. It looks like I have the odds on surviving the finale by itself at about 58.4% with 7 skill and the Rune Sword, which means we’d need about a 70% chance of beating the Spider Hag, Cobrax and the Gorgon to make it that a 40% chance overall.
The Spider Hag is easy peasy 🍋 squeezy. The Gorgon knocks a maximum of 1 provision’s worth of Stamina off you so I can’t see there being any significant chance of dying there. That leaves Cobrax who I guess I could see you having a 70%+ chance of killing at Skill 7 Stamina 14. (Maybe?)
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Post by scouserob on Oct 28, 2022 1:17:18 GMT
Skill 7 Adventurer Finale Probability with Rune/Dragon Sword:
2D6 + 6 < 10 = 2D6 < 4 = 3/36 = 1/12 2D6 > Skill = 2D6 > 7 = 15/36 = 5/12 Pass 1st Giant = 1 - (1/12)(5/12) = 139/144
2D6 - 3 > Skill = 2D6 > 10 = 3/36 = 1/12 Pass 2nd Giant = 1 - 1/12 = 11/12
Pass 3rd Giant = 11/12 (Same as 2nd)
2D6 + Skill + 3 < 16 = 2D6 < 6 = 10/36 = 5/18 Pass Entangled Giant = 1 - 5/18 = 13/18
Pass finale = (139/144)(11/12)(11/12)(13/18) About 58.6%
So that tallies with a high Skill 7 having about a 99.7% chance of getting to the finale with the Rune Sword.
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Post by johnbrawn1972 on Oct 28, 2022 11:53:44 GMT
Wow it feels like I am talking to Champskees all over again.
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Post by scouserob on Oct 28, 2022 11:59:54 GMT
Wow it feels like I am talking to Champskees all over again. 😂 I’m honoured to be compared to the legend. (I think.) To be honest I’m trying to convince myself as much as you. 😜 I love finding unintuitive results in the maths of Fighting Fantasy. I wouldn’t have guessed that with Skill 7 (+1 Attack Strength), when not using Luck in battle, Goose’s arrows save you an expected 18 Stamina points (!) in the fight against Cobrax. 😮 (And I only just discovered that beauty by hand cranking the probabilities last night.) I can’t access my code until next week to have a deep dive into it again. (I promise to hold my hands up if I’ve messed it up. 🙌🏻)
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Post by scouserob on Oct 30, 2022 20:45:11 GMT
All the below is for Skill 7, Stamina 14, Luck 7.
I've run the code just for the Rune Sword fight with Cobrax. Skill 7 (+1 Attack Strength), Stamina 13, Luck 7: About 78.95% chance of survival. (It is possible to have Skill 6 at this point due to the Zombie disposal plan being a tad over elaborate.)
Running the full code but stopping at various way points with all probabilities included, as well as those of losing Skill, are:
A 95.2433% probability of reaching Cobrax. (I calculated 98.263% for a Skill 7 adventurer of beating the Spider Hag but you can have Skill 6 from those runaway barrels, which lowers that a tad.)
A 71.3662% chance of surviving past Cobrax.
It seems there is 0% chance of dying in battle with the Gorgon as you will always have enough Provisions to boost yourself above 4 Stamina before Cobrax and if you get hit in that battle then you will get an extra 6 Stamina from the Potion of Health.
A 71.3391% chance of reaching the finale.
Unfortunately by this point it is possible for your provisions to have run out and there is only about : A 70.8776% chance to have enough Stamina to survive the four Rune Sword penalties for the Iron Giants at the end.
70.8776% * 58.6% = 41.5%, which tallies with the table in the Rune Sword solution, above. (58.6% is the hand calculated probability of surviving the finale in the post above.)
I think the only thing that would make a big difference to this final percentage is if the code giving the chance of surviving the Cobrax fight of 78.95% from scratch is wrong. I may hand calculate this in Excel with a branching probability tree to make sure and hopefully convince everyone, including myself, that the probabilities are reasonable. 🤞🏼
There can only be a maximum of 10 rounds but I'll have to have to include drawn rounds and my Luck strategy as outlined in the solution above. It may get slightly unwieldy...
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Post by scouserob on Nov 1, 2022 12:04:02 GMT
I've hand calculated the probability of winning the Cobrax fight with a Skill 7 Stamina 14 Luck 7 adventurer with both the Helmet (+1 Attack Strength) and the Rune Sword (1 Stamina Point Penalty).
