[NFP] Expected Tourists of Rock Bands

Discussion in 'Civ6 - Strategy & Tips' started by Lily_Lancer, Sep 21, 2020.

  1. Lily_Lancer

    Lily_Lancer Deity

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    Assuming they all played only on wonders, and there's enough wonder for them to play. (Ignore all other promotions)

    Assuming Goes to 11 affects 2 other Civs(So its tourism is doubled):

    With Hallyu:

    Promotion:
    Album Cover Art--Goes to 11: Average Tourism(before disband): 48444=30 tourists
    Goes to 11-- Album Cover Art: Average Tourism: 28993=17 tourists

    Definitely shall pick the 1st route.

    Without Hallyu:

    No promotions: Average Tourism=6665=4 tourists
    Start with Album Cover Art: Average Tourism=26225=16 tourists
    Start with Goes to 11: Average Tourism=13329=8 tourists

    Average Tourism=1/4*26225+9/44*13329+24/44*6665=12918=8 tourists, assuming all promotions appear uniformly random.

    So Rock band w. Hallyu: 30 tourists in average
    w.o. Hallyu: 8 tourists in average

    before they disband, assuming they only play on wonders & there're enough wonders.

    Code(In Python):
    Spoiler :

    import numpy as np

    dicecount=[1,3,6,10,15,21,25,27,27,25,21,15,10,6,3,1]

    print(np.sum(dicecount))

    print(np.sum(dicecount[14:]))

    alb=[0,0,1,2,3,4]

    this=[-25,100,-25,150,0,200]



    count=np.zeros((4,3,3,1001))



    for i in range(2):

    for j in range(2):

    for k in range(1001):

    num=0

    if i==0:

    num=50*k*6.17+2187

    else:

    num=50*k*10.8+8000

    if j==1:

    num*=2

    count[3][j][k]=num

    for k in range(1000,0,-1):

    for i in range(2):

    key=12-i

    prob=[np.sum(dicecount[key:])/216.0]

    for w in range(1,5):

    prob.append(np.sum(dicecount[key-w*2:])/216.0-np.sum(prob))

    prob.append(1-np.sum(prob))

    # print(prob)

    for j in range(2):

    sumthis=0

    for r in range(6):

    w=5-r

    al=k+alb[w]

    th=this[w]+k*50

    if j==1:

    th*=2

    if al>1000:

    al=1000

    upgrade=0

    if w>=4:

    upgrade=1

    if w>=2:

    sumthis+=prob[r]*(th+count[upgrade+2][j][al])

    else:

    sumthis+=prob[r]*th

    if (k==2):

    print(w,2,i,j,prob[r],th,count[upgrade+2][j][al])

    if k==2:

    print(sumthis)



    count[2][j][k]=sumthis



    for b in range(1,-1,-1):

    for k in range(1000,0,-1):

    for i in range(2):

    key=14-b-i

    prob=[np.sum(dicecount[key:])/216.0]

    for w in range(1,5):

    prob.append(np.sum(dicecount[key-w*2:])/216.0-np.sum(prob))

    prob.append(1-np.sum(prob))

    for j in range(2):

    sumthis=0

    for r in range(6):

    w=5-r

    al=k+alb[w]

    th=this[w]+k*50

    if al>1000:

    al=1000

    upgrade=0

    upi=0

    upj=0;

    if w>=4:

    upgrade=1

    if i==0:



    upi=3/(11-b)

    if j==0:

    upj=3/(11-b)*(8-b)/(10-b)

    #upi=1

    #upj=0

    if (i==1 and j==0):

    upj=3/(11-b)

    #upj=1

    if j==1:

    th*=2

    if w>=2:

    sumthis+=prob[r]*(th+upj*count[upgrade+b][j+upj][al]+upi*count[upgrade+b][i+upi][j][al]+(1-upi-upj)*count[upgrade+b][j][al])

    else:

    sumthis+=prob[r]*th

    if (k==2):

    print(w, b,i,j,prob[r],th,count[upgrade+b][i+upi][j+upj][al])

    if k==2:

    print(sumthis)

    count[j][k]=sumthis



    print(count[:,0,0,2])

    print(count[:,1,0,2])

    print(count[:,0,1,2])

    print(count[:,1,1,2])
     
    Last edited by a moderator: Oct 2, 2020
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  2. DanQuayle

    DanQuayle Prince

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    But it is not the case...

