add your total attack power and total hit points
add up their total defensive power and total hit points
When you exceed them by a combined total (hit points plus attack power) of 8 or more, you are very likely to win (55+%)
If you exceed them by 16 or more, it will be a wipeout, and casualty choosing/preserving forces) is your primary goal
If the ##s are equal, as far as total hits and total power, then it is a 50/50 battle.
These calculations are best done on the fly and I use estimating to evaluate the chances of success each turn.
Using a true calculator doesn’t take special rules into account (such as that the attackers carriers do not attack and thus do not lose him any attack power but can absorb hits, has won me several major battles) and it is not permitted in tournaments, its not particular fair or time thoughtful, and it doesn’t reveal any more information than on the fly addition
You wanted quick and dirty right, just repeat the process in case there are any defending/attacking units left. Basicaly you asume the average hits from both sides and then continue.
It is also usefull to determine if you should press the attack or retreat, sometimes it is better to leave 2 tanks standing then to expose your 10 tanks to a counterattackUnless you can do square root calculations without a calculator ofcourse ( i surely cant )
I already know how to do what you’re suggesting. And yes, I can do square root calculations without a calculator.
Marsh
@Baron:
Bumped.
Please, Wittmann or Panther, move this thread into Player help.
Thanks.
Done - Thank you for bringing it up.
Yes.
TLDR Version : (number Attacker units needed for 50% chance) = (Number of Defender units) * SQRT ( ( Average Defender Strength) / (Average Attacker Strength))
My formula is exact and easy to prove correct when you attack with only units of one type, against only units of a different type ( like inf v inf, inf v tanks, inf v ftrs, etc). I am a mathematician, I can send you the proof if you don’t trust me.
If average Defence power is 2, and average attack power is 1, then you need Sqrt(2) (1.141 number of units to win the attack 50%
I have made some calculations. If you assume you attack with only units with strength 1, and the defenders have only units of strength 2,3,4, then the number of units needed to have 50% chance of taking the terr is as follows;
1 v2 -> (sqrt(2) =) 1,41… This means that 141 infs will have less than 50%, while 142 has more than 50% against 100 infs defenders.
1v3 -> (sqrt(3) = )1.73… This means that 173 infs will have less than 50%, while 174 has more than 50% against 100 tanks defenders
1v4 -> (sqrt(4) =) 2 . So 200 infs have exactly 50% chance of winning against 100 planes.
2v4- > (sqrt(2) =) 1,41… This means that 141 art will have less than 50%, while 142 has more than 50% against 100 ftr defenders.The main advantage of the attacking infs is that they lose less of their combatstrenght when taking losses, than defenders does. This is why they need fewer dice than the defendes.
Lets assume that the defender has the highest average strength (it the attacker has the highest, just switch it around)
The quick and dirty formula will then be :
strenghtratio = (Defenders Average Strength) / (attackers average strength)
Number of units needed for 50% to win for the attackers will then be:
#Numbers needed = SQRT(Strength Ratio) * (#Number of Defender units)This will change depending on the “structure” of the strength, however it will not be a Huge change. The more diverse, the better the force is. A force defening force of 50% inf and 50% FTRs is better than a defending force of 100% tanks. So depending on Who I judge to have the better designed force, I add some Strength to that side when I calculate the average strength
Unless you can do square root calculations without a calculator ofcourse ( i surely cant )
You dont really need to, all you need is a ballpark.
If I tell you
Sqrt(1,25) = 1,12
SQRT(1,5) = 1,22
SQRT(2) = 1,41
SQRT(3) = 1,7
SQRT(4) = 2Now, if you just remember those, you can easily guess how many units you need. You don’t actually have to calculate anything, you can just use it to get a feel for the strength. You can just go : hmmm If I put my stack next to his, can he attack? I got 60 units, how many does he have? He has 90…. opps better not do that then. Or he has 70… hmm maybe I should, or does he have too many tanks and planes among those 70?.. hmm 30 planes and tanks,… better not do that then.
