Optimalize Notability Gain [Spoiler: math]

Fallen London
1

Delicious friends, [li]

until now i saw that most Londoneers which try to acquire notability aim to use the Slowcake card only when their probability to pass the check is around 100%.

Given that:

  • Once the BDR and Notability are fixed, the percentage of success depends linearly from the level of MW.
    (I.e. if I have BDR 17 and Notability 2, each level of MW gives a 4% more)

  • Increasing the levels of MW is not linear.
    (that is, from level 1 to level 2 i need 2 CP, from level 10 to level 11 i need 4 cp)

and

  • It is possible to force the Slowcake card at MW 15 just losing some CP of MW

  • If you pass the check, you lose ALL MW, and half of it (in levels, not CP) if you fail.

I do not believe that &quotfarming MW until i reach 100%&quot is the optimal (action-wise) way to gain notability at high levels of notability.

Does anyone of you calculated such &quotoptimal way&quot?[/li][li]
edited by Andrea Serafini on 12/5/2013

2

Yes, I reached a similar conclusion. Instead I’m grinding for BDR gear! Haven’t seen the Amanuensis since the Healocaust, my prediction is that he visits constantly at Notability 3/4, when the challenge is no longer trivial to me.

3

That’s what i would do, too. Apart from the fact that everything (but the yacht) is actually fate-locked to me.

Actually the amanuensis just visited me, when i foolishly tried to gain the 3rd point of notability with MW5

4

Yeah, I just posted a similar suspicion in another recent thread. I suspect you’re actually best off just grabbing the card whenever you can and taking the gamble, but I’d be really interested to see if anyone’s done the math.[li]

The main issue for me is sunk cost/lost profits; the more you devote to MW, the more you lose, either on a success or a failure.
edited by Dr. Hieronymous Alloy on 12/5/2013

5

Summoning him every time I hit 15.5 Making Waves is how I successfully got 5 Notability on two of my accounts. At this time that’s probably the best way.

6

There’s a Broad Difficulty calculator on the Wiki that can be used for the purpose; I’d say there are a lot of grinders checking it out lately.

7

Agreed. And if you happen to draw the card when you have less than 15 Making Waves, you may as well take the check with whatever you’ve got, no matter how low the chance is. (Maybe getting up to the next level first, if you’re really close.) What you lose is trivial compared to the points you’d need to get to 15 anyway.

(And picking up as much BDR gear as you’re able to is also worthwhile, since grinding for those tends to be independent of cards.)

8

Well, with the right datas it is possible to calculate it precisely.

Just two datas:

-which one is the best method (repeteable, so i would say coffee / supper) to gain MW

  • how is calculated how many MW you lose if you fail the check for gaining notability? I know the Level is halved, but i do not know the details.

  • How many CP does calling the amanuensis takes?

9

[quote=Andrea Serafini]Well, with the right datas it is possible to calculate it precisely.

Just two datas:

-which one is the best method (repeteable, so i would say coffee / supper) to gain MW

  • how is calculated how many MW you lose if you fail the check for gaining notability? I know the Level is halved, but i do not know the details.

  • How many CP does calling the amanuensis takes?[/quote]

I don’t know the first two, but calling him with Making Waves takes only a tiny amount of CP, maybe like 5

10

[/li][li]Also, I’m fairly sure the Amanuensis summon costs less than 5 CP. I’m thinking three.[/li][li][/li][li]
edited by OPG on 12/5/2013

11

[quote=Andrea Serafini]-which one is the best method (repeteable, so i would say coffee / supper) to gain MW[/quote]No clue, but Supper gives 6-8 CP to the host. I’ll have coffee when my MW gets reset.

