Always wanted to know how long sieges take in 1.13? Nobody ever checks the guides subforum, so here you go
I was made aware that the guides forum is subscription-only, so here is a copy of the post:
So, I wanted to find out how long sieges generally take in the current game version. I believe the table on the wiki is still from the olden days, when you'd always get 1 siege progress, but since then things have changed quite a bit. Since sieges now depend on the siege history, algebraic expressions become pretty much impossible to use since factoring in all the different outcomes is, well, not easily done. But if you are better at combinatorics than I am, please let me know how to do it.
The Basics
You can find info on how sieges work on the wiki. Apart from the mean siege times table, the info seems up-to-date.
Monte Carlo
The general idea of a Monte Carlo simulation is to take a problem that involves any kind of random process and run the problem a sufficiently large number of times, varying the starting parameters randomly or over a given representative sample if needed. Examples for this can be found in nearly any scientific field, for example you could use it to simulate the motion of molecules, the weather, or the spread of the flu. Generally, the questions the MC simulation is supposed to help answer are parameter changes: what happens if people wash hands more often?
In the case of sieges in EU4, I used MC simulations to investigate the probability distribution of how many siege phases you need for certain siege scenarios. Some of the questions one can answer with this are: how much does artillery help? How much do siege leaders help? How long does it take, on average, to siege down a fort of a given level? How long for the 19/20 quantile, or 95% probability of having sieged the fort?
I simulated the siege process to the best of my knowledge using Wolfram Mathematica and implementing a siege behaviour like that observed in the game. I started each scenario 10 000 times (i.e. ran 10k virtual sieges) and compiled a histogram from the results. 10k simulations seems good enough if you're not too interested in far outliers and can be calculated in a few seconds on my rig; the average value generally fluctuated less than 0.1 siege phases. I can also evaluate average siege progress on completion, shifted distribution after one already is at a certain siege progress, etc. but I'm too lazy to prepare all the data for presentation, and most players probably don't care about it much.
Results
All results are given in siege phases. How long these take depends on several values not covered here and not pertinent to the discussion. Since the distributions all look fairly similar (especially to the untrained eye), I put them in spoilers
Here is an overview table of the different scenarios mentioned in detail
Scenario 1: Fort level 2, no bonuses
This is the standard scenario for the early game non-capital forts.
Average: 11.5, Median: 11, 19th/20 quantile: 17
Scenario 2: Fort level 1, no bonuses
Capital-only fort. This is equivalent to a level 2 fort besieged by a 1-pip leader
Average: 9.9, Median: 10, 19th/20 quantile: 15
I actually expected more of a difference here, but capital forts aren't that much weaker than normal forts, requiring only 1.6 additional siege phases. In-game the intuitive difference is probably enlarged by capital forts requiring only 5 artillery for a full siege bonus (see below).
Scenario 3: Fort level 3, no bonuses
Capital plus normal fort, or bastion against a leader pip, etc
Average: 13.4, Median: 13, 19th/20 quantile: 21
Scenario 4: Fort level 2, -2 for coastal fort
If the fort is coastal, you need to blockade it or suffer an additional -2 modifier to the die roll. This also works for a bastion if you have no artillery.
Average: 15.7, Median: 15, 19th/20 quantile: 25
This takes quite a bit longer than the normal level 2 fort, so putting some ships there is a really big advantage. This observation corresponds nicely to my in-game experience.
Scenario 5: Fort level 2, +1 artillery bonus
This is a common scenario after artillery becomes available, but is not yet useful in battle, and when widespread application is too expensive.
Average: 9.5, Median: 9, 19th/20 quantile: 14
You may be wondering why this is not the same as a level 1 fort. The reason is that artillery, in addition to providing a bonus, increases your chance for a breach. Without artillery, you get a breach only on a die roll of 14. With a single artillery regiment, you get it on a roll of 13 or 14, so the probability for a breach doubles. Since breaches are high-impact events that provide a full +3 siege progress, and effectivel increase max progress, this is on average 0.4 siege phases shorter than the level 1 fort. Average number of breaches at siege won increases from 0.44 to 0.89 as expected.
+1 artillery is, however, equivalent to getting a +1 obsolete fort bonus, so this scenario also works out if you siege without art but when you already discovered bastions.
Scenario 6: Fort level 2, +5 artillery
You got the money, you got the siege.