If you really just want to do a short calc to get more familiar, you could count and approximate average strength and use the table from above. You will usually just have to figure out which ratio you are cloesest to among the ones in the list. The difference between 1.22 and 1.12 is rarely more than a couple of units. (unless the stacks re 50+ ofc)
So defender has 40 units, with avg strenght of 2,3 and I can attack with avg strength of 1,4. Then the ratio is about 1,5- 1.7, I should then have more than (if its 1,22) 55 units, bud do not need more than 65 units to have the minimum attack.I use it as a tool to get a feel for the combat powers of stacks , to better evaluate my position. For me it is all about NOT having to calculate. Whenever oyu check stacks, you count number of units and number of eyes anyways. The most surprising insight this will give to many is that you need only about 1,41 to win when inf is attacking inf.
This table below is also derived on Kreuzfeld formula.
It might help visualize all he is talking about 1.41, for instance.
Lanchester’s Tables for Axis and Allies 2nd Edition
I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
√(P2 / P1) = N1 / N2| Avg Power
1
1.5
2
2.5
3
3.5
4
4, 2hits | 1
1.00
0.82
0.70
0.63
0.58
0.53
0.50
0.31
| 1.5
1.22
1.00
0.87
0.77
0.70
0.65
0.62
0.38
| 2
1.41
1.15
1.00
0.89
0.82
0.76
0.70
0.43
| 2.5
1.58
1.29
1.12
1.00
0.91
0.85
0.79
0.50
| 3
1.73
1.41
1.22
1.10
1.00
0.93
0.87
0.53
| 3.5
1.87
1.53
1.32
1.18
1.08
1.00
0.94
0.58
| 4
2.00
1.62
1.41
1.26
1.15
1.07
1.00
0.62
| 4, 2hits
3.33
2.64
2.30
2.00
1.87
1.73
1.62
1.00| Avg Power
1
1.5
2
2.5
3
3.5
4
4, 2hits | 1
1:1
9:11
12:17
5:8
4:7
9:17
1:2
3:10|
1.5
11:9
1:1
13:15
7:9
12:17
9:14
5:8
3:8
| 2
17:12
15:13
1:1
9:10
9:11
3:4
12:17
3:7
| 2.5
8:5
9:7
10:9
1:1
10:11
5:6
4:5
1:2
| 3
7:4
17:12
11:9
11:10
1:1
19:20
13:15
9:17
| 3.5
17:9
14:9
4:3
6:5
20:19
1:1
20:21
4:7
| 4
2:1
8:5
17:12
5:4
15:13
21:20
1:1
5:8
| 4, 2hits
10:3
8:3
7:3
2:1
17:9
7:4
8:5
1:1|
|
Extended Lanchester’s Tables for Axis and Allies 2nd Edition
I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
√(P2 / P1) = N1 / N2
| Avg Power
0.5
1
1.5
2
2.5
3
3.5
4
4, 2hits
5 | 0.5
1.00
0.70
0.58
0.50
0.45
0.41
0.38
0.35
0.22
0.32
| 1
1.41
1.00
0.82
0.70
0.63
0.58
0.53
0.50
0.31
0.45
| 1.5
1.73
1.22
1.00
0.87
0.77
0.70
0.65
0.62
0.38
0.55
| 2
2.00
1.41
1.15
1.00
0.89
0.82
0.76
0.70
0.43
0.63
| 2.5
2.24
1.58
1.29
1.12
1.00
0.91
0.85
0.79
0.50
0.70
| 3
2.45
1.73
1.41
1.22
1.10
1.00
0.93
0.87
0.53
0.77
| 3.5
2.65
1.87
1.53
1.32
1.18
1.08
1.00
0.94
0.58
0.84
| 4
2.83
2.00
1.62
1.41
1.26
1.15
1.07
1.00
0.62
0.89
| 4, 2hits
4.58
3.33
2.64
2.30
2.00
1.87
1.73
1.62
1.00
1.41
| 5
3.16
2.24
1.83
1.58
1.41
1.29
1.20
1.12
0.70