    I once attempted to calculate the proper values using Monte Carlo simulations, but unless you know exactly how the promotion system works you will get inexact results...
    You also need to specify exactly what is your "promotion choice process" when selecting promotions without Hallyu (what promotions are prioritized?). The overall results are highly dependent on the assumptions you make...
    Also, expected values can be misleading. You need to consider the full distribution. If you hit promotions early you get "immortal rock bands" (rock bands with low disband probability) which gives a positive skew to the distribution.
     
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  3. Lily_Lancer

    Lily_Lancer Deity

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    I only consider Album Cover Art and Goes to 11. And it is obvious that Album Cover Art is better than Goes to 11 so always pick Album Cover Art first then Goes to 11.

    (This also means with other places possible for a performance, my calculation that a Band gets 8/30 tourists with/w.o. Hallyu is actually an underestimation.)
     
    Last edited: Sep 21, 2020
  4. cain3456

    cain3456 King

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    I have never understood the popularity of "Goes to 11". That bonus would best be used in border cities, but those cities have usually not been built up to have decent sites. Thus most desirable sites are in the interior, where Goes to 11 is wasted.
     
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  5. Victoria

    Victoria Regina Supporter

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    Yes, all types of assumptions but some measurement usefulness, it is more about targeting the leader than getting the tourism. Goes to 11 is good but only half as powerful in tourism as targeted tourism. If the culture leader has Rapa Nui and no wonders the whole approach changes.
    A big treat with care sticker on the post needed.
    The depth of rock bands in this area is surprising but can be generalised OK with the right chaos calculations. Would not like to go deeper personally.
    I thought I worked this out and gave it to you. Hmm will have to look through my stuff, just too damn busy this week teaching. If I remember it goes in a choice pattern always offering up at least one choice not yet chosen and rotates through. I think it was 3 times before diminishing choice in the other 2 slots. So with this in mind you are not going to get more than 3 promotions the same before 36 promotions.
    Would you like me to publish when I find it?
     
    Last edited: Sep 21, 2020
  6. Lily_Lancer

    Lily_Lancer Deity

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    Usually, when you get to Rock Band you just wish to hurry up their performance, unleash their tourism ASAP. A rock band can get in average 8 tourists before disband, however usually we only get 3~5 in average when victory is achieved, as at the time of victory usually we still have a lot of rock bands instead of everyone being disbanded.

    So you won't care a lot about "targeting a certain leader", but just perform on whatever adequate sites.
     
  7. Victoria

    Victoria Regina Supporter

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    No, you don’t care. Personally I prefer my tourism to be more powerful. You move fast enough by that time in the game that the delay is not as strong as the doubling. When every increase in my tourism also reduces the target number it becomes much stronger, especially with so many one shot bands.
     
  8. Archon_Wing

    Archon_Wing Vote for me or die

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    It can be good if some civs have banned your Rock Bands so you can play near them instead via other civs.
     
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  9. cain3456

    cain3456 King

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    sigh... you didn't even read my post.:sad:
     
  10. Archon_Wing

    Archon_Wing Vote for me or die

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    I don't think you read mine either.
     
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  11. hhhhhh

    hhhhhh Prince

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    I used to do something similar namely using Python code to simulate. However one observation is, the performance of rock bands usually have a huge standard deviation -- like when mean is 16k, the std is more than 20k. So this is not your "normal" random variable (pun intended) and luck does play a huge role.

    Given the huge fluctuation in performance, I think it's better to do some case by case simulation taking venue and their distance into account (e.g. the culture boss has 7 theatre square and 5 wonders, 8 campus, how do you plan your rock band tour), but that requires a lot more coding.
     
