[NFP] Expected Tourists of Rock Bands

[DanQuayle]

Great stuff. Is there any assumption about wonder contention? Even in a normal game you can get a queue.

Do you mean when you buy all your rock bands on the same turn and some of your rock bands cannot play yet because the venues are occupied by other rock bands (ie more rock bands than wonder venues available nearby)?
This is what I refer to as the "glut problem" and I am not taking this into account yet. If I were to take this factor into account, it would probably favor strategies that can produce more tourism earlier.

If you are talking about competition about building wonders (AIs vs player) which will determine the number of wonders available on the map where you can play at, I assume there is a normal distribution of mean 24 and standard deviation of 4 for the wonders. These are my current estimates for a deity game at standard speed between T150 and T200. A new number of wonders on the map is generated for each game in this distribution. I didn't look over a large number of games to create these estimates, so they may be a bit off.

 

[Victoria]

so they may be a bit off.

Hard to get perfect, but doing a great job. Yeah I was referring to the glut.
After the glut clears and I have 1-2 bands left they no longer can play the culture leaders wonders anymore so it’s a question of best alternatives. I guess as album sales are modified by location you are getting half the value by playing a non culture leaders wonders vs alternative location values from the culture leader.

 

[DanQuayle]

Hard to get perfect, but doing a great job.

To get better estimates, I would need
1. More games (Deity games with Cold War unlocked between T150 and T200)
2. More time (counting the number of venues available on a map isn't too bad: about 10-15mins, but if you want to know the number of civilizations in range of each venue, it takes about 45 mins per map with Radial Measuring Tool. I would need like 30 maps per map type to get good estimates)

After the glut clears and I have 1-2 bands left they no longer can play the culture leaders wonders anymore so it’s a question of best alternatives. I guess as album sales are modified by location you are getting half the value by playing a non culture leaders wonders vs alternative location values from the culture leader.

Focusing on culture leader(s) early on vs later on is an interesting issue.
If you are focusing on short term tourism output, I guess you should try to focus on culture leaders first to effectively get "double" tourism from "non-Goes to 11 tourism" since the domestic tourists of the cultural leader (target) is decreasing. Then you could try to focus on their neighbor to get "Goes to 11 tourism" against them.
If you are focusing on long term homerun rock bands, I believe you should do the reverse, wait until your rock bands have more album sales to get more tourism per concert from each venue from the cultural leader.
Now, modeling all this becomes increasingly complex...

If you are focusing on short term tourism output, I guess you should try to focus on culture leaders first to effectively get "double" tourism from "non-Goes to 11 tourism" since the domestic tourists of the cultural leader (target) is decreasing. Then you could try to focus on their neighbor to get "Goes to 11 tourism" against them.

Now I wonder which strategy would be better:
1. Hallyu (Album Cover - Goes to 11 - Roadies) by focusing on the cultural leader and then its neighbors
2. Hallyu (Goes to 11 - Album Cover - Roadies) by focusing on the neighbors of the cultural leader and then the cultural leader
3. Whichever strategy against your own closest neighbors to reduce travel time

 

[DanQuayle]

Hallyu (Goes to 11 - Album Cover Art - Roadies) when prioritizing venues in range of a high number of civilizations

I estimate there is around 10% of venues that are in range of 3 civilizations on Pangea, Archipelago and Lakes. That pourcentage is higher on Terra. I also estimate there is on average 24 wonders on the map. Thus, there should be around 2-3 wonders on each map that are in range of 3 civilization. There is also a good chance that these wonders are clustered in the middle of map. Since I found out in my last analysis that rock bands following that strategy produce their peak output in their first few concerts, that about half of them disband after 3 concerts or less and that it is best used as a "finisher" strategy, I try to maximize that early output by prioritizing wonders that are in range of a high number of civilizations. Let's see how that "turbo-charged" version of the last strategy performs.

Nb of games: 5000
Rock Bands per game: 20
Map types: Pangaea, Terra, Archipelago, Lakes
Promotion Pick Strategy: Hallyu (Goes to 11 - Album Cover Art - Roadies)
Venue Pick Strategy: Prioritize Tourism & Prioritize venues in range of a high number of civilizations

Spoiler :

Percentile | Tourism | Floor(VT)
10    1875    1
20    5000    3
30    5000    3
40    5000    3
50    6875    4
60    10625   6
70    13750   8
80    22375  13
90    48125  30

• Histogram bin width is 23.4K (100 bins)
• 80836 out of 100K simulated rock bands are in the first bin with total tourism under 23.4K
• Max: 2336625 tourism from a single rock band
  
• Min: 1500 tourism by 231 rock bands

Percentile | Tourism | Floor(VT)
10    217000    135
20    270375    168
30    338875    211
40    416688    260
50    518625    324
60    652438    407
70    817563    510
80    1042828   651
90    1422813   889

• Histogram bin width is 37K (100 bins)
• Min: 102375 Tourism in a game of 20 Rock Bands
• Max: 3782750 Tourism in a game of 20 Rock Bands

Percentile | Nb of concerts played by a rock band before disbanding
10    1
20    1
30    1
40    1
50    2
60    2
70    3
80    4
90    6

• After the first concert, 44663 out of 100K rock bands are already disbanded.

