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Dragon kill probabilities (first & second (w/LS) times)

Postby Thundercloud on Thu Mar 09, 2006 4:57 am

Here is a quick table of probabilities I put together for the first dragon kill. It assumes 2000 (75%) & 4000 (25%) for dragon attacks, 15k dragon HP, and no additional HP, STR, or DEF from gems (each additional 10 def points adds about a 1% chance). I ran 1m trials for each scenario.

PS. Edited 3/9/06 @ 10:44 PST... increased # of trials to 1m per scenario. Also, the relatively same probs at 4, 5, and 6T for the 100m weapon are most likely due to 4T being always enough to kill the dragon, if the dragon didn't hit back!

Code: Select all
                                     hott    hott    hott   fairy   fairy   fairy hot/fry hot/fry hot/fry
  equip        4T      5T      6T      4T      5T      6T      4T      5T      6T      4T      5T      6T
=========================================================================================================
  1/  1       0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.1     0.0     0.0     0.2
  1/  4       0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.2     0.0     0.1     0.5
  1/ 10       0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.1     0.6     0.0     0.2     1.2
  1/ 40       0.0     0.0     0.0     0.0     0.0     0.0     0.1     0.4     2.0     0.1     0.7     3.2
  1/100       0.0     0.1     0.3     0.0     0.2     0.7     1.5     4.3    11.3     2.3     6.2    14.9

  4/  1       0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.2     1.4     0.0     0.4     2.6
  4/  4       0.0     0.0     0.0     0.0     0.0     0.0     0.1     0.4     2.8     0.1     0.8     4.7
  4/ 10       0.0     0.0     0.0     0.0     0.0     0.0     0.1     0.9     5.1     0.3     1.6     7.9
  4/ 40       0.0     0.0     0.1     0.0     0.0     0.2     0.5     2.6    10.3     0.9     4.0    14.4
  4/100       0.1     0.4     1.7     0.2     0.9     3.3     5.0    12.7    28.2     7.1    16.6    33.9

 10/  1       0.0     0.0     0.0     0.0     0.0     0.0     0.5     3.7     7.3     0.9     6.0    12.1
 10/  4       0.0     0.0     0.0     0.0     0.1     0.1     1.0     6.1    12.4     1.7     9.2    18.5
 10/ 10       0.0     0.0     0.1     0.0     0.2     0.3     1.9     9.5    18.9     3.1    13.4    25.9
 10/ 40       0.0     0.3     0.5     0.1     0.7     1.3     4.4    16.1    29.5     6.5    21.2    37.0
 10/100       0.7     3.0     5.6     1.5     5.4     9.8    17.1    35.8    52.3    21.5    41.7    58.6

 40/  1       0.1     0.1     0.1     0.5     0.6     0.6    17.7    31.6    31.8    23.2    40.6    41.0
 40/  4       0.4     0.4     0.4     1.2     1.5     1.5    22.9    39.6    39.9    28.9    48.1    48.5
 40/ 10       0.9     1.2     1.2     2.2     3.4     3.4    29.0    47.3    47.8    35.5    55.2    55.8
 40/ 40       2.4     3.7     3.7     4.7     7.9     7.9    38.1    57.1    57.6    44.8    64.0    64.6
 40/100       9.9    15.9    16.1    15.1    23.5    23.7    57.7    73.2    73.7    63.2    77.7    78.3

100/  1       2.4     2.4     2.4     6.3     6.3     6.3    64.2    64.6    64.6    70.8    71.4    71.4
100/  4       4.6     4.6     4.6    10.5    10.5    10.5    69.2    69.8    69.8    75.1    75.7    75.7
100/ 10       8.1     8.1     8.1    15.8    15.9    15.9    73.9    74.4    74.4    78.9    79.6    79.6
100/ 40      14.9    15.0    15.0    24.3    24.4    24.4    79.1    79.7    79.7    83.2    83.9    83.9
100/100      32.4    32.6    32.6    41.4    41.7    41.8    86.9    87.3    87.3    89.6    89.9    89.9


I'm pretty confident about these numbers. Not sure how they'll help anyone, but it was fun to calculate. =)
Last edited by Thundercloud on Fri Mar 10, 2006 8:41 am, edited 3 times in total.
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Postby Soppis on Thu Mar 09, 2006 9:27 am

what about these:

40/10 and 5T
100/10 and 5T
100/100 and 5T

why it is harder to kill dragon with 6T, I don't get it
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Postby HotShot on Thu Mar 09, 2006 9:44 am

Soppis wrote:what about these:

40/10 and 5T
100/10 and 5T
100/100 and 5T

why it is harder to kill dragon with 6T, I don't get it


These numbers look right to me, although there are a few small irregularities probably because of the small sample size. It's not harder to kill the dragon with 6T than 5T, but because these are low probability outcomes, they may be undersampled.