1.00
| Avg Power
0.5
1
1.5
2
2.5
3
3.5
4
4, 2hits
5 | 0.5
1:1
12:17
4:7
1:2
4:9
5:12
5:13
5:14
2:9
5:16
| 1
17:12
1:1
9:11
12:17
5:8
4:7
9:17
1:2
3:10
4:9
|
1.5
7:4
11:9
1:1
13:15
7:9
12:17
9:14
5:8
3:8
5:9
| 2
2:1
17:12
15:13
1:1
9:10
9:11
3:4
12:17
3:7
5:8
| 2.5
9:4
8:5
9:7
10:9
1:1
10:11
5:6
4:5
1:2
12:17
| 3
12:5
7:4
17:12
11:9
11:10
1:1
19:20
13:15
9:17
7:9
| 3.5
13:5
17:9
14:9
4:3
6:5
20:19
1:1
20:21
4:7
5:6
| 4
14:5
2:1
8:5
17:12
5:4
15:13
21:20
1:1
5:8
9:10
| 4, 2hits
9:2
10:3
8:3
7:3
2:1
17:9
7:4
8:5
1:1
17:12
| 5
16:5
9:4
9:5
8:5
17:12
9:7
6:5
10:9
12:17
1:1
|
|
There’s not such a thing because the die rolls vary. :-( :-( :-(
Hey guys, this formula is really useful. I would love to see the proof for this. It’s not that I don’t trust you, I just want to see how you derived it, thanks!
-GK
Ok so I tested manually 141 infantry attacking 100 infantry defending and the results was 12 infantry left standing on the attacks vs 0 on the defense. AAcalc gives this result as well.
Shouldn’t the remaining infantry be the same on both sides if the battle is supposed to be exactly 50:50 according to the table/formula?
I find that this works exceedingly well with the well known Larry -Marx formula. Its well known.
Larry Marx has nothing to do with battle estimation, it’s for evaluating HR units and comparing unit to one another.
@Genghis:
Ok so I tested manually 141 infantry attacking 100 infantry defending and the results was 12 infantry left standing on the attacks vs 0 on the defense. AAcalc gives this result as well.
Shouldn’t the remaining infantry be the same on both sides if the battle is supposed to be exactly 50:50 according to the table/formula?
It gives a 1% avg of 11 Infs defenders winning compared to an avg of 1% 17 Infs attackers wins. If 142 vs 100 for a 51.6% vs 48.6%
If it is 141 vs 100, your odds are 48% vs 52%.
You may get a finner tuning but it is between 1.410… and 1.420 ratio.
50% is a put as 17 @1 vs 12 @2.
Which is 1.41666…
√(P2 / P1) = N1 / N2
√2/1= 1.4142
With more units in play, more accurate the formula will be.
Larry-Marx is the circle of life compared to Vann shoes formula…
@Genghis:
Hey guys, this formula is really useful. I would love to see the proof for this. It’s not that I don’t trust you, I just want to see how you derived it, thanks!
-GK
I think CalvinandHobbesliker made a PDF about this formula:
http://www.axisandallies.org/forums/index.php?topic=39526.msg1642941#msg1642941
I cannot find Kreuzfeld equations but I’m pretty sure he provided these somewhere.
The table above is more accurate and the fractions in the second table are an approximation from the first table.
I tried to provide as small number as possible on both part of fraction.
