Mutation Roulette Math

[MainiacJoe]

Several days ago I asked on CYC how to do a Monte Carlo simulation of the potion of mutation in fsim, and was directed towards calculating probabilities directly instead. Once I realized that not all "bad" mutations are actually bad, and that which are "bad" and which are "horrible" varies from character to character and player to player, the task became a lot more straightforward.

TLDR: These are the chances of at least one horrible mutation occurring when the potion is quaffed by a mundane character with no racial mutation restrictions. h = 100% means you want to avoid all "bad" mutations, h = 10% means that you are willing to live with nine out of ten "bad" mutations.

  Code:

  h   Occurs       h   Occurs
100%   60.8%      50%   34.9%
 90%   56.3%      40%   28.7%
 80%   51.4%      30%   22.1%
 70%   46.3%      20%   15.2%
 60%   40.8%      10%    7.8%

This suggests to me that Mutation Roulette is optimal once you have a few potions on hand given these two conditions:

1. You are willing to accept "bad" mutations that are not horrible
2. You will stop quaffing when you have no horrible mutations even if you didn't get an awesome one.

Full calculation below.

Spoiler: show

Potions of mutation, quaffed by a mundane character with no racial mutation restrictions, give one good mutation and 1-3 random mutations which are weighted 3/5 good and 2/5 bad. Assuming that each quantity of random mutation is equally likely, these are the probabilities of the eight possible outcomes.

Algebra1.png (21.1 KiB) Viewed 3247 times

But not all “bad” mutations are equally bad, nor are all “good” mutations equally good. For instance, a berserker is unaffected by Subdued Magic, and a blaster is unlikely to mind Deformed. Let h therefore be the percentage of bad mutations that are “horrible”. This value will vary from player to player and character to character, so from here on I’ll give algebraic results. A similar a for “awesome” exists for good mutations, but in this post (by analogy with Russian Roulette) I’ll restrict analysis of mutation roulette to the goal of avoiding horrible mutations. Following is the calculation of the probability that no horrible mutation will occur.

Algebra2.png (14.51 KiB) Viewed 3247 times

The overall chance that no horrible mutation will occur is the sum of the rightmost column.

Algebra3.png (7.95 KiB) Viewed 3247 times

Thus the probability that at least one horrible mutation will occur is

Algebra4.png (1.56 KiB) Viewed 3247 times

[advil]

One thing is that this will definitely be affected by mutation interactions, and I'm not sure how much (though my intuition based on running lots of trials says substantially). The lua interface already accounts for those, but it sounds like you didn't go that route? There's also some interactions with physiology, but those should be more minor.

I suspect your overall conclusions is still right even if this were taken into account, though.

[MainiacJoe]

One thing is that this will definitely be affected by mutation interactions, and I'm not sure how much (though my intuition based on running lots of trials says substantially). The lua interface already accounts for those, but it sounds like you didn't go that route? There's also some interactions with physiology, but those should be more minor.

I suspect your overall conclusions is still right even if this were taken into account, though.

Correct, I didn't go that route because I've never coded any lua at all.

[4Hooves2Appendages]

I wonder where the best threshold is. My feeling is that around 3+ !Mut it's fine to eat every mutagenic chunk one comes across. Alternatively (or in combination), quaff all !Mut except the last 3.

[MainiacJoe]

I did not think of using mutagenic chunks once one has insurance potions on hand!

[Sprucery]

Enjoy it while you can. I am pretty sure that the next version will see revised potions of mutation / mutagenic chunks. Hopefully mutagenic chunks will be removed.

[MainiacJoe]

We are so overdue for a Trunk Update on the blog. I jusr scanned the shortlog at git/commit and didn't find anything abut !Mut.

[VeryAngryFelid]

We are so overdue for a Trunk Update on the blog. I jusr scanned the shortlog at git/commit and didn't find anything abut !Mut.

I tried to google what you are talking about and found another blog about dcss instead.
http://colinmorris.github.io/blog/dcss_newbie_traps
It even talks about mutation roulette too

[raikaria]

Reading the changes to the mechanics of mutation pots; and to non-hostile mutation sources, made me try out a little Mutation roulette once again. The logic being if it's earlygame it's not bad to lose a character if something horrible happens.

Mutation Pots are guaranteed to give you at least 1 good mutation now; after all other rolls. And each roll is 60% good; 40% 'bad'.

So far I've had pretty good experiences with mutations in the current build. For example; I came across an early sky beast in this game; got 4 chunks; and decided I'd have a go at it:

  Code:

 
You eat one of the 4 mutagenic chunks of flesh.
This meat tastes really weird.
Molten scales grow over part of your body.
You eat one of the 3 mutagenic chunks of flesh.
This meat tastes really weird.
You feel resistant to hostile enchantments.
You eat one of the 2 mutagenic chunks of flesh.
This meat tastes really weird.
You feel resistant to cold.
You eat the mutagenic chunk of flesh. This meat tastes really weird.
You feel genetically stable.


+2 AC with potential for it to get larger made me want to go further. Then I got +MR; +rC and then Mut Resist.

Not exactly a bad outcome. So far I'm yet to see something truely horrible.

[Alphaeus]

I can't say much, but so far the ONLY bad mutations I see out of all runs quaffing potions are "Blurry Vision 1, Deformed Body, and Berserkitis."

Overall, not the worst (except for Deformed Body).

I've begun to wonder if there is a reason these are the ones I keep seeing, instead of others.