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  12. Lily_Lancer

    Lily_Lancer Deity

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    I'm not using a Monte Carlo to stimulate. As you can see I'm basically calculating the expected tourism using dynamic programming, instead of stimulation. So the resulted expected tourism is not affected by variance.
     
  13. Victoria

    Victoria Regina Supporter

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    Which is incorrect, I found my workings on it and they were described as above
    Also you have not depreciated the tourism for waiting for Hallyu which is significant.
    You could say, without hallyu but targeting the leader 16 tourism.
    Roadies have a effect
    Targeting their level benefit building has an effect
    TBH for the start, it’s jus felt like you had some fun with Python, which is not a bad thing.
     
    Last edited: Oct 1, 2020
  14. hhhhhh

    hhhhhh Prince

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    Expected value of any random variable is not affected by variance (since it's just a number!).

    Maybe I shouldn't have used the word "simulation". What I was saying is that when variance is large, expected value per se doesn't mean much.

    My point is even if I know the expected tourism in some case is 26225, it can still happen, with a non-negligible probability, that 5 rock bands of that kind together cannot generate 26225. I think a more meaningful piece of information is like finding the cdf of the total performance of a band, like if you have a band of a promotion, then you have 10% chance of getting ≤ a tourism, 20% chance of getting ≤ b tourism, etc.

    BTW instead of pasting code here can you paste somewhere like Github and then share a link?

    So I checked RandCalls.csv on the turn I bought a rock band. It has a series rand calls which looks like this:

    upload_2020-10-1_17-8-42.png

    Since it says "Random Promotion" and the range goes from 12 to 1 I believe this is a permutation of 0-11. So I loaded another late game to test this, in that save I already have lots of rock bands, so for the one I bought, RandCalls.csv only shows a permutation of 0-8 (a series randcalls from 9 to 1). Is this because several promotions are ruled out? How are they ruled out?

    So in theory, if we get Rock Bands with promotion we don't want, can we benefit from promoting them but keeping them alive instead of performing?
     
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  15. DanQuayle

    DanQuayle Prince

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    @hhhhhh Thank you for posting this. I have now figured how the promotion system works.

    I used an old save file @Victoria provided me some time ago with around 400K faith to do the testing. It was created using an older game version, but I do not believe anything regarding rock bands has changed since then.


    The mechanics

    The promotion choice odds are only affected by past selected promotions. Rock bands disbanding (promoted or not), performing and surviving or leveling up (but not assigned a new promotion) do not change the promotion choice odds.

    RandCalls for promotion choices are made
    1. On the turn, a new rock band is faith purchased
    2. On the turn, a rock band levels up due to a 5 or 6-star concert performance
    Selecting any promotion type will remove it from the “promotion pool” for one “round”. This may seem counter-intuitive, because it is frequently observed in-game that you can get the same promotion multiple times for different rock bands when you faith purchase a lot of them on the same turn. This is because the “promotion exclusion mechanism” is easily bypassed when you purchase multiple rock bands before promoting any of them. The odds are only changed once you promote a rock band and only affects the odds of the promotion choices of the rock bands purchased or promoted trough level up afterwards (when new RandCalls are made).

    Selecting X times the same promotion will make it unavailable for the next X “rounds”.

    The first, second and third promotion of a rock band all draw from the same “promotion pool”.


    Details

    I define the “promotion pool” as the 12 different types of promotion a rock band can get. They are ordered alphabetically. Their number corresponds to the Value column in RandCalls. If a promotion is selected, it is removed from the list for this “round”. All the promotions with a higher number get their number reduced by 1 for the next RandCall until all the promotions in the “promotion pool” for this round are exhausted. For example, if Album Cover Art is selected, for the next RandCall Arena Rock becomes the new 0, Glam Rock the new 1, etc. If all promotions are selected, except Surf Band, it becomes the new 0.

    The promotion choices are displayed alphabetically in the game regardless of whether they were drawn 1st, 2nd or 3rd.

    You can visualize all promotions as a big 12 by n matrix where each column represents a “promotion pool” and there is as many columns in the matrix as “rounds” are needed. (At least, I never hit a round limit or bug with 400K faith).