It matches the output of my code to 6 decimal places: 0.789492, or 78.9492%
Below is the hand calculation, which is basically a large probability tree going from the bottom up.
Each set of three rows consist of: Your Stamina (First of Stamina Pair) Cobrax's Stamina (Second of Stamina Pair) Probability (Starting from the bottom with Your Stamina 13, Cobrax's Stamina 10, probability of being in that state 100%.)
For each new round I split the Stamina pairs from the previous round into three for Win Round, Draw Round, Lose Round and calculate the probabilities accordingly.
Then I combine repeated Stamina pairs for the round, highlighted in yellow, add every pair where you have more than twice Cobrax's Stamina into the WON bucket and everything where you have 0 Stamina into the LOST bucket.
Hopefully this convinces those who were sceptical about there being such a high probability of beating Cobrax with a Skill deficit of 2. (I am now fully convinced, at least.)
Good old Goose. 🏹
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Post by johnbrawn1972 on Nov 2, 2022 13:13:46 GMT
I have had a think and basically Goose wins an attack round every round and then loses a luck roll which is one heck of a force multiplier.
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Post by pip on Nov 28, 2022 15:16:35 GMT
I finally got around to updating my solution, so that it directs you to the Dragon Sword or the Rune Sword, based on what is best for you. With a Stamina < 18 and a Skill > 8, the Dragon Sword is better; otherwise, the Rune Sword is either better, or produces the same winning odds if you have both high Stamina and high Skill.
I did not take your Luck calculation for the Cobrax fight into account, as I've tried it and saw that it can be improved (in some situations, it improves the winning odds, but in others, it decreases them). Either way the difference is minor anyway, only a couple of %.
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Post by scouserob on Nov 28, 2022 16:01:08 GMT
I finally got around to updating my solution, so that it directs you to the Dragon Sword or the Rune Sword, based on what is best for you. With a Stamina < 18 and a Skill > 8, the Dragon Sword is better. I did not take your Luck calculation for the Cobrax fight into account, as I've tried it and saw that it can be improved. Hi Pip Yeah, the aggressive Luck Strategy I had against Cobrax is a mess and wasn't really worth it except for High Luck/Stamina 14. (The best is an increase of 5.1% for SK7 ST14 L12.) Could you list a stat set that is clearly better for the Dragon Sword along with the percentages you get for both strategies? I don't get an any advantage over the entire range of starting stats for the Dragon Sword that is greater than 0.05% and would like to try and replicate your results.
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Post by pip on Nov 28, 2022 18:37:32 GMT
Here is a sample using the Rune Sword, to be compared to my updated stats which use the Dragon Sword in these configurations. The differences are not huge, but they are consistent (the program ran 10 million times for each configuration). skill 9 stamina 14 luck 7
survival rate: 73,1%
skill 10 stamina 14 luck 7
survival rate: 84,9%
skill 11 stamina 14 luck 7
survival rate: 91,1%
skill 12 stamina 14 luck 7
survival rate: 93,6%
--------------------
skill 9 stamina 14 luck 8
survival rate: 74,9%
skill 10 stamina 14 luck 8
survival rate: 86,6%
skill 11 stamina 14 luck 8
survival rate: 93%
skill 12 stamina 14 luck 8
survival rate: 95,7%
--------------------
skill 9 stamina 14 luck 9
survival rate: 76,4%
skill 10 stamina 14 luck 9
survival rate: 88%
skill 11 stamina 14 luck 9
survival rate: 94,5%
skill 12 stamina 14 luck 9
survival rate: 97,4%
--------------------
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Post by scouserob on Nov 29, 2022 12:06:39 GMT
Hi Pip
For Skill 9 Stamina 14 Luck 7 you get 73.1% and I get 88.3%.
I've been doing some hand calculations for the Skill 9 Stamina 14 Luck 7 Rune Sword strategy to try to replicate the 88.3% output of my code.
I think you can only die at the Spider Hag, Cobrax or the Iron Giants. (The Gorgon can't kill you as you will always have more than 4 Stamina if you reach her.)