@Baron:
Extended Lanchester’s Tables for Axis and Allies 2nd Edition
I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
√(P2 / P1) = N1 / N2| Avg Power
0.5
1
1.5
2
2.5
3
3.5
4
4, 2hits
5 | 0.5
1.00
0.70
0.58
0.50
0.45
0.41
0.38
0.35
0.22
0.32
| 1
1.41
1.00
0.82
0.70
0.63
0.58
0.53
0.50
0.31
0.45
| 1.5
1.73
1.22
1.00
0.87
0.77
0.70
0.65
0.62
0.38
0.55
| 2
2.00
1.41
1.15
1.00
0.89
0.82
0.76
0.70
0.43
0.63
| 2.5
2.24
1.58
1.29
1.12
1.00
0.91
0.85
0.79
0.50
0.70
| 3
2.45
1.73
1.41
1.22
1.10
1.00
0.93
0.87
0.53
0.77
| 3.5
2.65
1.87
1.53
1.32
1.18
1.08
1.00
0.94
0.58
0.84
| 4
2.83
2.00
1.62
1.41
1.26
1.15
1.07
1.00
0.62
0.89
| 4, 2hits
4.58
3.33
2.64
2.30
2.00
1.87
1.73
1.62
1.00
1.41
| 5
3.16
2.24
1.83
1.58
1.41
1.29
1.20
1.12
0.70
1.00| Avg Power
0.5
1
1.5
2
2.5
3
3.5
4
4, 2hits
5 | 0.5
1:1
12:17
4:7
1:2
4:9
5:12
5:13
5:14
2:9
5:16
| 1
17:12
1:1
9:11
12:17
5:8
4:7
9:17
1:2
3:10
4:9
|
1.5
7:4
11:9
1:1
13:15
7:9
12:17
9:14
5:8
3:8
5:9
| 2
2:1
17:12
15:13
1:1
9:10
9:11
3:4
12:17
3:7
5:8
| 2.5
9:4
8:5
9:7
10:9
1:1
10:11
5:6
4:5
1:2
12:17
| 3
12:5
7:4
17:12
11:9
11:10
1:1
19:20
13:15
9:17
7:9
| 3.5
13:5
17:9
14:9
4:3
6:5
20:19
1:1
20:21
4:7
5:6
| 4
14:5
2:1
8:5
17:12
5:4
15:13
21:20
1:1
5:8
9:10
| 4, 2hits
9:2
10:3
8:3
7:3
2:1
17:9
7:4
8:5
1:1
17:12
| 5
16:5
9:4
9:5
8:5
17:12
9:7
6:5
10:9
12:17
1:1|
|
Awesome Baron, I will go over the math later but does this proof validate the Lanchester table?
Taking the original question in a different direction (strategy instead of math), I noticed recently that I always try to send just enough force to a region that it would be inefficiently expensive for my opponent to challenge me.
For example, as Japan, when invading eastern Russia, how much force do you need to send? If you are much, much stronger than Russia, and you can sack the capital, fine, do that. Not interesting. If you are much, much weaker than Russia, and you are not going to even be able to keep an active beachhead, fine, stay home. Also not interesting. The interesting case is the middle ground, where you are strong enough to be a real pain in Russia’s behind, but not strong enough yet to be seriously planning an attack on Moscow.
In that case, you want to send enough force that it would cost Russia more to repel your forces than to just let you sit in Kazakh and Novosibirsk and Evenki. If you are conquering, e.g., 5 IPCs’ worth of territory, and you expect to hold it for roughly 3 turns before the global strategic situation changes again, then the stakes are a 30 IPC swing (5 IPCs * 3 turns * 2 players), so you need a force that’s large enough that Russia can’t kill it without losing at least 30 IPCs’ worth of troops. Depending on Russia’s force mix, this could be more or less than 30 IPCs’ worth of your units. If Russia has almost nothing but infantry, then even a small Japanese force of, e.g., 4 infantry and 2 tanks (24 IPCs) might be a fair match on defense against 10 attacking Russian infantry. If Russia has plenty of artillery and air support, then even a large Japanese force of, e.g., 4 infantry and 5 tanks (42 IPCs) might get crushed by a Russian counter-attack of 6 infantry, 3 artillery, and 6 fighters – Russia’s not going to lose more than 30 IPCs on that battle, and the planes are not really going to be taken away from their positions, but Russia can still repel your 42-IPC force.
So you want to think about what it would actually cost your enemy to repel your forces, and then make your invasion force just large enough that your enemy will lose more money from building or diverting the counter-attack than it would lose by letting you have the extra territories. That way you set up a win-win situation: if they let you have the territory without a fight, you win because your income goes up and theirs goes down, but if they fight you for the territory, then they lose so many resources that holding the ground winds up being a net economic loss for them.