    Spoiler :
    Code:
    0              Album Cover Art
    1              Arena Rock
    2              Glam Rock
    3              Goes to 11
    4              Indie
    5              Music Festival
    6              Pop Star
    7              Reggae Rock
    8              Religious Rock
    9              Roadies
    10             Space Rock
    11             Surf Band

    Depending on the number of different promotions selected, the range or the odds of the promotions (1 out of …) for a level 1 rock band are:

    Spoiler :
    Code:
    0 Promo:             12-11-10 (The different odds ensure no duplicate promotion choices for the same rock band)
    1 Promo:             11-10-9
    2 Promo:             10-9-8
    3 Promo:             9-8-7
    4 Promo:             8-7-6
    5 Promo:             7-6-5
    6 Promo:             6-5-4
    7 Promo:             5-4-3
    8 Promo:             4-3-2
    9 Promo:             3-2-1 (The last 3 unselected promotions are guaranteed, not sure why rand calls are made, especially one with a range of 1)
    10 Promo:            10 (The last 2 unselected promotions are guaranteed; the other promotion choice is drawn from a new pool in the next round excluding the 2 previously unselected promotions)
    11 Promo:            11-10 (The last unselected promotion is guaranteed; the other 2 promotion choices are drawn from a new pool in the next round excluding the previously unselected promotion)
    12 Promo:            12-11-10 (As all promotions of the pool are selected for the round, all promotions of the pool for the next round are available)

    For 10 & 11 promotions selected, the range for the promotion choices in the next round will decrease by 1 for the next rock band purchase or level up promotion if you select that promotion. You can thus avoid selecting 1 or 2 promotions if you want at the cost of them reappearing every time and reducing your odds of getting another promotion choice.

    Bug: For the 2nd promotion of a level 2 rock band (or the 3rd promotion of a level 3 rock band), the 1st (and the 2nd promotion in the case of a level 3 rock band) are not excluded from the range of promotion choices. If a promotion previously selected for that rock band is randomly chosen, one less promotion choice will appear on the list of promotions. It is thus possible to get only 2 or even 1 promotion on the list (the latter is theorized as I did not personally observe it as it is a very low probability event).

    Example
    If you mass faith purchase multiple rock bands on the turn you unlock Cold War, they will all be 12-11-10 rock bands since you have promoted no rock band yet. The more you purchase of them, the more you are likely to be offered the same promotion type for multiple rock bands.


    “Synthetic Hallyu”

    As you may have already noticed, selecting 9 different promotion types will guarantee you to get the 3 remaining ones for as long as you do not promote another rock band. You can thus get the exact 3 promotions that you want with a 100% guarantee in the order that you want for any number of rock band that you can afford to faith purchase as long as you follow these steps.

    First, you need to exclude the 9 promotion types that you do not want from the “promotion pool” for the first “round”. In order to achieve this, you need to promote rock bands with the 9 different unwanted promotions.

    Spoiler :
    You now need to ask yourself if you want to adopt a faster approach that can end up being more faith costly or a slower approach that will minimize the amount of faith needed, but will require more turns to achieve. In the former approach, the additional needed faith will not be totally wasted per se, but only invested in rock bands with lower expected tourism output.

    The most risk-averse to faith loss approach requires faith buying 1 rock band per turn and touring them asap in the hope they get a level 2 promotion. You do not need to wait for it to disband or level up to purchase the next one (for the first few ones at least). Each purchased rock band has the potential to get 3 promotions each. The minimal number of rock band required to get the 9 promotion types is thus 3. If all rock bands disband before leveling up, you will need to purchase 9. This represents a 9K faith investment (without any faith discount).

    On the contrary, if you judge you have ample faith, you can buy all 9 rock bands (or even more) on the same turn. They will all be 12-11-10 rock bands and you thus run the risk of getting multiple times the same promotion choices. (Note: this is a favorable outcome if you want the same promotion type quickly for multiple rock bands). You should examine the 3 promotion choices of all rock bands, before beginning to promote any of them. Even after careful analysis, you may not be able to get the 9 unwanted promotion on the 9 different rock bands due to RNG. With this approach, you have a high risk of needing to buy more than 9 rock bands to get the 9 unwanted promotions.