Think of it this way: if you wanted to know the probability of winning the lottery, you can't simply buy 100 tickets and count how many times you won. If you bought several trillion tickets, however, you'd probably get a good estimate of the probability of winning.

If Thundercloud increases the number of simulations to 100,000 or more per weapon/armor pair, I think these numbers would come out cleaner. But that might take hours to calculate with this many weapon/armor pairs, and I think these numbers are within 1-2% of the actual probabilities anyways.

EDIT: Looking at it again, there does seem to be something strange going on with hott fairy 5Ts vs 6Ts. The numbers in the 5T column seem to be systematically higher. Maybe this is a mistake in copying numbers into the chart?
Last edited by HotShot on Thu Mar 09, 2006 11:07 am, edited 1 time in total.
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Postby Che Guevara on Thu Mar 09, 2006 10:56 am

i found this very cool :)!
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Postby Meatwad on Thu Mar 09, 2006 11:07 am

Definitely very cool... I'd be glad to donate compute time to run more iterations to get things more exact. :)!
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Postby Thundercloud on Thu Mar 09, 2006 1:55 pm

Soppis wrote:what about these:

40/10 and 5T
100/10 and 5T
100/100 and 5T

why it is harder to kill dragon with 6T, I don't get it


Check the table again. I reran it with 1m trials per scenario. As HotShot already mentioned, relationships between scenarios are not always stable with a low number of simulations.

This table took about 30 mins to calculate. Each 1m iterations takes about 10 seconds for me (probably would be alot faster if I compiled it instead of running it in the interpreter!).
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Postby Meatwad on Thu Mar 09, 2006 3:21 pm

Can you include Light Shield in the table? :mrgreen:
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Postby Thundercloud on Fri Mar 10, 2006 8:09 am

Meatwad wrote:Can you include Light Shield in the table? :mrgreen:


Here is the same table, w/ Light Shield activated. I used

Damage = ((Strength/2 + rand(Strength/2 - 1)) * PowerMoveMult - Defense) * 0.5

I'm not completely sure that's the right formula (can somone confirm?), but I also ran a version with

Damage = (Strength/2 + rand(Strength/2 - 1)) * PowerMoveMult * 0.5 - Defense

...and it yielded far higher numbers which just didn't seem right, so I think the version I'm posting here is correct.

Code: Select all
            w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS   w/ LS
                                     hott    hott    hott   fairy   fairy   fairy hot/fry hot/fry hot/fry
  equip        4T      5T      6T      4T      5T      6T      4T      5T      6T      4T      5T      6T
  1/  1       0.0     0.0     0.0     0.0     0.0     0.1     0.6     2.9    11.0     1.4     5.3    17.3
  1/  4       0.0     0.0     0.0     0.0     0.0     0.3     1.3     5.1    16.2     2.7     8.7    23.8
  1/ 10       0.0     0.0     0.2     0.0     0.1     0.7     2.7     8.7    22.7     4.8    13.7    31.5
  1/ 40       0.0     0.1     0.7     0.1     0.5     2.2     6.3    15.9    33.7    10.3    23.0    43.6
  1/100       0.6     2.0     5.7     1.6     4.4    10.8    23.7    39.6    58.9    32.0    49.3    68.1

  4/  1       0.0     0.0     0.3     0.0     0.2     1.4     3.7    13.1    35.7     6.5    19.8    45.9
  4/  4       0.0     0.1     0.8     0.1     0.5     2.9     6.2    18.5    43.3    10.2    26.6    53.5
  4/ 10       0.0     0.3     1.9     0.2     1.0     5.2    10.0    25.4    50.9    15.4    34.6    61.1
  4/ 40       0.2     1.0     4.6     0.7     2.7    10.0    17.8    36.6    61.5    25.3    46.4    70.9
  4/100       2.3     6.6    16.3     5.0    12.2    26.0    41.9    61.6    80.0    51.9    70.5    86.1

 10/  1       0.1     1.2     2.0     0.5     3.6     7.2    19.1    46.0    70.3    27.2    56.5    79.3
 10/  4       0.3     2.3     4.3     1.0     5.9    11.9    25.4    53.5    75.8    34.7    63.3    83.7
 10/ 10       0.7     4.1     8.1     2.0     9.1    17.8    33.2    60.7    80.7    42.9    70.0    87.5
 10/ 40       1.9     7.9    15.2     4.5    15.1    26.8    44.5    69.9    86.4    54.7    78.1    91.6
 10/100       9.2    21.7    33.8    16.1    32.9    47.7    68.0    85.1    94.1    76.4    90.1    96.6