Average: 5.2, Median: 5, 19th/20 quantile: 8
Turbo siege mode. More than twice as fast as without artillery
Scenario 7: Fort level 2, +5 artillery, +4 leader bonus
Just out of curiosity how far you can push it. This happened to me in a game only once or twice so far
Average: 3.0, Median: 3, 19th/20 quantile: 6
Scenario 8: Fort level 4, +1 artillery
For bastions or coastal forts
Average: 12.4, Median: 12, 19th/20 quantile: 19
Artillery is even more useful here, saving you >3 siege phases
Scenario 9: Fort level 4, +5 artillery
Probably the most common bastion scenario
Average: 6.4, Median: 6, 19th/20 quantile: 10
Scenario 10: Fort level 6
Star forts or bastions with an unchallenged coastal modifier
Average: 23.7, Median: 21, 19th/20 quantile: 44
To put it simply: you could be here a while. Even the average is more than 2 years on a 30 day siege timer
Scenario 11: Fort level 6, +1 artillery
Star forts with a sprinkle of artillery
Average: 16.4, Median: 15, 19th/20 quantile: 27
Still a while, but more manageable.
Scenario 12: Fort level 5
Technically a bastion with capital fort, or a star fort against a leader pip
Average: 18.9, Median: 18, 19th/20 quantile: 31
Almost two siege phases longer than with an artillery unit on a level 6 fort. The breach chance increase really makes itself felt here
Scenario 13: Fort level 6, +5 artillery
Star forts or bastions with an unchallenged coastal modifier
Average: 7.8, Median: 8, 19th/20 quantile: 12
Now we're talking. Get artillery, lots of it.
Scenario 14: Fort level 8
Well, this is only for academic purposes, really. Or are you willing to wait 4 years for each siege on average?
Average: 43.2, Median: 38, 19th/20 quantile: 86
Scenario 15: Fort level 8, +1 artillery
Let's see if adding artillery helps
Average: 23.2, Median: 21, 19th/20 quantile: 41
This is still quite painful...
Scenario 16: Fort level 8, +5 artillery
Maybe morey arty?
Average: 9.5, Median: 9, 19th/20 quantile: 14
Well, I guess this is sort of ok, but still, those high-level forts are a royal pain in the backside
Scenario 17: Fort level 10, +5 artillery
You sure you don't wanna put a few ships out there?
Average: 11.6, Median: 11, 19th/20 quantile: 18
Batch Results
I also ran a larger dataset, for which I didn't compile the results manually. To understand this table, you first need to realize that the artillery bonus and fort level are effective values. A larger fort level, blockade and leader bonus all work the same way - except that in the game, you need more troops for the higher fort level, you will get the same result for a level 4 fort and a level 6 fort besieged by a 2 pip general. So
effective fort level = fort level - leader siege pips + blockade
That is, a fort level of -6 in the table below can be a level 6 fort, a level 4 fort with no blockade, a level 7 fort with a 1 pip leader, etc.
The same reasoning applies to artillery and the obsolete fort bonus,
effective artillery bonus = artillery bonus + obsolete bonus
Therefore, the effective fort level varies from +3 (siege 4 leader on a capital fort) to -11 (level 8 coastal capital fort without blockade), while the effective artillery bonus varies from 0 to 8 (5 art + 3 levels obsolete)
Then there is MaxProgress: as you discover higher-level forts, the game lets you accumulate higher levels of siege progress. It starts at 12, and increases by 1 for every new fort building you discover. So if you are at tech 14, MaxProgress would be 13.
Note that a value of 10000 siege phases means the siege will not terminate
Notebook
If you have Mathematica and would like to play around with this, here is a copy of my notebook: https://dl.dropboxusercontent.com/u/95609184/sieges.nb
I was made aware that the guides forum is subscription-only, so here is a copy of the post:
So, I wanted to find out how long sieges generally take in the current game version. I believe the table on the wiki is still from the olden days, when you'd always get 1 siege progress, but since then things have changed quite a bit. Since sieges now depend on the siege history, algebraic expressions become pretty much impossible to use since factoring in all the different outcomes is, well, not easily done. But if you are better at combinatorics than I am, please let me know how to do it.
The Basics
You can find info on how sieges work on the wiki. Apart from the mean siege times table, the info seems up-to-date.
Monte Carlo
The general idea of a Monte Carlo simulation is to take a problem that involves any kind of random process and run the problem a sufficiently large number of times, varying the starting parameters randomly or over a given representative sample if needed. Examples for this can be found in nearly any scientific field, for example you could use it to simulate the motion of molecules, the weather, or the spread of the flu. Generally, the questions the MC simulation is supposed to help answer are parameter changes: what happens if people wash hands more often?
In the case of sieges in EU4, I used MC simulations to investigate the probability distribution of how many siege phases you need for certain siege scenarios. Some of the questions one can answer with this are: how much does artillery help? How much do siege leaders help? How long does it take, on average, to siege down a fort of a given level? How long for the 19/20 quantile, or 95% probability of having sieged the fort?
