VF (Germany) vs. DoMan (Allies) | Original Europe, Game 6 - Balance 3.0


  • @VictoryFirst British attack Germans in Celtic Sea SZ:

    764b74de-f8ce-4f10-a372-a9826b177b5f-image.png

    [dice 3d6<=3]
    [dice 1d6<=4]


  • 3d6<=3: 6, 6, 5; Hits: 0
    1d6<=4: 6; Hits: 0


  • @VictoryFirst Game History

    Round: 1
    
        Purchase Units - British
            British buy nothing; Remaining resources: 25 PUs; 
    
        Combat Move - British
            Turning on Edit Mode
            EDIT: Turning off Edit Mode
            1 destroyer moved from Davis Strait Sea Zone to Celtic Sea Sea Zone
            1 infantry moved from Syria to Eastern Mediterranean Sea Zone
            1 infantry moved from Palestine to Eastern Mediterranean Sea Zone
            1 infantry moved from Iraq to Syria
            2 infantry moved from Eastern Mediterranean Sea Zone to Egypt
            1 armour moved from Egypt to Libya
                  British take Libya from Germans
            1 armour moved from Libya to Egypt
            1 bomber and 2 fighters moved from United Kingdom to Celtic Sea Sea Zone
            EDIT: 1 bomber, 1 destroyer and 2 fighters moved from Celtic Sea Sea Zone to Halifax Sea Sea Zone
    
        Combat - British
    
        Non Combat Move - British
            Turning on Edit Mode
            EDIT: Turning off Edit Mode
            EDIT: 1 destroyer moved from Halifax Sea Sea Zone to Celtic Sea Sea Zone
            EDIT: 2 fighters moved from Halifax Sea Sea Zone to United Kingdom
            1 bomber moved from Halifax Sea Sea Zone to United Kingdom
    
        Turn Complete - British
            British collect 16 PUs; end with 41 PUs
    

    Combat Hit Differential Summary :


  • @VictoryFirst Trying again with the Americans:

    e7331e41-7348-404f-9a76-8f7b1208854e-image.png

    [dice 2d6<=3]
    [dice 1d6<=4]


  • 2d6<=3: 4, 2; Hits: 1
    1d6<=4: 5; Hits: 0


  • @VictoryFirst The German sub fires back:

    [dice 1d6<=2]


  • 1d6<=2: 5; Hits: 0


  • @VictoryFirst Game History

    Round: 1
    
        Purchase Units - Americans
            Americans buy 2 fighters and 2 submarines; Remaining resources: 0 PUs; 
    
        Combat Move - Americans
            Turning on Edit Mode
            1 bomber and 1 fighter moved from United States to Celtic Sea Sea Zone
            1 destroyer moved from U.S. Eastern Coast Sea Zone to Celtic Sea Sea Zone
            1 transport moved from U.S. Eastern Coast Sea Zone to Celtic Sea Sea Zone
    
        Combat - Americans
            EDIT: Battle in Celtic Sea Sea Zone
                EDIT: British loiter and taunt; Americans attack with 1 bomber, 1 destroyer, 1 fighter and 1 transport
                EDIT: Germans defend with 3 submarines
                    EDIT: 2/3 hits, 1.67 expected hits
                    EDIT: 2/3 hits, 1.00 expected hits
                EDIT: 1 destroyer owned by the Americans and 1 transport owned by the Americans lost in Celtic Sea Sea Zone
                EDIT: 3 submarines owned by the Germans lost in Celtic Sea Sea Zone
                EDIT: Americans win
                EDIT: Battle casualty summary: Battle score (TUV change) for attacker is 4
            EDIT: Recording Battle Statistics
    
        Non Combat Move - Americans
            EDIT: Adding units owned by Germans to Celtic Sea Sea Zone: 2 submarines
            EDIT: Adding units owned by Americans to Celtic Sea Sea Zone: 1 destroyer and 1 transport
            EDIT: Turning off Edit Mode
            1 bomber and 1 fighter moved from Celtic Sea Sea Zone to United Kingdom
    
        Place Units - Americans
            2 submarines placed in U.S. Eastern Coast Sea Zone
            2 fighters placed in United States
    
        Turn Complete - Americans
            Americans collect 40 PUs; end with 40 PUs
    

    Combat Hit Differential Summary :

    AAE-modified-game4-A1.tsvg


  • @DoManMacgee

    I wanted to calculate the statistics here but I realized I have been calculating the sub battles incorrectly. When subs are NOT hit, they submerge and don’t fire back. This is not represented in the battle calculator, which assumes the subs do fire back. Fortunately you can calculate it by hand however for that I need to calculate the odds for 1, 2, and 3 hits and I am not sure how to do that.