[quote=Andrea Serafini]how is calculated how many MW you lose if you fail the check for gaining notability? I know the Level is halved, but i do not know the details.[/quote]Take your number of MW levels and divide by two; there are no details.
[li]

12

[quote=Dr. Hieronymous Alloy]…but I’d be really interested to see if anyone’s done the math.
[/quote]

So I just finished a big project for work, and clearly needed more nerdy math things to do. This time, let’s do a Monte Carlo simulation. I wrote a short program to simulate someone trying to pass at different levels of making waves. Assuming you can get 2 CP of making waves per action and you need 40 levels of making waves to get 100%, I come up with the following:
[li] Attempting with 15 making waves (assuming you have to get at least this high to force a draw), you should expect to spend about 149 actions. There’s about a 25% chance you’ll spend 200+ actions, and 2.5% chance you’ll spend 400+ actions.
[/li][li] Attempting with higher making waves generally takes more actions.
[/li][li] Attempting with 40 making waves takes 417 actions (using my probably wrong assumptions).

The program is in the spoiler tag. Run it in a python terminal if you want to play with it.

from random import random

def actionsForSuccess(attemptLevel = 40, challengeLevel = 40, CPperAction = 2.0, drawCPpenalty = 10):

~~~~Uses a RNG to figure out how many actions it will take to gain a point of notability.

~~~~challengeLevel - the level you need to get 100% success rate
~~~~CPperAction - how many actions it takes to get 1 CP of making waves
~~~~attemptLevel - the level at which you take a gamble
~~~~drawCPpenalty - how many CP you lose to force draw the card

~~~~Number of actions it took to gain the point.
~~~~&quot&quot&quot

~~~~actions = 0
~~~~CP = 0
~~~~attemptCP = attemptLevel*(attemptLevel+1)/2
~~~~while True:
~~~~~~~~delta_CP = attemptCP + drawCPpenalty - CP
~~~~~~~~actions += delta_CP / CPperAction
~~~~~~~~actions += 2 # one for draw, one for trying to pass
~~~~~~~~success_probability = attemptLevel * 1.0 / challengeLevel
~~~~~~~~if (success_probability > random()):
~~~~~~~~~~~~# success!
~~~~~~~~~~~~return actions 
~~~~~~~~else:
~~~~~~~~~~~~# fail...
~~~~~~~~~~~~# Assume your making waves level gets cut in half, rounded up
~~~~~~~~~~~~newLevel = attemptLevel//2 + attemptLevel%2
~~~~~~~~~~~~CP = newLevel*(newLevel+1)/2

# Now run this a bunch of times, and see what the distribution is
def runManyTimes(n = 10**6, **args):
~~~~action_distribution = {}
~~~~for i in xrange(n):
~~~~~~~~actionsForThisTrial = actionsForSuccess(**args)
~~~~~~~~if actionsForThisTrial not in action_distribution:
~~~~~~~~~~~~action_distribution[actionsForThisTrial] = 0.0
~~~~~~~~action_distribution[actionsForThisTrial] += 1./n
~~~~
~~~~expectedActions = 0
~~~~for actionCount in action_distribution.keys():
~~~~~~~~expectedActions += actionCount * action_distribution[actionCount]
~~~~return expectedActions, action_distribution


expectedActions, action_distribution = runManyTimes(attemptLevel = 15)
print expectedActions
print action_distribution

edit: Evidently I can’t post things with leading spaces. Remove the tildes and put in spaces if you want to run the code.[/li]
edited by Guy Scrum on 12/5/2013

13

Before I throw math at this I’d like to double check what the N in the 20-BDR+6*N difficulty level means. Is this your current notability, or the level of notability you’re trying to achieve? For example, at 20 BDR is going from notability 2 to notability 3 a difficulty 12 or difficulty 18 challenge?

14

It’s current Notability – so in your example, the difficulty would be twelve.

15

Alright, here we go. If our strategy is to grind to MW 15 + 3 or 4 cp before calling the Amanuensis and then take the challenge at MW 15, how many actions can we expect to spend going from 0 Notability to 5?