I simulated the siege process to the best of my knowledge using Wolfram Mathematica and implementing a siege behaviour like that observed in the game. I started each scenario 10 000 times (i.e. ran 10k virtual sieges) and compiled a histogram from the results. 10k simulations seems good enough if you're not too interested in far outliers and can be calculated in a few seconds on my rig; the average value generally fluctuated less than 0.1 siege phases. I can also evaluate average siege progress on completion, shifted distribution after one already is at a certain siege progress, etc. but I'm too lazy to prepare all the data for presentation, and most players probably don't care about it much.
Results
All results are given in siege phases. How long these take depends on several values not covered here and not pertinent to the discussion. Since the distributions all look fairly similar (especially to the untrained eye), I put them in spoilers
Here is an overview table of the different scenarios mentioned in detail
Code:
Scenario Artillery Leader Lvl Blockade Obsolete Mean Median 95% quantile
1 0 0 -2 0 0 11.5 11. 17
2 0 0 -1 0 0 9.8 10. 15
3 0 0 -3 0 0 13.4 13. 21
4 0 0 -2 -2 0 15.7 15. 25
5 1 0 -2 0 0 9.5 9. 14
6 5 0 -2 0 0 5.2 5. 8
7 5 4 -2 0 0 3.0 3. 6
8 1 0 -4 0 0 12.4 12. 19
9 5 0 -4 0 0 6.4 6. 10
10 0 0 -6 0 0 23.7 21. 44
11 1 0 -6 0 0 16.4 15. 27
12 0 0 -5 0 0 18.9 18. 31
13 5 0 -6 0 0 7.85 8. 12
14 0 0 -8 0 0 43.2 38. 86
15 1 0 -8 0 0 23.2 21. 41
16 5 0 -8 0 0 9.5 9. 14
17 5 0 -10 0 0 11.6 11. 18
Scenario 1: Fort level 2, no bonuses
This is the standard scenario for the early game non-capital forts.
Average: 11.5, Median: 11, 19th/20 quantile: 17
View attachment 138016
For the experts: As you can see, the distribution looks sorta Poisson-like, which is very much to be expected given that sieges are random and independent.
For the experts: As you can see, the distribution looks sorta Poisson-like, which is very much to be expected given that sieges are random and independent.
Scenario 2: Fort level 1, no bonuses
Capital-only fort. This is equivalent to a level 2 fort besieged by a 1-pip leader
Average: 9.9, Median: 10, 19th/20 quantile: 15
I actually expected more of a difference here, but capital forts aren't that much weaker than normal forts, requiring only 1.6 additional siege phases. In-game the intuitive difference is probably enlarged by capital forts requiring only 5 artillery for a full siege bonus (see below).
Scenario 3: Fort level 3, no bonuses
Capital plus normal fort, or bastion against a leader pip, etc
Average: 13.4, Median: 13, 19th/20 quantile: 21
Scenario 4: Fort level 2, -2 for coastal fort
If the fort is coastal, you need to blockade it or suffer an additional -2 modifier to the die roll. This also works for a bastion if you have no artillery.
Average: 15.7, Median: 15, 19th/20 quantile: 25
This takes quite a bit longer than the normal level 2 fort, so putting some ships there is a really big advantage. This observation corresponds nicely to my in-game experience.
Scenario 5: Fort level 2, +1 artillery bonus
This is a common scenario after artillery becomes available, but is not yet useful in battle, and when widespread application is too expensive.
Average: 9.5, Median: 9, 19th/20 quantile: 14
You may be wondering why this is not the same as a level 1 fort. The reason is that artillery, in addition to providing a bonus, increases your chance for a breach. Without artillery, you get a breach only on a die roll of 14. With a single artillery regiment, you get it on a roll of 13 or 14, so the probability for a breach doubles. Since breaches are high-impact events that provide a full +3 siege progress, and effectivel increase max progress, this is on average 0.4 siege phases shorter than the level 1 fort. Average number of breaches at siege won increases from 0.44 to 0.89 as expected.
+1 artillery is, however, equivalent to getting a +1 obsolete fort bonus, so this scenario also works out if you siege without art but when you already discovered bastions.
Scenario 6: Fort level 2, +5 artillery
You got the money, you got the siege.
