Grasshopper's 8d System - Conversion tables for 1940 Global units

@Young:

So you both want Artillery that Att and Def 3/8?

Yes

@SS:

@Young:

So you both want Artillery that Att and Def 3/8?

Yes

Yes.
There is more reasons this will make a more interesting game.
Such Artillery, I bet will improve the game.
Same as Cruiser A5 D5 will be more interesting purchase, so Artillery A3 D3 too.

YG’s complete D8s roster

Here is the comparative with Enigma formula (still using a 12 IPCs unit reference) based on odds, not dice number.
144*Odds/cost^2 = strength of unit on same odds by hit per IPCs basis.

I bolded the greatest number between D8 or D6 for same unit.
When there is no difference, I quoted it.
So, you can see at glance which is boosted or nerfed compared to OOB.

Unit type  Combat value  (D8 system) (D6 OOB)
Infantry       A1-2 D2    (2.00-** / 4.00)         (2.67-3.92 / 5.33)
Inf A2+Arty A2 D2         2.94**  /  2.94         (3.92 / 3.92)
Inf A2+Arty A3 D2         3.67**  /  2.94         Same as above
Inf A2+Arty A3 D3         3.67**  /  3.67         Same as above

MechInfantry A1-2 D2  (1.125-** / 2.25)       (1.50-3.00 / 3.00)
MechInf A2+Art A2 D2  (2.25** / 2.25) vs       (3.00 / 3.00)
MechInf A2+Art A3 D2  (2.81** / 2.25) vs        Same as above
MechInf A2+Art A3 D3  (2.81** / 2.81) vs        Same as above

Artillery   A2 D2       (2.25 / 2.25)                  (3.00 / 3.00)
Artillery    A3 D2    (3.375 / 2.25) avg: 2.813  Same as above
Artillery    A3 D3       (3.375 / 3.375)             Same as above

Tank         A4 D4            (2.00 / 2.00)            (2.00 / 2.00)

Anti-Air A  A0 D1* (0.00 / 0.72 per plane)       (0.00 / 0.96 per plane)

Fighter      A4 D5    (0.72 / 0.90 )              (0.72 / 0.96)

TcBomber  A4-5 D4 (0.595-** / 0.595)       (0.595 / 0.595)

TcB A5+Tank C17    (1.12** / 1.00)         (1.16 / 1.00)
TcB A5+Fighter C21 (0.735** / 0.653)     (0.761 / 0.653)
StBomber  A5 D1    (0.625 / 0.125)         (0.667 / 0.167)

Submarine  A2 D1 (1.00, fs: 1.50 / 0.50 fs: 0.67)   (1.33, fs: 2.00 / 0.67 fs: 0.89)
Submarine  A3 D1 (1.50, fs: 2.25 / 0.50 fs: 0.67)  (1.33, fs: 2.00 / 0.67 fs: 0.89)
Submarine  A3 D2 (1.50, fs: 2.25 / 1.00 fs: 1.33)   (1.33, fs: 2.00 / 0.67 fs: 0.89)
Destroyer    A2 D2 (0.563 / 0.563)                        (0.75 / 0.75)
Destroyer    A2 D3 (0.563 / 0.844) avg:   0.704       (0.75 / 0.75)
Destroyer    A3 D3 (0.844 / 0.844)                        (0.75 / 0.75)
Cruiser        A5 D5  (0.625 / 0.625)                       (0.50 / 0.50)
Carrier, 2 hits A0 D2 (0.0 / 0.368)                            (0.00 / 0.491)
Carrier, 2 hits A0 D3 (0.0 / 0.552)                          As above
Battleship    A6 D6   (0.707 / 0.707)                      (0.628 / 0.628)

understand by putting the art attack @ 3 makes it the strongest unit on the board with regards to attack for the cost…
I think we all agree it should not have that status…
now at 2 is not right either…so…
my feeling is use combine arms for art…
besides inf and mechs getting boosted 1 attack…why not also boost art to 3 as well…
that would be a good compromise imo

Unit Type Cst Mve Att Def CPHa CPHd
AA GUN 5 1 N/A 1 40.0
MCH INF 4 2 1 2 32.0 16.0
INF          3 1 1 2 24.0 12.0
ART          4 1 3 2 10.7 16.0
TANK         6 2 4 4 12.0 12.0
FIGHTER 10 4 4 5 20.0 16.0
TACT 11 4 4 4 22.0 22.0
STR BMB 12 6 5 1 19.2 96.0
TRANS 7 2 N/A N/A N/A N/A
SUB          6 2 3 2 16.0 24.0
DEST 8 2 3 3 21.3 21.3
CRUISER 12 2 5 5 19.2 19.2
AC            16 2 N/A 2 N/A 64.0
BSHIP 20 2 6 6 26.7 26.7

see the art imo too powerful at 3 attack straight up, but a good way to get around this is again by doing the 2 attack stand alone and 3 when combined with either inf and/or mech