    A balanced approach consists of only buying 3 rock bands per turn. Since you get 3 promotion choices per rock band, you are assured to get at least 1 unique promotion per rock band in the worst case scenario where all 3 rock bands have the exact same 3 promotion choices. However, since you likely have 3 specific wanted promotions in mind that you do not want to select in this first phase, you may still need to purchase an additional rock band. This is likely to happen in the 3rd turn where the 3 rock bands you will purchase will be 6-5-4 rock bands that have 95%/50%/5% chance of getting 1/2/3 promotion(s) of choice (which in this case, you do not necessarily want since you do not want to exclude them!). It will still be a “high quality” rock band since it will at least have one wanted promotion choice. You will be able to use it in one of the later steps.

    Note: The whole point of this first phase is to get a 100% guarantee to get your first promotion of choice for all your rock bands during the next phase. If during the first phase, this first promotion of choice comes up in the promotion choices through luck, you already have a post-draw favorable outcome. You should put it aside and not promote it yet!
    If your second promotion of choice comes up during this phase, you can also put it aside, but know that you will only be able to get the second and third promotion of choice with a 100% guarantee in that case as your first and second promotion.
    Similarly, if your third promotion of choice comes up, you will only be able to get that third promotion of choice with a 100% guarantee as your first promotion.

    Second, as the unwanted promotions are now eliminated, you simply buy as many rock bands as you can afford. You can do it over multiple turns if you do not have enough cities. You must however buy all your rock bands before you start to promote them. All the promotions selected need to be the same (ie your first promotion of choice).

    Third, you start to tour with your rock bands. Some of them will disband and some of them will level up. If and when they level up, you must not promote them already! You must first wait before all your rock bands either disband or level up. Leveled up rock bands should be put to sleep until that point is reached, because if you continue to tour with them they will not benefit from the additional promotion they should have got at that point (with lower disband probability and higher tourism output) and if they level up again before you assign them their second promotion they will lose that second promotion. When rock bands get their second promotion choices under those specific conditions, no Randcall will be made and only 2 promotion choices will be made available: your second promotion of choice and your third promotion of choice.

    Fourth, this step is identical to the third one. Here, you are simply dealing with level 2 rock bands that may disband or level up to level 3 and get their third promotion. Here again, you should wait until all rock bands either disband or level up to give them all your third promotion of choice. When rock bands get their third promotion choices under those specific conditions, they will be 9-8 rock bands with the third promotion choice locked as your third promotion of choice and your two previous promotions of choice locked out. Your 3 promotions of choice will now be locked out for as many “rounds” as you selected them as promotions (many rounds!).

    Overall, the main advantage of a “Synthetic Hallyu” strategy is that it comes much earlier than Hallyu ie at Cold War when rock bands are unlocked instead of at Cultural Hegemony when the Hallyu policy card is actually unlocked. This strategy is however slower to execute than if you had unlocked the card (tentative estimation at around 10 turns slower overall). You also need an additional upfront investment of around 9K faith that will be wasted on rock bands with lesser expected tourism output. I suggest you have at least a 20-30K faith stockpile to make this strategy worthwhile. Here is a table of how many “Synthetic Hallyu” rock bands you can get when your first 9 rock bands are promoted with 9 unwanted promotions (and you are getting no faith discount from Theocracy).

    Spoiler :
    Code:
    Faith      Synthetic Hallyu rock bands
    20K         6
    30K        10
    40K        14
    50K        17
    75K        24
    100K       30

    Things to consider when choosing what late game strategy you should adopt for a CV
    1. How close are you to victory? How many visiting tourists are needed to win?
    2. How much faith do you have?
    3. What is your culture output? Are you aiming for the first moon landing? How many turns can you expect between Cold War and Cultural Hegemony?
     