The reason why you don’t just go in with everything you can afford to build is that you might need some of those forces to set up a similar no-win scenario for your opponents on another front – sticking with Japan, if you send too many assets into Russia, you usually won’t have enough cash left over to make sure that the Pacific islands are too expensive for America to take, and so on. There are exceptions; sometimes you can just steamroll everyone at once – but in those games, you don’t need a strategy guide!
@Genghis:
Awesome Baron, I will go over the math later but does this proof validate the Lanchester table?
I know from various empirical use of AACalc, these table works and Lanchester is working too.
To assess strength of a stack, you need to sum all attack or defense points then multiply by hits instead of adding hits. This work easily for 1 hit units.
the tables and formula (and its proof) work for when all attacking units are the same unit and when all the defending units are the same unit. Otherwise you have to approximate by calculating an average power and average number of units. Example:
on attack: 5 infantry, 4 tanks, 2 fighter.
Total pips: 5+4(3)+2(3) = 23.
Number of units = 5+4+2 = 11
23/11=2
So we can approximate this stack with 11 units hitting at 2, or 11 artillery.
I guess you would use power level 2 and number of units 11 for the purposes of lanchester tables.
@Genghis:
the tables and formula (and its proof) work for when all attacking units are the same unit and when all the defending units are the same unit. Otherwise you have to approximate by calculating an average power and average number of units. Example:
on attack: 5 infantry, 4 tanks, 2 fighter.
Total pips: 5+4(3)+2(3) = 23.
Number of units = 5+4+2 = 1123/11=2
So we can approximate this stack with 11 units hitting at 2, or 11 artillery.
I guess you would use power level 2 and number of units 11 for the purposes of lanchester tables.
Yes, exactly.
This table is made for square number basically.
I extended to half, like 1.5 or 2.5 to make for average power of a mixed stack.
Like 1 A3 and 3 A1 means A6 for 4 hits, hence 1.5 avg.
So, such stack will be about same as 7 D 0.5, for instance 5 AAA with 2 Infs (D4/7 = 0.57)
The table say 50% is 0.58. And table below is an approximate to 4:7 ratio.
Now, if there is a big skew between stack, (not the case in last example because both stack have skew)
I learned from the general formula that you get a 10% meta-power increase. However, such results have to be divided by number of hits to get a better avg of power per unit.
For instance, 1 Tank and 3 Inf gives A64 = 241.1= 26.4 metapower /4 hits = 6.6 for this stack or 1.65 per 1 hit unit.
2 Infs and 5 AAA D4 means 4.4 divided by 7 = 0.63 per 1 hit unit.
Of course, using the whole formula get more accurate result but for fast reference you can use avg and this table.
@Baron:
Extended Lanchester’s Tables for Axis and Allies 2nd Edition
I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
P = Average Power of a given stack
N = Number of units of a given stack√(P2 / P1) = N1 / N2
| Avg Power
0.5
1
1.5
2
2.5
3
3.5
4
4, 2hits
5 | 0.5
1.00
0.70
0.58
0.50
0.45
0.41
0.38
0.35
0.22
0.32
| 1
1.41
1.00
0.82
0.70
0.63
0.58
0.53
0.50
0.31
0.45
| 1.5
1.73
1.22
1.00
0.87
0.77
0.70
0.65
0.62
0.38
0.55
| 2
2.00
1.41
1.15
1.00
0.89
0.82
0.76
0.70
0.43
0.63
| 2.5
2.24
1.58
1.29
1.12
1.00
0.91
0.85
0.79
0.50
0.70
| 3
2.45
1.73
1.41
1.22
1.10
1.00
0.93
0.87
0.53
0.77
| 3.5
2.65
1.87
1.53
1.32
1.18
1.08
1.00
0.94
0.58
0.84
| 4
2.83
2.00
1.62
1.41
1.26
1.15
1.07
1.00
0.62
0.89
| 4, 2hits
4.58
3.33
2.64
2.30
2.00
1.87
1.73
1.62
1.00
1.41
| 5
3.16
2.24
1.83
1.58
1.41
1.29
1.20
1.12
0.70
1.00| Avg Power