@bigalmeacham:

understand by putting the art attack @ 3 makes it the strongest unit on the board with regards to attack for the cost…
I think we all agree it should not have that status…
now at 2 is not right either…so…
my feeling is use combine arms for art…
besides inf and mechs getting boosted 1 attack…why not also boost art to 3 as well…
that would be a good compromise imo

In fact, OOB it was the case by itself or combined arms with Inf, and it should IMO.
Artillery was slow but best on offense.
Unit type  Combat value  (D8 system) (D6 OOB)
Infantry    A1-2 D2  (2.00-3.67 / 4.00)  (2.67**-3.92** / 5.33)
Inf+Art A3 D3           3.67  /  3.67         (3.92 / 3.92)
MechInf    A1-2 D2  (1.125-2.81 / 2.25) (1.50-3.00 / 3.00)
Artillery    A2 D2       (2.25 / 2.25)         (3.00 / 3.00)
Artillery    A3 D3       (3.375 / 3.375)       Same as above
Tank         A4 D4        (2.00 / 2.00)         (2.00 / 2.00)

I did not make the numbers for Art A2 D2 combined arms:
Infantry+Art    A1-2 D2  (2.00-2.94 / 2.94) vs 3.92 / 2.94
MechInf+Art    A1-2 D2  (1.125-2.25 / 2.25) vs 1.50-3.00 / 2.25

But it showed that A2 D2 is a big drop from 5.33 to 2.94 on defense.

I’m trying to keep the same type of combined arms than OOB.

I think it is easier for comparison to use odds in formula rather than absolute number which make only for comparison within the same dice system.

How do you get your 12.0 for Tank?

=if(and(E26 <> ʺN/Aʺ, C26 <> ʺN/Aʺ), (1/(E26/8))*C26, ʺN/Aʺ)

that’s the formula for the tank…
its right…

we made the tank stronger…
pretty much all the navy units as well…
this way the term “obsolete” should be eliminated…
all units are worthwhile buying now in this system

just look at the defense of the inf…
half the cost and defend at 2

tank double the cost and defend at 4

both at 12 for cost to defend…

checks out

@bigalmeacham:

Unit Type Cst Mve Att Def CPHa CPHd
AA GUN 5 1 N/A 1 40.0
MCH INF 4 2 1 2 32.0 16.0
INF           3 1 1 2 24.0 12.0
ART          4 1 3 2 10.7 16.0
TANK        6 2 4 4 12.0 12.0
FIGHTER 10 4 4 5 20.0 16.0
TACT 11 4 4 4 22.0 22.0
STR BMB 12 6 5 1 19.2 96.0
TRANS 7 2 N/A N/A N/A N/A
SUB �  �  �  �  � 6 2 3 2 16.0 24.0
DEST 8 2 3 3 21.3 21.3
CRUISER 12 2 5 5 19.2 19.2
AC            16 2 N/A 2 N/A 64.0
BSHIP 20 2 6 6 26.7 26.7

see the art imo too powerful at 3 attack straight up, but a good way to get around this is again by doing the 2 attack stand alone and 3 when combined with either inf and/or mech

If you show attack before defense, then there is a few discrepancies in your table.
Some numbers are probably not right, such as TcB compared to Fg.

@bigalmeacham:

=if(and(E26 <> ʺN/Aʺ, C26 <> ʺN/Aʺ), (1/(E26/8))*C26, ʺN/Aʺ)

that’s the formula for the tank…
its right…

we made the tank stronger…
pretty much all the navy units as well…
this way the term “obsolete” should be eliminated…
all units are worthwhile buying now in this system

Except for Artillery A2 D2 (2.25) which will be almost like Tank (2.00).
The mobility would make Tank a better investment than a M1.
Artillery OOB was not that purchased even with a high combined arms factor for Infantry (3.92)
But, with a low 2.94 it will be still less interesting for offense.

@Young:

I think where it currently falls on the list provides the best interpretation of the Oob unit (Att 3/8 - Def 2/8). its a much better unit in amphibious assaults, but still a very weak unit for long drives across land.

Why don’t try it the other way?
Att 2/8 - Def 3/8 +1A bonus to Inf or MI?

It would make more sense that big guns be good for defensive stance while providing a boost to Inf and MI.
And moving them constantly forward during attack is less convenient.

On amphibious assault, it does not seem right that Artillery is better than Tank from historical POV.
If the other way (Art A2 D3):
Inf A2 + Art A2 = A4
Inf A1 + Tank A4 = A5

But, in pure number, from game POV, it seems to work almost as OOB TP (67% odds):
Inf A2 + Art A3 = A5 (62.5%)
Inf A1 + Tank A4 = A5

Anyway, I did my best to make the case for Artillery A3 D3 +1A to Inf or MI.

where are the marines need that to make arty awesome…

@Young:

Baron,

With the differences between my 8D units and VANNs 8D units… which do you like best? Please don’t give me a bunch of analytics and than play neutral, give me a straight opinion. Thanks.