Some initial numbers: MW 15 + 3 cp is 123 cp total, MW 7 is 28 cp, and we’re assuming we can grind at 2 cp/action. So going from MW 0 to 15 is 62 actions, and 7 to 15 is 48. Add 2 to both of these to summon and play the Amanuensis for 64 and 50 actions to try again after success or failure, respectively. Finally, I’m assuming BDR = 20 so the challenge difficulty is exactly 6*N.

Going from 0 to 2 Notability at BDR 20 is entirely straightforward, so worst case you’ll spend 128 actions if you somehow need to summon the Amanuensis for both of these but it will probably be a lot less. Ultimately it depends on your deck and calculating an expected actions to Notability 2 just isn’t worth it, so we’re going to assume you can get there without much trouble.

The next step is going from 2 to 5, which is harder. At MW 15 2 to 3 is a 75% challenge, 3 to 4 is a 50% challenge, and 4 to 5 is a 37% challenge. So let N(x,y) be the expected number of attempts to go from Notability x to Notability y. Then…

N(2,5) = 1 + .75N(3,5) + .25N(2,5) #We always spend an action, but only advance 75% of the time
N(3,5) = 1 + .50N(4,5) + .50N(3,5) #Same idea, different numbers
N(4,5) = 1 + .37N(5,5) + .63N(4,5) #And again
N(5,5) = 0 #It of course takes 0 actions to go from notability 5 to notability 5

Working backwards to solve all this, we get N(2,5) = 8.7 Or at least I get that, someone should double check. So it’s going to take let’s just say 9 attempts to go from Notability 2 to Notability 5, but how many actions is this?

Recall that once we got to Notability 2 we had to spend 64 actions to get MW back to 15. Similarly, once we hit Notability 3 it will take another 64 actions to build it back up, and the same for when we hit Notability 4, so three of our attempts cost 64 actions. Our other attempts were all failures, though, and failures only require us to spend 50 actions to get back to MW 15 since we start at 7.

So using this strategy we can expect to make 3 attempts costing 64 actions and 6 attempts costing 50, for a total cost of 492 actions to go from Notability 2 to 5, plus whatever it takes to get to Notability 2 in the first place. So absolutely worst possible case is 620 actions, and around 530 might be a more reasonable guess.

Obviously, getting lucky on your first 37% challenge or bombing a 50% challenge twice in a row will swing this pretty far from that number in either direction, but as far as my math skills go (and feel free to tell me I’m doing something hilariously wrong, it’s very possible) that’s what you should expect when you begin the grind.

tl;dr - This strategy should take you from no notability to notability 5 in about 530 actions.

16

[quote=OPG]Take your number of MW levels and divide by two; there are no details.
[/quote]

I think the details are actually &quotround up to exact level (no extra change points)&quot, but I won’t be checking that any time soon.

17

[quote=Sackville]

tl;dr - This strategy should take you from no notability to notability 5 in about 530 actions.[/quote]

[li]
And, i would stress,

  1. with no use of Scheme - A salon

  2. Considering 2MW/Action. If the supper gives 6-8 MW, it is definitely better.

530 actions are pretty much a week, or so.

Let us try.

18

Do keep in mind that’s assuming you can just draw the Amanuensis for levels 1 and 2. Grinding all the way up to 15 for those adds an extra hundred actions or so.

Whether or not you’re likely to see the Amanuensis twice within a hundred something actions (Honestly, probably not) is an entire different problem that I don’t know enough about opp. cards to really say anything about.

19

Does it really matter how much MW you get per action? No matter whether you go to 15 repeatedly or always to 100%, you will (almost definitely) spend overwhelmingly more actions on MW than amanuensis.
So getting your notability up while gaining 6 MW/action will just be roughly 3 times as fast as getting it with 2 MW/action.
And then you can simplify to just &quothow much total MW CPs do I have to grind for options A, B&quot and compare.
No?

20

A hesitant clarification: inviting someone to a Private Supper costs 3 actions, not 1. Even if the supper grants 6MW upon acceptance, it’s still 2MW/action. (If more, than it gives an advantage, but not an enormous one.)