Probability of failing to jump over the barrels and dropping to Skill 8: 1/6 Probability of surviving Spider Hag with Skill 8 Stamina 13 ≈ 99.8060% Probability of surviving Spider Hag with Skill 9 Stamina 13 ≈ 99.9881% Total probability of surviving Spider Hag ≈ [(1/6) * 99.8060%] + [(5/6) * 99.9881%] ≈ 99.9578%
Probability of dropping to Skill 8 by messing up the Zombie lemming plan ≈ 7.2% Probability of surviving Cobrax with Skill 8 Stamina 13 ≈ 92.5147% Probability of surviving Cobrax with Skill 9 Stamina 13 ≈ 98.1828% Total probability of surviving Cobrax ≈ [7.2% * 92.5147%] + [92.8% * 98.1828%] ≈ 97.7747%
Probability of dying whilst chasing Giants due to a combination of using all your Provisions and Stamina depletion is negligible.
You would pretty much need to do all, or almost all, of the following: Fail Barrel Jump Skill Test Lose a lot of Stamina against the Spider Hag Fail Luck Test on the Throne Fail Skill Test with the Bats Fail Luck Test and roll high at the Dart Trap Fail both the Luck and the Skill Test at the Zombies Lose a lot of Stamina against Cobrax Lose both rounds against the Gorgon Fail Skill Test when chasing Giants Probability of surviving first Iron Giant = 1 - [(3/36) * (1/6)] = 71/72 Probability of surviving 2nd and 3rd Iron Giants = 100% Probability of surviving entangled Iron Giant = 33/36 Total probability of surviving Iron Giants = (71/72) * (33/36) = 781/864
Probability of winning Shadow of the Giants ≈ 99.9578% * 97.7747% * 781/864 ≈ 88.3%
For which of the three does your probability differ? (Spider Hag/Cobrax/Iron Giants) Or have I messed up somewhere else and missed out a chance to die?
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Post by pip on Nov 29, 2022 14:11:30 GMT
I've only tried the Hag fight and I get a 99.5% chance to win that with this configuration, so I think there must be something wrong in your fight calculations (unless it's me, but it's such a simple piece of code that I doubt it). Also, did you take other stamina losses into account, such as the possible non trivial -2D6 stamina loss?
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Post by scouserob on Nov 29, 2022 14:55:57 GMT
I've only tried the Hag fight and I get a 99.5% chance to win that with this configuration, so I think there must be something wrong in your fight calculations (unless it's me, but it's such a simple piece of code that I doubt it). Also, did you take other stamina losses into account, such as the possible non trivial -2D6 stamina loss? I'll hand calculate the Hag fight to try to find my error. Before the possible Dart Trap's 2 x 1D6 Stamina loss you can be on the full 14 Stamina with a minimum of 4 Provisions remaining to buff you back up for Cobrax. Worst Case, everything goes wrong, Stamina Loss up to the start of the Iron Giant Chase: 14 Stamina (Start) 12 Stamina (If fail Skill Test for Giant Stomp - Unimportant) 14 Stamina (Inn) 13 Stamina (If fail Barrel Skill Test) 14 Stamina (Eat - 9 Provisions Remaining) 1 Stamina (Bad fight against the Spider Hag) 5 Stamina (Eat - 8 Provisions Remaining) 3 Stamina (Thirst) 1 Stamina (If fail Bats Skill Test) 13 Stamina (Eat x3 - 5 Provisions Remaining) 1 Stamina (If fail Dart Trap Luck Test and Roll a 6) 5 (Eat - 4 Provisions Remaining) 3 (If fail both Luck and Skill Test at Zombies) 14 (Eat x3 - 1 Provision Remaining) 1 (Bad Fight Against Cobrax) 7 (Healing Potion) 2 (Lose both rounds against the Gorgon) 4 (Eat with Goose) 8 (Eat Last Provision)
(Hopefully haven't missed any Stamina losses.) After eating with Goose you will be on a minimum of 8 Stamina. You will lose between 4 and 14 Stamina after this point and so will only need 2 more provisions to avoid death by Stamina loss. The chance of not having 2 Provisions left at this point is miniscule.
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Post by scouserob on Nov 29, 2022 15:22:56 GMT
I've only tried the Hag fight and I get a 99.5% chance to win that with this configuration I've gone to the raw mathematics for the Spider Hag fight due to it being a binomial distribution of whether you are the next winner or loser of a round.