Average: 5.2, Median: 5, 19th/20 quantile: 8
Turbo siege mode. More than twice as fast as without artillery
Scenario 7: Fort level 2, +5 artillery, +4 leader bonus
Just out of curiosity how far you can push it. This happened to me in a game only once or twice so far
Average: 3.0, Median: 3, 19th/20 quantile: 6
Scenario 8: Fort level 4, +1 artillery
For bastions or coastal forts
Average: 12.4, Median: 12, 19th/20 quantile: 19
Artillery is even more useful here, saving you >3 siege phases
Scenario 9: Fort level 4, +5 artillery
Probably the most common bastion scenario
Average: 6.4, Median: 6, 19th/20 quantile: 10
Scenario 10: Fort level 6
Star forts or bastions with an unchallenged coastal modifier
Average: 23.7, Median: 21, 19th/20 quantile: 44
To put it simply: you could be here a while. Even the average is more than 2 years on a 30 day siege timer
Scenario 11: Fort level 6, +1 artillery
Star forts with a sprinkle of artillery
Average: 16.4, Median: 15, 19th/20 quantile: 27
Still a while, but more manageable.
Scenario 12: Fort level 5
Technically a bastion with capital fort, or a star fort against a leader pip
Average: 18.9, Median: 18, 19th/20 quantile: 31
Almost two siege phases longer than with an artillery unit on a level 6 fort. The breach chance increase really makes itself felt here
Scenario 13: Fort level 6, +5 artillery
Star forts or bastions with an unchallenged coastal modifier
Average: 7.8, Median: 8, 19th/20 quantile: 12
Now we're talking. Get artillery, lots of it.
Scenario 14: Fort level 8
Well, this is only for academic purposes, really. Or are you willing to wait 4 years for each siege on average?
Average: 43.2, Median: 38, 19th/20 quantile: 86
Scenario 15: Fort level 8, +1 artillery
Let's see if adding artillery helps
Average: 23.2, Median: 21, 19th/20 quantile: 41
This is still quite painful...
Scenario 16: Fort level 8, +5 artillery
Maybe morey arty?
Average: 9.5, Median: 9, 19th/20 quantile: 14
Well, I guess this is sort of ok, but still, those high-level forts are a royal pain in the backside
Scenario 17: Fort level 10, +5 artillery
You sure you don't wanna put a few ships out there?
Average: 11.6, Median: 11, 19th/20 quantile: 18
Batch Results
I also ran a larger dataset, for which I didn't compile the results manually. To understand this table, you first need to realize that the artillery bonus and fort level are effective values. A larger fort level, blockade and leader bonus all work the same way - except that in the game, you need more troops for the higher fort level, you will get the same result for a level 4 fort and a level 6 fort besieged by a 2 pip general. So
effective fort level = fort level - leader siege pips + blockade