0.5
1
1.5
2
2.5
3
3.5
4
4, 2hits
5 | 0.5
1:1
12:17
4:7
1:2
4:9
5:12
5:13
5:14
2:9
5:16
| 1
17:12
1:1
9:11
12:17
5:8
4:7
9:17
1:2
3:10
4:9
|
1.5
7:4
11:9
1:1
13:15
7:9
12:17
9:14
5:8
3:8
5:9
| 2
2:1
17:12
15:13
1:1
9:10
9:11
3:4
12:17
3:7
5:8
| 2.5
9:4
8:5
9:7
10:9
1:1
10:11
5:6
4:5
1:2
12:17
| 3
12:5
7:4
17:12
11:9
11:10
1:1
19:20
13:15
9:17
7:9
| 3.5
13:5
17:9
14:9
4:3
6:5
20:19
1:1
20:21
4:7
5:6
| 4
14:5
2:1
8:5
17:12
5:4
15:13
21:20
1:1
5:8
9:10
| 4, 2hits
9:2
10:3
8:3
7:3
2:1
17:9
7:4
8:5
1:1
17:12
| 5
16:5
9:4
9:5
8:5
17:12
9:7
6:5
10:9
12:17
1:1|
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Taking the original question in a different direction (strategy instead of math), I noticed recently that I always try to send just enough force to a region that it would be inefficiently expensive for my opponent to challenge me.
For example, as Japan, when invading eastern Russia, how much force do you need to send? If you are much, much stronger than Russia, and you can sack the capital, fine, do that. Not interesting. If you are much, much weaker than Russia, and you are not going to even be able to keep an active beachhead, fine, stay home. Also not interesting. The interesting case is the middle ground, where you are strong enough to be a real pain in Russia’s behind, but not strong enough yet to be seriously planning an attack on Moscow.
In that case, you want to send enough force that it would cost Russia more to repel your forces than to just let you sit in Kazakh and Novosibirsk and Evenki. If you are conquering, e.g., 5 IPCs’ worth of territory, and you expect to hold it for roughly 3 turns before the global strategic situation changes again, then the stakes are a 30 IPC swing (5 IPCs * 3 turns * 2 players), so you need a force that’s large enough that Russia can’t kill it without losing at least 30 IPCs’ worth of troops. Depending on Russia’s force mix, this could be more or less than 30 IPCs’ worth of your units. If Russia has almost nothing but infantry, then even a small Japanese force of, e.g., 4 infantry and 2 tanks (24 IPCs) might be a fair match on defense against 10 attacking Russian infantry. If Russia has plenty of artillery and air support, then even a large Japanese force of, e.g., 4 infantry and 5 tanks (42 IPCs) might get crushed by a Russian counter-attack of 6 infantry, 3 artillery, and 6 fighters – Russia’s not going to lose more than 30 IPCs on that battle, and the planes are not really going to be taken away from their positions, but Russia can still repel your 42-IPC force.
So you want to think about what it would actually cost your enemy to repel your forces, and then make your invasion force just large enough that your enemy will lose more money from building or diverting the counter-attack than it would lose by letting you have the extra territories. That way you set up a win-win situation: if they let you have the territory without a fight, you win because your income goes up and theirs goes down, but if they fight you for the territory, then they lose so many resources that holding the ground winds up being a net economic loss for them.
The reason why you don’t just go in with everything you can afford to build is that you might need some of those forces to set up a similar no-win scenario for your opponents on another front – sticking with Japan, if you send too many assets into Russia, you usually won’t have enough cash left over to make sure that the Pacific islands are too expensive for America to take, and so on. There are exceptions; sometimes you can just steamroll everyone at once – but in those games, you don’t need a strategy guide!
Bumped. I don’t want this be burried too fast in past page.