    UK attacked with 2 F, 1 DD and 1 B.

    The chance for exactly one hit would be (3/6)^3 * (4/6) + (3/6)^3 * (2/6) ?


  • Oh actually I think it should be

    (3/6)(3/6)(3/6)(2/6)3 + (3/6)(3/6)(3/6)*(4/6)


  • TripleA Turn Summary: Germans round 2

    TripleA Turn Summary for game: Europe Improved

    Game History

    Round: 2
    
        Purchase Units - Germans
            Germans buy 14 infantry; Remaining resources: 1 PUs; 
    
        Combat Move - Germans
            1 submarine moved from Celtic Sea Sea Zone to U.S. Convoy 2 Sea Zone
                  Germans take U.S. Convoy 2 Sea Zone from Americans
            1 submarine moved from North Sea Sea Zone to Celtic Sea Sea Zone
            2 fighters moved from Netherlands-Belgium to Celtic Sea Sea Zone
            1 bomber moved from Germany to Celtic Sea Sea Zone
            1 armour, 1 artillery and 1 infantry moved from Tunisia to Libya
                  Germans take Libya from British
            1 fighter moved from Algeria to Eastern Mediterranean Sea Zone
            1 battleship moved from Sicilian Sea Sea Zone to Eastern Mediterranean Sea Zone
            2 fighters moved from Finland to North Atlantic Sea Zone
            1 fighter moved from Norway to North Atlantic Sea Zone
            1 infantry moved from Finland to Karelia
                  Germans take Karelia from Russians
    
        Combat - Germans
            Battle in Celtic Sea Sea Zone
                Germans attack with 1 bomber, 2 fighters and 2 submarines
                British defend with 1 destroyer; Americans defend with 1 destroyer and 1 transport
                    Germans roll dice for 2 submarines in Celtic Sea Sea Zone, round 2 : 0/2 hits, 0,67 expected hits
                    Germans roll dice for 1 bomber and 2 fighters in Celtic Sea Sea Zone, round 2 : 1/3 hits, 1,67 expected hits
                    Americans roll dice for 2 destroyers and 1 transport in Celtic Sea Sea Zone, round 2 : 2/3 hits, 1,17 expected hits
                    2 submarines owned by the Germans lost in Celtic Sea Sea Zone
                    1 transport owned by the Americans lost in Celtic Sea Sea Zone
                    Germans roll dice for 1 bomber and 2 fighters in Celtic Sea Sea Zone, round 3 : 2/3 hits, 1,67 expected hits
                    Americans roll dice for 2 destroyers in Celtic Sea Sea Zone, round 3 : 0/2 hits, 1,00 expected hits
                    1 destroyer owned by the British and 1 destroyer owned by the Americans lost in Celtic Sea Sea Zone
                Germans win with 1 bomber and 2 fighters remaining. Battle score for attacker is 16
                Casualties for Germans: 2 submarines
                Casualties for Americans: 1 destroyer and 1 transport
                Casualties for British: 1 destroyer
            Battle in North Atlantic Sea Zone
                Germans attack with 3 fighters
                Russians defend with 1 submarine and 1 transport
                1 submarine owned by the Russians submerged
                    Germans roll dice for 3 fighters in North Atlantic Sea Zone, round 2 : 1/3 hits, 1,50 expected hits
                    Russians roll dice for 1 transport in North Atlantic Sea Zone, round 2 : 0/1 hits, 0,17 expected hits
                    1 transport owned by the Russians lost in North Atlantic Sea Zone
                Germans win with 3 fighters remaining. Battle score for attacker is 8
                Casualties for Russians: 1 transport
            Battle in Eastern Mediterranean Sea Zone
                Germans attack with 1 battleship and 1 fighter
                British defend with 1 destroyer and 1 transport
                    Germans roll dice for 1 battleship and 1 fighter in Eastern Mediterranean Sea Zone, round 2 : 0/2 hits, 1,17 expected hits
                    British roll dice for 1 destroyer and 1 transport in Eastern Mediterranean Sea Zone, round 2 : 2/2 hits, 0,67 expected hits
                    1 battleship owned by the Germans lost in Eastern Mediterranean Sea Zone
                1 fighter owned by the Germans retreated
                British win with 1 destroyer and 1 transport remaining. Battle score for attacker is -24
                Casualties for Germans: 1 battleship
            Battle in Libya
    