• At the 16th percentile, all 20 rock bands of a game will have disbanded after 6 concerts played.
• At the median, all 20 rock bands of a game will have disbanded after 14 concerts played.
• At the 84th percentile, all 20 rock bands of a game will have disbanded after 26 concerts played.
• 100% probability of having all rock bands disbanded is only reached at the 68th concert for this simulation where one rock band was left with no more venues to play at.

• At the 16th percentile, a rock band disbands at its 1st concert. Max output is reached at the first concert with a value of 1875.
• At the median, a rock band disbands at its 2nd concert. Max output is reached at the 2nd concert with a value of 3125.
• At the 84th percentile, a rock band disbands at its 4th concert. Max output is reached at the 2nd, 3rd and 4th concert with a value of 7500.

• At the 16th percentile, all 20 rock bands will have disbanded at the 6th concert. Max output is reached at the 1st concert for a value of 65K tourism.
• At the median, all 20 rock bands will have disbanded at the 14th concert. Max output is reached at the 1st concert for a value of 73.125K tourism.
• At the 84th percentile, all 20 rock bands will have disbanded at the 26th concert. Max output is reached at the 1st concert for a value of 81.875K tourism.

• At the 16th percentile, the maximum cumulative tourism is reached at the 1st concert for a value of 1875.
• At the median, the maximum cumulative tourism is reached at the 3rd concert for a value of 6875.
• At the 84th percentile, the maximum cumulative tourism is reached at the 6th concert for a value of 28.375K.
• The expected cumulative tourism for a single rock band is estimated at 34756 which is above the original strategy of not prioritizing venues in range of a high number of civilizations.

• At the 16th percentile, the maximum cumulative game tourism is reached at the 13th concert for a value of 248K.
• At the median, the maximum cumulative game tourism is reached at the 25th concert for a value of 518.6K.
• At the 84th percentile, the maximum cumulative game tourism is reached at the 42nd concert for a value of 1.169M.
• The maximum cumulative expected game tourism is 695K which is 20 * 34.8K. It is attained at the 68th concert when no rock band are left playing (out of 100K).

A posteriori, the percentage of tourism that comes from Goes to 11 is 44.93%. This translates to a ratio of 0.8159, so a bit more than 1.6 civilizations in range for each concert. Since Goes to 11 does not grant performance level bonuses only a few rock bands get to survive and get promoted. Indeed, 81.20% of rock bands stay at level 1, 9.20% reach level 2 before disbanding, 2.8% disband at level 3 and 6.80% reach level 4.

Comparison with standard Hallyu (Album Cover Art - Goes to 11 - Roadies)

• This strategy has lower downside risk: you are guaranteed a higher minimum of tourism for each rock band. Even at the 84th percentile, we are observing higher values than with the standard strategy.
• This strategy has also lower upside: the "homerun" rock bands above the 84th percentile generate less tourism (see lower maximum value). This is because the venues with a high number of civilizations in range are exhausted early and are not played at by rock bands with a high number of album sales.
• The disband probabilities are the same obviously
• This strategy "turbo charges" early tourism output.
• This strategy increases expected tourism even if "homerun" rock bands are less powerful, because of the low probability of reaching this status and the associated high disband probability of this strategy.

 

[DanQuayle]

Hallyu (Glam Rock - Album Cover Art - Goes to 11)

Nb of games: 5000
Rock Bands per game: 20
Map types: Pangaea, Terra, Archipelago, Lakes
Promotion Pick Strategy: Hallyu (Glam Rock - Album Cover Art - Goes to 11)
Venue Pick Strategy: Prioritize Performance Level

Spoiler :

Percentile | Tourism | Floor(VT)
10    500      0
20    500      0
30    813      0
40    1375     0
50    2375     1
60    4563     2
70    14688    9
80    92234    57
90    356656   222

• Histogram bin width is 35K (100 bins)
• 74637 out of 100K simulated rock bands are in the first bin with total tourism under 35K
• Max: 3.49M tourism from a single rock band
  
• Min: 187.5 tourism by 7667 rock bands

Percentile | Tourism | Floor(VT)
10    689250     430
20    1051953    657
30    1379188    861
40    1691297    1057
50    2002594    1251
60    2334469    1459
70    2754031    1721
80    3208641    2005
90    3989750    2493

• Histogram bin width is 98.2K (100 bins)
• Max: 9.81M Tourism in a game of 20 Rock Bands
• Min: 40563 Tourism in a game of 20 Rock Bands

Percentile | Nb of concerts played by a rock band before disbanding
10    1
20    1
30    2
40    2
50    3
60    5
70    7
80    12
90    19

• After the first concert, 24840 out of 100K rock bands are already disbanded.