It agrees with my results above, assuming that I've got the initial probabilities and the formula correct.
Spider Hag Fight: Skill 9: +3 Base Attack Strength Advantage (+2 Skill and +1 Helmet). Probability of being the next winner of a round = 493/596 Skill 8: +2 Base Attack Strength Advantage (+1 Skill and +1 Helmet). Probability of being the next winner of a round = 861/1171 [Edited to convey the advantage including the +1 Attack Strength Helmet]
Skill 9 (+1 Attack Strength) Stamina 13 v Skill 7 Stamina 6 Maximum 9 Attack Rounds. You need to win 3 of them. Probability of winning ≈ 99.9881% (See Wolfram Alpha output below)
Skill 8 (+1 Attack Strength) Stamina 13 v Skill 7 Stamina 6 Maximum 9 Attack Rounds. You need to win 3. Probability of winning ≈ 99.8060% (See Wolfram Alpha output below)
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Post by pip on Nov 29, 2022 15:55:02 GMT
I've only tried the Hag fight and I get a 99.5% chance to win that with this configuration I've gone to the raw mathematics for the Spider Hag fight due to it being a binomial distribution of whether you are the next winner or loser of a round.
It agrees with my results above, assuming that I've got the initial probabilities and the formula correct.
Spider Hag Fight: Skill 9: +3 Skill Advantage. Probability of being the next winner of a round = 493/596 Skill 8: +2 Skill Advantage. Probability of being the next winner of a round = 861/1171
I can't comment on your calculations as I am not well versed in statistics (for those reading the thread who don't know, my method is not to calculate individual statistics but to have a program run, 10 million times, simulating a run through the book and giving me the % of survival). But shouldn't it be: Skill 9: + 2 Skill Advantage Skill 8: + 1 Skill Advantage ? Unless it's a typo.
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Post by scouserob on Nov 29, 2022 16:24:34 GMT
I can't comment on your calculations as I am not well versed in statistics (for those reading the thread who don't know, my method is not to calculate individual statistics but to have a program run, 10 million times, simulating a run through the book and giving me the % of survival). But shouldn't it be: Skill 9: + 2 Skill Advantage Skill 8: + 1 Skill Advantage ? Unless it's a typo. I meant to convey the combined Skill and Helmet Attack Strength advantage. 😬 The effective modifier to your 2D6 roll in battle, I guess. I'll edit the wording, for clarity, to:
Skill 9: +3 Base Attack Strength Advantage (+2 Skill and +1 Helmet). Skill 8: +2 Base Attack Strength Advantage (+1 Skill and +1 Helmet).
That is what generates the probabilities to be the next winner of a round.
I think you may have forgotten the +1 Attack Strength bonus from the Helmet. Without that you get: [(1/6)*98.2630%]+[(5/6)*(99.8060%)] ≈ 99.549% That matches your figure.
The Helmet's Attack Strength Bonus would make a big difference in the Cobrax fight.
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Post by pip on Nov 29, 2022 17:21:53 GMT
Oh, indeed, I forgot to add the helmet for this test (but not in my main solution). With the helmet, I also get 99.9%, so the discrepancy is elsewhere.
"Probability of dropping to Skill 8 by messing up the Zombie lemming plan ≈ 7.2%" >> how do you calculate this? Assuming you start this sequence with full Luck and full Stamina (I didn't check if you necessarily have full Luck when you get there, full Stamina is likely thanks to provisions), I get 97.2 for Cobrax.
Edit: Ok, I think I see where the discrepancy comes from. I made a check for the last giant's roll being <= 16, when it should be <16. I will correct and redo my stats.
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Post by scouserob on Nov 29, 2022 18:17:22 GMT
"Probability of dropping to Skill 8 by messing up the Zombie lemming plan ≈ 7.2%" >> how do you calculate this? For the Zombies: If you passed the barrel jump you should have the full 7 luck here. If you failed the barrel jump and passed the first luck test at the Throne you should have 7 Luck here. If you failed the barrel jump and failed the first luck test at the Throne you should have 6 Luck here. Probability of losing a Skill point at the Zombies would then be: The sum of the three possibilities above of: (Zombie Luck)*(Zombie Skill)*(Barrel Skill)*(Throne Luck) (15/36)*(1/6)*(5/6) +(15/36)*(1/6)*(1/6)*(21/36) +(21/36)*(1/6)*(1/6)*(15/36) Which is 185/2582 I rounded it up to 7.2% (I think)
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Post by pip on Nov 29, 2022 21:40:20 GMT
My solution and stats have been updated. I use provisions more aggressively in my new version (using them to restore stamina even if some of the 4 points restored might be wasted) and I see that it improves the odds. Playing this way, the Rune Sword option is indeed either as good or better than the Vampire Sword option, and never worse.