        Non Combat Move - Germans
            Turning on Edit Mode
            EDIT: Changing ownership of Ukraine S.S.R. from Russians to Germans
            EDIT: Turning off Edit Mode
            1 fighter moved from Eastern Mediterranean Sea Zone to Crete
            1 artillery and 1 infantry moved from Malta to Sicilian Sea Sea Zone
            1 artillery and 1 infantry moved from Sicilian Sea Sea Zone to Libya
            1 infantry moved from Algeria to Tunisia
            1 bomber and 2 fighters moved from Celtic Sea Sea Zone to Netherlands-Belgium
            1 bomber moved from Netherlands-Belgium to Germany
            3 fighters moved from North Atlantic Sea Zone to Finland
            2 infantry moved from Norway to Finland
            1 armour moved from Bessarabia to Ukraine S.S.R.
            1 armour moved from Ukraine S.S.R. to Bessarabia
            2 infantry moved from Rumania to Bessarabia
            2 armour, 1 artillery and 3 infantry moved from Hungary to Bessarabia
            2 armour moved from Germany to Poland
            21 infantry moved from Germany to Poland
            1 aaGun moved from Germany to Poland
            1 aaGun moved from Austria to Germany
            1 artillery and 2 infantry moved from Netherlands-Belgium to Germany
            1 artillery and 2 infantry moved from Yugoslavia to Rumania
            1 infantry moved from Yugoslavia to Northern Italy
    
        Place Units - Germans
            14 infantry placed in Germany
    
        Turn Complete - Germans
            Germans collect 44 PUs; end with 45 PUs
    

    Combat Hit Differential Summary :

    Americans regular : -0,17
    Russians regular : -0,17
    Germans regular : -2,67
    British regular : 1,33
    

    Savegame


  • @VictoryFirst It’s worse, actually. UK scored 0 hits in their attack with 3 @ 3 and 1 @ 4:
    (1/2)^3*(1/3) = ~4.125%

    Expanding that to include the US attackers and the fact that in total only one hit was scored between all of them would be more difficult. I could probably do it but will need a bit to hash it out.


  • @DoManMacgee

    Yeah so what I wanted to calculate is the average TUV swing of the battle. For that, you would multiply the TUV swing of each scenario from the German perspective with the chance of that scenario coming up.

    So to give an example, I will use this notation X / Y where X is the number of hits that the British scored and Y the number of German hits.

    0 / 0
    This would have a TUV swing of 0 so no need to look at this.

    0 / 1 would be 4.125% * 33% = 1.4%
    TUV swing: +12
    1.4% * 12 = 0.17 IPC

    1 / 0 not sure how to calculate this chance
    TUV swing: -8

    1 / 1 something times 33%
    TUV swing: +4

    2 / 0

    etc.

    Probably the best way to do this is to write a program that rolls these dice 10000 times and then let it add up the number of times a certain number of hits has been scored. Or even better, let it simulate the combat entirely and calculate the average TUV swing from there. However right now I am too tired to work on that lol.


  • @VictoryFirst said in VF (Germany) vs. DoMan (Allies) | Original Europe, Game 6 - Balance 3.0:

    (3/6)(3/6)(3/6)(2/6)3 + (3/6)(3/6)(3/6)*(4/6)

    That is correct for exactly one hit for just the UK stuff. To add in the USA stuff, it becomes a bit more involved:

    UK Force: 3 @ 3, 1 @ 4
    US Force: 2 @ 3, 1 @ 4
    Total force: 5@3, 2 @ 4

    So to expand it, we have:
    (ODDS OF 1 @3 HIT * ODDS OF 0 @4 HIT) + (ODDS OF 0 @3 HIT * ODDS OF 1 @4 HIT)
    (5*(1/2)^5 * (1/3)^2) + (1/2)^5 * 2*(2/3)(1/3)
    .0016/9 + .013889 = .0141 = 1.41%

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