@Dauvio:

The destroyer strength is lower then the cruiser, and the combo of the cruiser&battleship makes the cruiser, and battleship worth buying (not obsolete). Having a higher defense strength for the carrier composites the lower fighter defense strength.

OK, hear this YG.
If you really want to solve the issue about Cruiser and Battleship, I can see what was intended by Vann.

It is SS that pushed me on this track.
In his heavily HR game, Destroyer and Cruiser are at 7 IPCs and 9 IPCs.
Even with this revised cost, he told me that Cruiser is not very popular.

In fact, to create an interesting incentive, Destroyer has to be as Vann suggested @2 and not higher:

| Destroyer | attack 2 | defense 2 | move 2 | Cost 8 | Anti-Submarine Weapon | Strength: 0.563 | OOB: 0.750 |
| Destroyer | attack 3 | defense 3 | move 2 | Cost 8 | Anti-Submarine Weapon | Strength: 0.844!!! |
| Cruiser | attack 5 | defense 5 | move 2 | Cost 12 | Shore bombard @5 | Strength: 0.625 | OOB: 0.50 |
| Battleship | attack 6 | defense 6 | move 2 | Cost 20 | Shore bombard @6  Hits 2 | Strength: 0.707 | OOB: 0.628 |

Otherwise, Cruiser A5 D5 (0.625) remains a sub-optimal purchase compared to Destroyer A3 D3 (0.844) and 2 hits Battleship A6 D6 (0.707).

By keeping a slow increase in strength with higher cost unit, each warship will have a specific function:

• Destroyer A2 D2 (0.563) at 8 IPCs will be cheap fodder and blocker and useful against Submarine.

• Cruiser A5 D5 (0.625) at 12 IPCs will be a medium purchase but will provide a better firepower against enemy’s warships and aircraft while giving the best shore bombardment per cost (0.625) vs BB (0.27).

• Battleship A6 D6 (0.707) at 20 IPCs will be the most expensive warship but, with a repair capacity, it is strongest of all too.

This keeps open what to do with Submarine.
However, a weaker A2 D2 Destroyer pushes the envelop in Vann’s direction:

| Submarine | attack 2 | defense 1 | move 2 | Cost 6 | Submarine’s capacities |

| Strength: 1.00 / 0.50 | OOB: 1.33 / 0.667 |
| Strength for surprise strike: 1.50 / 0.667 | OOB: 2.00 / 0.89 |

Compared to:

| Submarine | attack 3 | defense 2 | move 2 | Cost 6 | Submarine’s capacities |

| Strength: 1.50 / 1.00 | OOB: 1.33 / 0.67 |
| Strength for surprise strike: 2.25 / 1.50 | OOB: 2.00 / 0.89 |

@Baron:

YG’s complete D8s roster

Here is the comparative with Enigma formula (still using a 12 IPCs unit reference) based on odds, not dice number.
144*Odds/cost^2 = strength of unit on same odds by hit per IPCs basis.

I bolded the greatest number between D8 or D6 for same unit.
When there is no difference, I quoted it.
So, you can see at glance which is boosted or nerfed compared to OOB.

Unit type  Combat value  (D8 system) (D6 OOB)
Infantry       A1-2 D2    (2.00-** / 4.00)         (2.67-3.92 / 5.33)
Inf A2+Arty A2 D2         2.94**  /  2.94         (3.92 / 3.92)
Inf A2+Arty A3 D2         3.67**  /  2.94         Same as above
Inf A2+Arty A3 D3         3.67**  /  3.67         Same as above

MechInfantry A1-2 D2  (1.125-** / 2.25)       (1.50-3.00 / 3.00)
MechInf A2+Art A2 D2  (2.25** / 2.25) vs       (3.00 / 3.00)
MechInf A2+Art A3 D2  (2.81** / 2.25) vs        Same as above
MechInf A2+Art A3 D3  (2.81** / 2.81) vs        Same as above

Artillery   A2 D2       (2.25 / 2.25)                  (3.00 / 3.00)
Artillery    A3 D2       (3.375 / 2.25)               Same as above
Artillery    A3 D3       (3.375 / 3.375)             Same as above

Tank         A4 D4            (2.00 / 2.00)            (2.00 / 2.00)

Anti-Air A  A0 D1* (0.00 / 0.72 per plane)       (0.00 / 0.96 per plane)

---

Fighter      A4 D5    (0.72 / 0.90 )              (0.72 / 0.96)