 40/  1       8.1    14.3    14.3    16.0    28.2    28.4    73.6    90.7    91.3    81.2    94.6    95.1
 40/  4      11.5    20.3    20.4    20.7    34.8    35.1    78.3    92.7    93.3    85.0    95.9    96.4
 40/ 10      15.6    26.9    27.0    26.1    41.6    42.0    82.6    94.4    94.9    88.4    97.0    97.4
 40/ 40      22.6    35.8    36.1    34.6    50.8    51.3    87.6    96.3    96.7    92.1    98.1    98.4
 40/100      40.0    54.0    54.5    53.3    68.5    69.0    94.5    98.6    98.7    96.7    99.2    99.3

100/  1      39.7    39.9    39.9    55.4    55.8    55.8    98.1    98.4    98.4    99.0    99.2    99.2
100/  4      45.4    45.7    45.7    60.9    61.3    61.3    98.5    98.8    98.8    99.2    99.4    99.4
100/ 10      51.0    51.4    51.4    66.2    66.8    66.8    98.9    99.1    99.1    99.4    99.6    99.6
100/ 40      58.3    58.7    58.7    73.0    73.5    73.5    99.2    99.4    99.4    99.6    99.7    99.7
100/100      72.5    72.9    72.9    84.0    84.3    84.3    99.7    99.8    99.8    99.8    99.9    99.9
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Postby Sombra on Fri Mar 10, 2006 9:48 pm

this ain´t no fun!! :x

let´s just play with the skills we got during all these years playing the game!!


:)!
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Postby Hidden Imp on Fri Mar 10, 2006 10:17 pm

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You can't set the science aside
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Postby HotShot on Fri Mar 10, 2006 10:35 pm

Hidden Imp wrote:When you've got it down to a science,
You can't set the science aside


No, these charts really don't help that much. There's plenty of art left for dragon killing.

It does give evidence, however, for my belief that 40/40 on the first kill is a waste. Even 100/1 is better.
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Postby Hidden Imp on Fri Mar 10, 2006 10:46 pm

It's not about art, it's about setting yourself up to have the best run possible and when the luck hits you you need to have given it room to take off.

It's well known that 100/1, some Ts and a fairy is better than 40/40, some Ts and a fairy.
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Postby HotShot on Fri Mar 10, 2006 11:22 pm

Hidden Imp wrote:when the luck hits you you need to have given it room to take off.


Relying on luck is exactly what it's not about.
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Postby Zydar the Unpleasant on Fri Mar 10, 2006 11:28 pm

Heh, I personally don't care much about these numbers, but good work to you guys for figuring it out. I'll take whatever the game gives me; luck, forest events, power moves, etc. Studying the game takes away the reason why I play it; for enjoyment, nostalgic purposes. But I guess for you bigshots out there who want the "edge", good luck. :biggergrin:
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Postby the mystical one on Sat Mar 11, 2006 7:13 am

HotShot wrote:
Hidden Imp wrote:when the luck hits you you need to have given it room to take off.


Relying on luck is exactly what it's not about.


You don't rely on the luck. He's not saying that. What he's saying is that when the luck happens (ie: you catch that fairy), that you need to know something about which acgtions are most effective with that luck. Before that luck hits, you need to know how to be patient correctly.
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Postby Sombra on Wed Mar 29, 2006 12:07 am

do you have anything for gambling? :?
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Postby HotShot on Wed Mar 29, 2006 12:49 am

HAHAHA :lol: :lol: :lol:

Even if I had a good gambling strategy, I wouldn't publish it :rasp:
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Postby Amadeus on Fri Mar 31, 2006 2:06 pm

Sometimes I am so sorry that people prefer to play as calculators than warriors.
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Postby Thundercloud on Sat Apr 01, 2006 3:31 pm

Amadeus wrote:Sometimes I am so sorry that people prefer to play as calculators than warriors.


The best warriors are also great calculators. =P. Generals don't ride a horse blindly into battle, they look at maps & troop formations & make decisions based on relative value. So it's good to know what your options are worth.

The point of these stats is really to determine when is the best time to spend money on weapons & armour to kill the dragon, given the circumstances of the day (fairy and/or hott). Based on these tables, if you don't have a fairy that day, spending money on 40/40 if you have enough for it would be foolish, it would be better to wait 1-2 more days & get enough money from bank interest & extra FF's to get the 100 weapon (which gives significantly higher odds of killing the dragon).
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Postby Che Guevara on Mon Apr 03, 2006 3:00 pm

FYI.

Playing at Time Warp, 150 FF, etc... well...

I´m with 10M-10M, 1500 STrentgh, and 1000 defense...
used TWO light shields...

and two sequences of flaming breath take my head off... wtf?!!?!?!
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