That is, a fort level of -6 in the table below can be a level 6 fort, a level 4 fort with no blockade, a level 7 fort with a 1 pip leader, etc.
The same reasoning applies to artillery and the obsolete fort bonus,
effective artillery bonus = artillery bonus + obsolete bonus
Therefore, the effective fort level varies from +3 (siege 4 leader on a capital fort) to -11 (level 8 coastal capital fort without blockade), while the effective artillery bonus varies from 0 to 8 (5 art + 3 levels obsolete)
Then there is MaxProgress: as you discover higher-level forts, the game lets you accumulate higher levels of siege progress. It starts at 12, and increases by 1 for every new fort building you discover. So if you are at tech 14, MaxProgress would be 13.
Note that a value of 10000 siege phases means the siege will not terminate
Code:
MaxProgress Lvl Art Mean Median 95% quantile
12 3 0 5.86 6 9
12 3 1 5.04 5 8
12 3 2 4.31 4 7
12 3 3 3.63 3 6
12 3 4 3.12 3 6
12 3 5 2.68 3 5
12 3 6 2.35 2 5
12 3 7 2.11 2 4
12 3 8 1.88 2 4
12 2 0 6.62 6 10
12 2 1 5.63 5 9
12 2 2 4.84 5 8
12 2 3 4.19 4 7
12 2 4 3.56 3 6
12 2 5 3.03 3 6
12 2 6 2.62 2 5
12 2 7 2.32 2 4
12 2 8 2.06 2 4
12 1 0 7.53 7 11
12 1 1 6.39 6 10
12 1 2 5.52 5 9
12 1 3 4.73 5 8
12 1 4 4.13 4 7
12 1 5 3.48 3 6
12 1 6 3.02 3 5
12 1 7 2.60 2 5
12 1 8 2.26 2 4
12 0 0 8.59 8 13
12 0 1 7.32 7 11
12 0 2 6.28 6 10
12 0 3 5.40 5 8
12 0 4 4.68 5 7
12 0 5 4.10 4 7
12 0 6 3.46 3 6
12 0 7 2.99 3 5
12 0 8 2.60 2 5
12 -1 0 9.92 10 15
12 -1 1 8.33 8 12
12 -1 2 7.10 7 11
12 -1 3 6.16 6 9
12 -1 4 5.27 5 8
12 -1 5 4.57 4 7
12 -1 6 4.02 4 7
12 -1 7 3.42 3 6
12 -1 8 2.96 3 5
12 -2 0 11.6 11 18
12 -2 1 9.56 9 14
12 -2 2 8.12 8 12
12 -2 3 6.88 7 10
12 -2 4 5.95 6 9
12 -2 5 5.17 5 8
12 -2 6 4.49 4 7
12 -2 7 3.92 4 6
12 -2 8 3.36 3 6
12 -3 0 13.5 13 21
12 -3 1 10.9 11 17
12 -3 2 9.12 9 14
12 -3 3 7.69 7 12
12 -3 4 6.67 6 10
12 -3 5 5.79 6 9
12 -3 6 5.01 5 8
12 -3 7 4.41 4 7
12 -3 8 3.86 4 6
12 -4 0 15.8 15 25
12 -4 1 12.4 12 19
12 -4 2 10.2 10 16
12 -4 3 8.63 8 13
12 -4 4 7.39 7 11
12 -4 5 6.40 6 10
12 -4 6 5.60 5 9
12 -4 7 4.87 5 7
12 -4 8 4.25 4 7
12 -5 0 18.8 18 31
12 -5 1 14.2 13 23
12 -5 2 11.5 11 18
12 -5 3 9.61 9 15
12 -5 4 8.19 8 12
12 -5 5 7.07 7 11
12 -5 6 6.16 6 9
12 -5 7 5.41 5 8
12 -5 8 4.73 5 7
12 -6 0 24.0 21 44
12 -6 1 16.4 15 27
12 -6 2 12.9 12 20
12 -6 3 10.7 10 17
12 -6 4 9.04 9 14
12 -6 5 7.83 8 12
12 -6 6 6.80 7 10
12 -6 7 5.97 6 9
12 -6 8 5.24 5 8
12 -7 0 32.0 28 65
12 -7 1 19.2 18 33
12 -7 2 14.5 14 23
12 -7 3 11.9 11 19
12 -7 4 10.1 10 16
12 -7 5 8.62 8 13
12 -7 6 7.50 7 11
12 -7 7 6.48 6 10
12 -7 8 5.73 6 9
12 -8 0 43.7 39 87
12 -8 1 22.9 21 40
12 -8 2 16.9 16 28
12 -8 3 13.3 13 21
12 -8 4 11.1 11 17
12 -8 5 9.46 9 14
12 -8 6 8.24 8 12
12 -8 7 7.17 7 11
12 -8 8 6.29 6 9