• At the 16th percentile, all 20 rock bands of a game will have disbanded after 20 concerts played.
• At the median, all 20 rock bands of a game will have disbanded after 30 concerts played.
• At the 84th percentile, all 20 rock bands of a game will have disbanded after 40 concerts played.

• At the 16th percentile, a rock band disbands at its 1st concert. Max output is reached at the 1st concert with a value of 187.5.
• At the median, a rock band disbands at its 3rd concert. Max output is reached at the 3rd concert with a value of 687.5.
• At the 84th percentile, a rock band disbands at its 14th concert. Max output is reached at the 13th concert with a value of 13750.

• At the 16th percentile, all 20 rock bands will have disbanded at the 20th concert. Max output is reached at the 15th concert for a value of 42K tourism.
• At the median, all 20 rock bands will have disbanded at the 30th concert. Max output is reached at the 14th concert for a value of 98.6K tourism.
• At the 84th percentile, all 20 rock bands will have disbanded at the 40th concert. Max output is reached at the 15th concert for a value of 167.7K tourism.

• At the 16th percentile, the maximum cumulative tourism is reached at the 2nd concert for a value of 500.
• At the median, the maximum cumulative tourism is reached at the 5th concert for a value of 2375.
• At the 84th percentile, the maximum cumulative tourism is reached at the 23rd concert for a value of 162.6K.
• The expected cumulative tourism for a single rock band is estimated at 110.3K which is more than twice than what a Hallyu (Album Cover Art - Goes to 11 - Roadies) strategy is expected to generate.

• At the 16th percentile, the maximum cumulative game tourism is reached at the 36th concert for a value of 911K.
• At the median, the maximum cumulative game tourism is reached at the 49th concert for a value of 2M.
• At the 84th percentile, the maximum cumulative game tourism is reached at the 56th concert for a value of 3.47M.
• The maximum cumulative expected game tourism is 2.2M which is 20 * 110K. It is attained at the 59th concert when no rock band are left playing (out of 100K).

A posteriori, the percentage of tourism that comes from Goes to 11 is 38.60%. This translates to a ratio of 0.6288, so a bit more than 1.2 civilizations in range for each concert. However, one should keep in mind that only rock bands that survive long enough to get their 3rd promotion benefit from Goes to 11 here. With this strategy, 49.02% of rock bands stay at level 1, 15.49% reach level 2 before disbanding, 6.15% disband at level 3 and 29.35% reach level 4.

Analysis

• This strategy has a high downside risk for individual rock bands. This is explained by the fact that you only get a base 250 tourism for playing in Amphitheaters.
• This strategy can lead to the most extreme outcomes (in the low probability tail ends). This strategy has both the lowest total minimum and highest total maximum tourism observed for a game of 20 rock bands.
• Since you are getting a +2 performance level bonus from the get go, this strategy has a noticeably lower number of rock bands disbanding early on. (This however also means that it is more likely to suffer from the glut problem, since there are fewer rock bands disbanding early on which would have "cleared" the venue for another rock band to play at on the same turn).
• This strategy is also noticeably slower than the other ones. The peak tourism output is reached past the 14th concert.
• This strategy has by far the highest expected cumulative tourism with 110K which is more than twice than what a Hallyu (Album Cover Art - Goes to 11 - Roadies) strategy is expected to generate.
• Although individually rock bands following this strategy are risky in isolation, with the power of diversification (ie purchasing multiple rock bands (20) with this strategy), even at the 16th percentile you are expected to generate near 1M tourism which is more than thrice than what a Hallyu (Album Cover Art - Goes to 11 - Roadies) strategy would yield at the same percentile. For the same reason, I do not recommend pursuing this strategy when you do not have a lot of faith and can only afford a few rock band.
• This strategy has the most potential to hit "homerun" rock bands and is probably the best one to pursue as a "comeback strategy" ie when you are lagging behind in tourists and have a large gap to fill.
• If I were to posit that you are expected to find multiple broadcast towers on the map (which is not the case here since I assume there are none), this strategy would be even better and it would substantially reduce the downside risk.