Our stats are much more similar now, even though there are still (very) small discrepancies. I go by the official rule that you may only eat one meal at a time, and I have two instances where I don't allow the character to eat more than one meal (between the bats and the darts, and between Cobrax and the Gorgon). Could that possibly be it?
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Post by scouserob on Nov 29, 2022 23:10:50 GMT
I was very naughty with my Provisions and gobbled them down willy-nilly so it probably is that. 😂
The Gorgon shouldn’t be able to kill you, Provision rationing or not, due to the Healing Potion buffing you up to 7 Stamina minimum after the Cobrax fight.
As for the Darts … I know without looking that I coded a potential Provision feast immediately before the Dart Trap to buff up to at least 13 Stamina so that there was no chance at all of dying there.
If it is possible for you to die via the Darts with your Provision rule interpretation then there will definitely be a small difference in probabilities for us. 😀
I think playing by a strict 1 Provision per paragraph rule you should be able to be on at least 12 Stamina before the Bats and then take a provision either after the balm in that paragraph or before the dart trap Luck Test in that paragraph, to be OK for the Darts. (That is my story and I’m sticking to it. 🫣)
Unfortunately the Provision rule of “one at a time” is rather ambiguous.
Can you take a Provision once per paragraph? Once per location? Only once at the start/end of a paragraph? Once any time you wish per paragraph either before or after Skill/Luck tests or Stamina losses, at your leisure? Even once prior/post commencing a fight in a paragraph?
I did have a little moan about that ambiguity in the main book thread. 😉
I should probably take my now redundant solution walkthrough down but if you, greenspine and other mods don’t mind then I’d like to keep it up.
I put a few hours of work into the wording and formatting of it and despite the vast majority of the solution being yours (and those who helped tweak it with the Throne branch, etc.), I think I may have been the first to propose the pure Rune Sword path (without swapping it for the Serpent Sword).
Barring tiny improvements from overly complex Luck/Provision strategy tweaking we all must be close to an optimal solution now.
At least until JohnBrawn intuits a completely unforeseen new path for an adventurer with a very particular set of Skills (and Staminas, and Lucks).
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sylas
Baron
"Don't just adventure for treasure; treasure the adventure!"
Posts: 1,678
Favourite Gamebook Series: Fighting Fantasy, Way of the Tiger
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Post by sylas on Nov 30, 2022 22:38:45 GMT
It's kinda fascinating seeing the solutions to this adventure becoming a sort of gamebook autopsy.
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Post by misomiso on Dec 9, 2022 16:37:24 GMT
Has anyone done a map for this adventure? A map of the Hamelin Streets and the Gorgon's tomb would be very interesting. ty
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Post by scouserob on Dec 9, 2022 18:35:29 GMT
Has anyone done a map for this adventure? A map of the Hamelin Streets and the Gorgon's tomb would be very interesting. ty I've done a kind of map, although it is a paragraph to paragraph map rather than a location to location map. 😬 Fighting Fantasy Solution Maps, Page 2.
You can kind of make out the Hamelin Streets and the Gorgon's Tomb if you squint in the right way. 😂
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Post by misomiso on Dec 9, 2022 22:38:17 GMT
It's very interesting the breakdown of the book by number of paragraphs. I don't mind Hamelin but others have found it quite long which tallies with your breakdown.
A slightly longer journey to Hamelin, a shorter Hamelin, and then maybe a slightly extended Final Fight would have been great I think.
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Post by scouserob on Mar 29, 2024 15:36:21 GMT
Taking my cue from CharlesX in the solution thread for The Warlock of Firetop Mountain: I get the percentage chance of winning Shadow of the Giants, pre-rolling for your Initial Skill, Stamina and Luck, to be: 86.3% [Edited to account for the non-uniform Initial Stamina Distribution]
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