12 -9 0 56.9 52 107
12 -9 1 27.8 26 51
12 -9 2 19.3 18 32
12 -9 3 15.2 14 25
12 -9 4 12.4 12 20
12 -9 5 10.5 10 16
12 -9 6 9.04 9 14
12 -9 7 7.85 8 12
12 -9 8 6.90 7 10
12 -10 0 10000 10000 10000
12 -10 1 37.2 34 70
12 -10 2 22.8 21 40
12 -10 3 17.2 16 28
12 -10 4 13.9 13 22
12 -10 5 11.6 11 18
12 -10 6 9.94 10 15
12 -10 7 8.53 8 13
12 -10 8 7.47 7 11
12 -11 0 10000 10000 10000
12 -11 1 10000 10000 10000
12 -11 2 31.2 28 60
12 -11 3 20.7 19 36
12 -11 4 15.7 15 26
12 -11 5 13.1 12 21
12 -11 6 11.0 10 17
12 -11 7 9.44 9 14
12 -11 8 8.14 8 12
---------------------------------------------------------------
13 3 0 5.86 6 9
13 3 1 5.03 5 8
13 3 2 4.32 4 7
13 3 3 3.63 3 6
13 3 4 3.11 3 6
13 3 5 2.68 2 5
13 3 6 2.38 2 5
13 3 7 2.11 2 4
13 3 8 1.87 2 4
13 2 0 6.61 6 10
13 2 1 5.60 5 9
13 2 2 4.83 5 8
13 2 3 4.22 4 7
13 2 4 3.53 3 6
13 2 5 3.04 3 6
13 2 6 2.63 2 5
13 2 7 2.32 2 4
13 2 8 2.04 2 4
13 1 0 7.50 7 11
13 1 1 6.43 6 10
13 1 2 5.49 5 9
13 1 3 4.75 5 8
13 1 4 4.13 4 7
13 1 5 3.51 3 6
13 1 6 3.01 3 5
13 1 7 2.60 2 5
13 1 8 2.31 2 4
13 0 0 8.58 8 13
13 0 1 7.27 7 11
13 0 2 6.24 6 9
13 0 3 5.38 5 8
13 0 4 4.65 4 7
13 0 5 4.09 4 7
13 0 6 3.47 3 6
13 0 7 2.97 3 5
13 0 8 2.61 2 5
13 -1 0 9.84 10 14
13 -1 1 8.30 8 12
13 -1 2 7.07 7 11
13 -1 3 6.09 6 9
13 -1 4 5.29 5 8
13 -1 5 4.57 4 7
13 -1 6 4.01 4 6
13 -1 7 3.40 3 6
13 -1 8 2.92 3 5
13 -2 0 11.4 11 17
13 -2 1 9.49 9 14
13 -2 2 8.01 8 12
13 -2 3 6.92 7 10
13 -2 4 5.98 6 9
13 -2 5 5.17 5 8
13 -2 6 4.50 4 7
13 -2 7 3.91 4 6
13 -2 8 3.36 3 6
13 -3 0 13.2 13 20
13 -3 1 10.7 10 16
13 -3 2 9.00 9 13
13 -3 3 7.73 8 12
13 -3 4 6.66 7 10
13 -3 5 5.79 6 9
13 -3 6 5.02 5 8
13 -3 7 4.40 4 7
13 -3 8 3.85 4 6
13 -4 0 15.2 15 23
13 -4 1 12.2 12 18
13 -4 2 10.1 10 15
13 -4 3 8.58 8 13
13 -4 4 7.39 7 11
13 -4 5 6.39 6 10
13 -4 6 5.59 5 8
13 -4 7 4.84 5 8
13 -4 8 4.28 4 7
13 -5 0 17.7 17 27
13 -5 1 13.7 13 21
13 -5 2 11.3 11 17
13 -5 3 9.51 9 14
13 -5 4 8.16 8 12
13 -5 5 7.05 7 11
13 -5 6 6.15 6 9
13 -5 7 5.43 5 8
13 -5 8 4.72 5 7
13 -6 0 21.2 20 35
13 -6 1 15.8 15 25
13 -6 2 12.6 12 19
13 -6 3 10.5 10 16
13 -6 4 9.03 9 14
13 -6 5 7.77 8 12
13 -6 6 6.75 7 10
13 -6 7 5.96 6 9
13 -6 8 5.27 5 8
13 -7 0 26.1 24 46
13 -7 1 18.2 17 30
13 -7 2 14.2 14 23
13 -7 3 11.7 11 18
13 -7 4 9.93 10 15
13 -7 5 8.55 8 13
13 -7 6 7.46 7 11
13 -7 7 6.49 6 10
13 -7 8 5.72 6 9
13 -8 0 34.2 30 67
13 -8 1 21.1 20 35
13 -8 2 16.1 15 26
13 -8 3 13.1 13 20
13 -8 4 11.0 11 17
13 -8 5 9.40 9 14
13 -8 6 8.16 8 12
13 -8 7 7.15 7 11
13 -8 8 6.26 6 9
13 -9 0 44.9 40 87
13 -9 1 25.1 23 44
13 -9 2 18.3 17 30
13 -9 3 14.6 14 23
13 -9 4 12.2 12 19
13 -9 5 10.4 10 16
13 -9 6 8.95 9 13
13 -9 7 7.79 8 12
13 -9 8 6.88 7 10
13 -10 0 57.3 52 107
13 -10 1 29.1 27 51
13 -10 2 20.6 19 34