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  16. Lily_Lancer

    Lily_Lancer Deity

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    Do you mean that you can sacrifice the first 9 rock bands and then all others can all get Album Cover Art? Very Interesting strategy.
     
  17. hhhhhh

    hhhhhh Prince

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    There is actually a lot of random call with range 1 in this game. For example on the start of a turn, the next buyable tile (i.e. tile expansion via culture) will be picked for every city and most of the time it's a call of randrange(1). I wonder if the game will be slightly more efficient if devs spend a little resource on optimizations. Changing randrange(n) to if (n-1) randrange(n) else 0 shouldn't be that hard.

    upload_2020-11-8_11-4-57.png

    I think if you exclude 7 promotions it's good enough. The next one will have 3 promotions to choose, there can be two unwanted ones and 1 you want.
     
  18. DanQuayle

    DanQuayle Prince

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    If by sacrifice you mean getting bad/unwanted promotions on your first 9 rock bands, then yes you can do exactly that if you want.

    Yes exactly, you can do all sorts of variation of this strategy with higher risk profiles. Depending how close you are to victory and how much faith you have, it may be tempting to do so.

    By excluding 7 promotions, you are getting 5-4-3 rock bands. Like you said, if there are 3 promotions left that you want, then you are 100% guaranteed to get one of them

    However, some of them may only have "Promotion of Choice A", others "Promotion of Choice B" or "Promotion of Choice C" as choices.

    If you promote them all with either A, B or C, then when (and if) they level up, you will get as promotion choices (10 Promo excluded): the 2 previously unwanted promotions left in the first round of the "promotion pool" + 1 random promotion choice from the next round (with a range of 10 and an unavailable choice if the promotion choice randomly chosen is the same as the one picked as the first promotion, see the Bug section of my previous post).

    If you are aiming for a more long term strategy of getting rock bands with promotions A, B and C then this not the best way to achieve this.

    However, if your strategy is to spam the map with +1000 tourism per concert asap and you do not care much about the longevity and the second promotion of your rock bands then this is a good approach.

    An alternate way to make this work with 5-4-3 rock bands is the following:
    Promote only the rock bands that can get "Promotion of Choice A" (60% chance of being available)
    Promote the rock bands that only got "Promotion of Choice B" when the first batch of rock bands has leveled up to level 2 (give them all "Promotion of Choice B")
    Promote the rock bands that only got "Promotion of Choice C" when the first batch of rock bands has leveled up to level 3 and the second batch leveled up to level 2 (give them all "Promotion of Choice C")

    You will then get rock bands with the following promotions:
    A+B+C
    B+C+?
    C+?+?

    EDIT: Added probability in italic
     
    Last edited: Nov 8, 2020
  19. Lily_Lancer

    Lily_Lancer Deity

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    Perfect. I guess 10 album cover art bands with 9 other bands are enough for a victory , this means you only have to collect faith for 19 rock bands, which means 0.85*1500*19=24225 faith is enough for a CV.
     
  20. DanQuayle

    DanQuayle Prince

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    If I take your initial estimates in the first post:
    9 rock bands with unwanted promotions * 4 tourists + 10 Hallyu rock bands with Album Cover Art--Goes to 11 * 30 tourists = 336 tourists

    That should be more than enough to win, if not overkill, however...
    As I stated before, there is a positive skew to the distribution and you most likely have a much lesser probability than 50% to reach such numbers.



    The surface under the curve and below the median (50% of the outcomes) with a positively skewed distribution is smaller than below the mean / expected value.

    The only way to be sure is to create the whole distribution through simulations to get the probability density function and cumulative density function.

    Now that we know how the promotion system works exactly, it is possible to program such simulations much more precisely.
    I may do so in the future if I feel like it, but that would require a lot of work.

    Also, a lot of hypotheses will need to be made, namely:
    about how many concert locations are available: wonders, seaside resorts (do AIs actually build those?), harbors (shipyard or not?), theater squares (has AI built Broadcast Towers?), natural wonders settled, etc.
    how many civilizations are in range for Goes to 11
    how much faith is it reasonable to get?
    etc.
     
    Last edited: Nov 8, 2020

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