TcBomber  A4-5 D4 (0.595-** / 0.595)       (0.595 / 0.595)

TcB A5+Tank C17    (1.12** / 1.00)         (1.16 / 1.00)
TcB A5+Fighter C21 (0.735** / 0.653)     (0.761 / 0.653)
StBomber  A5 D1    (0.625 / 0.125)         (0.667 / 0.167)

---

Submarine  A2 D1 (1.00, fs: 1.50 / 0.50 fs: 0.67)   (1.33, fs: 2.00 / 0.67 fs: 0.89)
Submarine  A3 D2 (1.50, fs: 2.25 / 1.00 fs: 1.33)   (1.33, fs: 2.00 / 0.67 fs: 0.89)
Destroyer    A2 D2 (0.563 / 0.563)                        (0.75 / 0.75)
Destroyer    A3 D3 (0.844 / 0.844)                        (0.75 / 0.75)
Cruiser        A5 D5  (0.625 / 0.625)                       (0.50 / 0.50)
Carrier, 2 hits A0 D2 (0.0 / 0.368)                            (0.00 / 0.491)
Carrier, 2 hits A0 D3 (0.0 / 0.552)                          As above
Battleship    A6 D6   (0.707 / 0.707)                      (0.628 / 0.628)

Yes, cost per hit ratio is considered by the Enigma formula. It does not directly appear but it is.
A higher cost make for weaker hit/cost value.
That is considered when divided by squared cost.

A 1 hit @1 per 3 IPCs is as strong as 1 hit @4 per 6 IPCs.
1/ (3^2) or 9 = 4 / (6^2) or 36
In both case, you get 0.111 which is in power*hit.

Using odds instead of number: 16.7% / 9  =  66.7% / 36
You get : 1/54 or  0.0185 odds* hit

@Baron:

@Dauvio:

It came to my attention that one of my formulas are already out there that I discovered 30 years ago.
http://www.axisandallies.org/forums/index.php?action=profile;u=185969 has also discovered the formula P^2*N=S
And just for fun you can try these formulas also. S/P^2=N. √(S/N)=P
P=POINTS
N=NUMBER OF UNITS
S=STRENGTH OF ONE KIND OF UNITS IN A TERRITORY
This formula should replace the punch formula. It is much better then the punch formula.

Now the next formula is (P100)/(C^26)=S
P=POINTS
C=COST
S=STRENGTH OF THE UNIT BASED ON COST
With this formula you can also price units according to their strength. √((P100)/(S6))=C
This formula is for points. (S*(C^2*6))/100=P

For better results for some of these formulas, have all your units cost ten times then what they are. These are some of the VANN FORMULAS I came up 30 years ago.

If you have any questions about these formulas, please ask.

I found how you can get the main part of Vann formula or Baron-Larrymarx according to a specific unit as benchmark.

I took the Fighter A3 D4 C10 and I wanted to convert into Tank A3 D3 C6 as benchmark (Baron-Larrymarx formula).

Then I saw what I did.

Power (of attacking Fighter): A3 * C6 (cost of Tank)/C10 (cost of Fg) * 1 Hit Point C6 (cost of Tank)/C10 (cost of Fg) = 1.08
You can reduce this equation because (cost of Tank)(cost of Tank)/ (cost of Fg)*(cost of Fg) is same to
(cost of Tank) IPCs^2 / (cost of Fg) IPCs^2 and give a simple ratio.

C6^2*A3/C10^2 = 1.08
36 squared IPCs 3 Power * 1 Hit /100 squared IPCs = 1.08 PowerHit Point

This explained what is hidden in Baron-Larrymarx formula:
Offence or defence strength factor= 36*Power/Cost^2.

The whole Enigma formula is
Refence unit Cost^2Power of the actual unit1 HP/Cost of the actual unit^2

So, the Basic offence or defence strength factor result (1.08, in this case) is express in Power*Hit Point
1^2*Power (of a given unit)*1 hit/Cost (of this same given unit)^2

And this formula can be adapt according to any benchmark, for instance a 1 IPC unit:
131 hit/10^2 = 0.300

And this is a very small number. That’s why Vann formula:
Strength= (Power100)/(Cost^26)

add an arbitrary 1001/6= 16.667…
So, 16.667131 hit/10^2 = 0.5
And this would provide the Fighter strength attack factor based on an hypothetical benchmark unit of √16.667 = 4.0825 IPCs.
A 5 IPCs revised Tank in Vann formula gives a Strength : 16.66731 hit/5^2 = 2.00 powerhit

@Young:

you and Vann are not looking at the cost per hit calculations.

Also, D8 system keeps the same as OOB D6 if looking directly to cost per hit:
Sub is 6 IPCs/hit
DD is 8 IPCs/hit
Cruiser 12 IPCs/hit
BB is 10 IPCs/hit