13 -10 3 16.3 15 26
13 -10 4 13.5 13 21
13 -10 5 11.4 11 17
13 -10 6 9.78 9 15
13 -10 7 8.45 8 12
13 -10 8 7.46 7 11
13 -11 0 10000 10000 10000
13 -11 1 38.4 35 70
13 -11 2 24.3 23 41
13 -11 3 18.4 17 29
13 -11 4 15.0 14 24
13 -11 5 12.6 12 19
13 -11 6 10.7 10 16
13 -11 7 9.30 9 14
13 -11 8 8.05 8 12
---------------------------------------------------------------
14 3 0 5.85 6 9
14 3 1 5.02 5 8
14 3 2 4.31 4 7
14 3 3 3.61 3 6
14 3 4 3.09 3 6
14 3 5 2.70 3 5
14 3 6 2.36 2 5
14 3 7 2.10 2 4
14 3 8 1.89 2 4
14 2 0 6.60 6 10
14 2 1 5.65 6 9
14 2 2 4.87 5 8
14 2 3 4.20 4 7
14 2 4 3.55 3 6
14 2 5 3.02 3 6
14 2 6 2.62 2 5
14 2 7 2.30 2 4
14 2 8 2.05 2 4
14 1 0 7.43 7 11
14 1 1 6.39 6 10
14 1 2 5.51 5 9
14 1 3 4.78 5 8
14 1 4 4.14 4 7
14 1 5 3.48 3 6
14 1 6 3.00 3 5
14 1 7 2.61 2 5
14 1 8 2.30 2 4
14 0 0 8.54 8 12
14 0 1 7.33 7 11
14 0 2 6.27 6 10
14 0 3 5.39 5 8
14 0 4 4.66 5 7
14 0 5 4.11 4 7
14 0 6 3.45 3 6
14 0 7 2.97 3 5
14 0 8 2.60 2 5
14 -1 0 9.77 10 14
14 -1 1 8.29 8 12
14 -1 2 7.09 7 11
14 -1 3 6.16 6 9
14 -1 4 5.28 5 8
14 -1 5 4.58 4 7
14 -1 6 4.03 4 7
14 -1 7 3.38 3 6
14 -1 8 2.93 3 5
14 -2 0 11.3 11 16
14 -2 1 9.44 9 14
14 -2 2 8.01 8 12
14 -2 3 6.88 7 10
14 -2 4 5.97 6 9
14 -2 5 5.15 5 8
14 -2 6 4.51 4 7
14 -2 7 3.94 4 6
14 -2 8 3.37 3 6
14 -3 0 13.0 13 19
14 -3 1 10.6 10 16
14 -3 2 9.03 9 13
14 -3 3 7.69 7 11
14 -3 4 6.65 6 10
14 -3 5 5.77 6 9
14 -3 6 5.01 5 8
14 -3 7 4.40 4 7
14 -3 8 3.87 4 6
14 -4 0 14.9 14 22
14 -4 1 12.1 12 18
14 -4 2 10.0 10 15
14 -4 3 8.59 8 13
14 -4 4 7.35 7 11
14 -4 5 6.42 6 10
14 -4 6 5.59 5 8
14 -4 7 4.83 5 8
14 -4 8 4.27 4 7
14 -5 0 17.3 17 26
14 -5 1 13.6 13 21
14 -5 2 11.2 11 17
14 -5 3 9.58 9 14
14 -5 4 8.18 8 12
14 -5 5 7.07 7 11
14 -5 6 6.18 6 9
14 -5 7 5.43 5 8
14 -5 8 4.71 5 7
14 -6 0 20.2 19 32
14 -6 1 15.4 15 24
14 -6 2 12.5 12 19
14 -6 3 10.5 10 16
14 -6 4 9.01 9 14
14 -6 5 7.77 8 12
14 -6 6 6.75 7 10
14 -6 7 5.95 6 9
14 -6 8 5.24 5 8
14 -7 0 24.0 23 39
14 -7 1 17.6 17 28
14 -7 2 14.0 13 22
14 -7 3 11.7 11 18
14 -7 4 9.87 10 15
14 -7 5 8.56 8 13
14 -7 6 7.41 7 11
14 -7 7 6.49 6 10
14 -7 8 5.72 6 9
14 -8 0 29.7 27 52
14 -8 1 20.1 19 33
14 -8 2 15.7 15 25
14 -8 3 13.0 12 20
14 -8 4 10.9 11 17
14 -8 5 9.33 9 14
14 -8 6 8.12 8 12
14 -8 7 7.11 7 10
14 -8 8 6.22 6 9
14 -9 0 37.9 34 71
14 -9 1 23.7 22 40
14 -9 2 17.8 17 29
14 -9 3 14.4 14 22
14 -9 4 12.0 11 18
14 -9 5 10.3 10 16
14 -9 6 8.93 9 13
14 -9 7 7.77 8 11
14 -9 8 6.89 7 10
14 -10 0 46.2 42 88
14 -10 1 26.5 25 45
14 -10 2 19.8 19 32
14 -10 3 15.9 15 25
14 -10 4 13.2 13 20
14 -10 5 11.2 11 17
14 -10 6 9.67 9 14
14 -10 7 8.41 8 12
14 -10 8 7.46 7 11
14 -11 0 58.6 54 108
14 -11 1 31.3 29 53
14 -11 2 22.3 21 36
14 -11 3 17.8 17 28
14 -11 4 14.6 14 22
14 -11 5 12.3 12 19
14 -11 6 10.6 10 16
14 -11 7 9.22 9 13
14 -11 8 8.04 8 12
---------------------------------------------------------------
15 3 0 5.86 6 9
15 3 1 5.00 5 8
15 3 2 4.35 4 7
15 3 3 3.64 3 6
15 3 4 3.13 3 6
15 3 5 2.70 3 5
15 3 6 2.34 2 5
15 3 7 2.09 2 4
15 3 8 1.87 2 4
15 2 0 6.62 6 10
15 2 1 5.62 5 9
15 2 2 4.82 5 8
15 2 3 4.16 4 7
15 2 4 3.52 3 6
15 2 5 3.01 3 6
15 2 6 2.62 2 5
15 2 7 2.32 2 4
15 2 8 2.05 2 4
15 1 0 7.42 7 11
15 1 1 6.44 6 10
15 1 2 5.48 5 9
15 1 3 4.76 5 8
15 1 4 4.13 4 7
15 1 5 3.49 3 6
15 1 6 3.00 3 5
15 1 7 2.63 2 5
15 1 8 2.29 2 4
15 0 0 8.53 8 12
15 0 1 7.26 7 11
15 0 2 6.23 6 10
15 0 3 5.38 5 8
15 0 4 4.67 5 7
15 0 5 4.09 4 7
15 0 6 3.42 3 6
15 0 7 2.98 3 5
15 0 8 2.60 2 5
15 -1 0 9.76 10 14
15 -1 1 8.26 8 12
15 -1 2 7.06 7 11
15 -1 3 6.12 6 9
15 -1 4 5.27 5 8
15 -1 5 4.58 4 7
15 -1 6 4.01 4 7
15 -1 7 3.41 3 6
15 -1 8 2.92 3 5
15 -2 0 11.3 11 16
15 -2 1 9.35 9 14
15 -2 2 8.05 8 12
15 -2 3 6.87 7 10
15 -2 4 5.98 6 9
15 -2 5 5.13 5 8
15 -2 6 4.51 4 7
15 -2 7 3.95 4 6
15 -2 8 3.35 3 6
15 -3 0 12.9 13 19
15 -3 1 10.6 10 16
15 -3 2 8.99 9 13
15 -3 3 7.72 8 11
15 -3 4 6.64 6 10
15 -3 5 5.80 6 9
15 -3 6 5.00 5 8
15 -3 7 4.40 4 7
15 -3 8 3.84 4 6
15 -4 0 14.8 14 22
15 -4 1 12.0 12 18
15 -4 2 10.0 10 15
15 -4 3 8.55 8 13
15 -4 4 7.37 7 11
15 -4 5 6.40 6 10
15 -4 6 5.60 5 8
15 -4 7 4.89 5 8
15 -4 8 4.26 4 7
15 -5 0 17.0 17 25
15 -5 1 13.6 13 20
15 -5 2 11.2 11 17
15 -5 3 9.49 9 14
15 -5 4 8.14 8 12
15 -5 5 7.05 7 10
15 -5 6 6.18 6 9
15 -5 7 5.41 5 8
15 -5 8 4.72 5 7
15 -6 0 19.6 19 30
15 -6 1 15.3 15 23
15 -6 2 12.6 12 19
15 -6 3 10.5 10 16
15 -6 4 8.94 9 13
15 -6 5 7.75 8 11
15 -6 6 6.80 7 10
15 -6 7 5.92 6 9
15 -6 8 5.25 5 8
15 -7 0 23.2 22 37
15 -7 1 17.3 17 27
15 -7 2 13.9 13 21
15 -7 3 11.6 11 18
15 -7 4 9.82 10 15
15 -7 5 8.52 8 13
15 -7 6 7.43 7 11
15 -7 7 6.48 6 10
15 -7 8 5.72 6 9
15 -8 0 28.0 26 46
15 -8 1 19.7 19 32
15 -8 2 15.6 15 24
15 -8 3 12.9 12 20
15 -8 4 10.9 11 17
15 -8 5 9.39 9 14
15 -8 6 8.06 8 12
15 -8 7 7.11 7 11
15 -8 8 6.26 6 9
15 -9 0 35.1 32 65
15 -9 1 22.9 21 38
15 -9 2 17.5 17 28
15 -9 3 14.3 14 22
15 -9 4 12.0 11 18
15 -9 5 10.3 10 15
15 -9 6 8.90 9 13
15 -9 7 7.80 8 11
15 -9 8 6.86 7 10
15 -10 0 40.1 37 73
15 -10 1 25.5 24 43
15 -10 2 19.2 18 30
15 -10 3 15.6 15 24
15 -10 4 13.1 13 20
15 -10 5 11.2 11 17
15 -10 6 9.64 9 14
15 -10 7 8.45 8 12
15 -10 8 7.42 7 11
15 -11 0 48.6 44 88
15 -11 1 28.8 27 48
15 -11 2 21.3 20 34
15 -11 3 17.2 16 26
15 -11 4 14.2 14 21
15 -11 5 12.2 12 18
15 -11 6 10.5 10 15
15 -11 7 9.19 9 13
15 -11 8 8.07 8 12
Notebook
If you have Mathematica and would like to play around with this, here is a copy of my notebook: https://dl.dropboxusercontent.com/u/95609184/sieges.nb
Last edited:
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