Posts made by dinosaur

Thanks Frimmel.  I’m not done yet, but because the permutations are becoming extensive, I am having to slow down.  It takes me five to six sheets of paper to run the numbers on a single example right now.  For example, my next installment will include the case where one bomber with four fighters goes up against one destroyer and two transports.  My first three pages just list the permutations of the six dice.  My fourth page accumulates the number of dice rolls qualify for a specific result.  My fifth sheet summarizes the numbers from the fourth sheet.  The sixth sheet determines the ‘worth’ of a specific result depending on the cargo loadout of the convoy.  These numbers go into a spreadsheet with about sixty lines, to add up the final score.  One of the beauties is that often I can check the results by comparing to other values already computed.

About the results …

As I said before it seems a good rule of thumb is to have one bomber for each target you hope to hit, plus 3/4 the fighters equal to the number of AA dice the enemy is going to throw.  This does provide a small chance you might lose a bomber, but very small (~1.25%).  On the plus side, you can expect to hit more than 0.60 x # bombers you bring to the fight.  If you don’t bring at least twice as many bombers as screening ships, you can only expect to hit screening ships with an occasional hit on a transport.  (Please understand, after the 3/4 fighter screen, every extra 2 fighters count for 1 bomber on the target)

The original observation that planes are not very reliable against main fleets appears to be completely justifiable.  A typical main fleet is going to have at least five ships with one AA die each, and a fighter screen of at least two fighters.  This means nine or more AA dice.  Just to get started against a fleet with transports and an escort like this, you would need seven fighters and five bombers.  But a fleet with only 5-AA dice and two fighter CAP is a modest fleet indeed in game terms.  But an air only attack of this size would certainly be classified as a main effort.

So it appears unless you need to make a big gamble, aircraft should best be used to attack small supply convoys, deter air attacks against your airfields, fly CAP over your fleet or join a main effort fleet engagement against the enemy.  Going after a main body with only aircraft appears to be a big gamble at best.

I may run some odds that include one or two fighters in CAP over these small fleets later.

This game, the Trilogy Edition, is very good, IMO.  It gives you the flavor of Risk and the flavor of LOTR.  The events are all based on the trilogy.  The game introduces a new Risk piece called the “leader.”  The game does not suffer from the problem of original Risk because each game is played a little different due to missions required along the way.  It has a timeline so it is unusual for someone to get eliminated.  I’d give it at least three-and-a-half thumbs up, if you consider A&A Revised four thumbs.

@frimmel:

Guadalcanal isn’t a battle of attrition, it is a race.

And this is the point of my question.  I am computing the ‘value’ of an air attack based on the economic value of the damaged and destroyed units.  But if a ‘damaged’ ship can never be brought into contact with the enemy to any substantive extent, then it may as well be a full kill.  What thoughts do you have about other ways to establish the value of killing or damaging an enemy unit?  For example, a cruiser might be worth 1 point for each turn it can help control an island with its ground phase attack.  A battleship would be worth two points in this case.  Infantry and artillery would also be worth one point each.  But how much would a point of ground attack be worth compared to the cost of buying a plane?  This game causes us to completely reevaluate our priorities.  Of course, a battleship and a carrier are worth a real victory point also.  But they can only be killed once.  Assigning a number in this case is all new ground for me.

I have added a few more, but the calculation length is becoming too long for me to want to write it all out any longer.  I’m just going to give the ‘answers’.  However, I’d like also to summarize the earlier results:

One Fighter                vs. one SS … $1.33
One Bomber                vs. one SS … $2.22
One Bomber                vs. two SS … $2.67
One Bomber and one Fighter vs. one SS … $2.81
One Bomber and one Fighter vs. two SS … $3.85
One Bomber and 2-Fighters vs. one SS … $3.21
One Bomber and 2-Fighters vs. two SS … $4.84

One Bomber                vs. one DD with no cargo … -$0.26
One Bomber                vs. one DD with $2 Cargo … $0.48
One Bomber and one Fighter vs. one DD with no Cargo … $1.65
One Bomber and one Fighter vs. one DD with $2 Cargo … $2.91
One Bomber and 2-Fighters vs. one DD with no cargo … $2.23
One Bomber and 2-Fighters vs. one DD with $2 Cargo … $3.77

One Bomber                vs. one DD and one TRN with no cargo … -$0.185
One Bomber                vs. one DD and one TRN with $2 Cargo … -$0.111
One Bomber                vs. one DD and one TRN with $4 Cargo … -$0.037
One Bomber                vs. one DD with $2 Cargo and one TRN with $4 Cargo … $0.630
One Bomber and one Fighter vs. one DD and one TRN with no cargo … $1.84
One Bomber and one Fighter vs. one DD and one TRN with $2 Cargo … $2.07
One Bomber and one Fighter vs. one DD and one TRN with $4 Cargo … $2.31
One Bomber and one Fighter vs. one DD with $2 Cargo and one TRN with $4 Cargo … $3.62
One Bomber and 2-Fighters vs. one DD and one TRN with no cargo … $2.67
One Bomber and 2-Fighters vs. one DD and one TRN with $2 Cargo … $3.12
One Bomber and 2-Fighters vs. one DD and one TRN with $4 Cargo … $3.56
One Bomber and 2-Fighters vs. one DD with $2 Cargo and one TRN with $4 Cargo … $5.10

One Bomber and one Fighter vs. one DD and 2-TRN with no cargo … $1.87
One Bomber and one Fighter vs. one DD and 2-TRN, one with $2 Cargo … $1.99
One Bomber and one Fighter vs. one DD and 2-TRN, one with $4 Cargo … $2.11
One Bomber and one Fighter vs. one DD and 2-TRN, one with $4 and other with $2 Cargo … $2.26
One Bomber and one Fighter vs. one DD and 2-TRN, each with $4 Cargo … $2.47
One Bomber and one Fighter vs. one DD with $2 Cargo and 2-TRN, each with $4 Cargo … $3.76
One Bomber and 2-Fighters vs. one DD and 2-TRN with no cargo … $2.77
One Bomber and 2-Fighters vs. one DD and 2-TRN, one with $2 Cargo … $3.04
One Bomber and 2-Fighters vs. one DD and 2-TRN, one with $4 Cargo … $3.46
One Bomber and 2-Fighters vs. one DD and 2-TRN, one with $4 and other with $2 Cargo … $3.60
One Bomber and 2-Fighters vs. one DD and 2-TRN, each with $4 Cargo … $4.20
One Bomber and 2-Fighters vs. one DD with $2 Cargo and 2-TRN, each with $4 Cargo … $5.74
One Bomber and 3-Fighters vs. one DD and 2-TRN with no cargo … $3.48
One Bomber and 3-Fighters vs. one DD and 2-TRN, one with $2 Cargo … $4.01
One Bomber and 3-Fighters vs. one DD and 2-TRN, one with $4 Cargo … $4.54
One Bomber and 3-Fighters vs. one DD and 2-TRN, one with $4 and other with $2 Cargo … $5.07
One Bomber and 3-Fighters vs. one DD and 2-TRN, each with $4 Cargo … $5.60
One Bomber and 3-Fighters vs. one DD with $2 Cargo and 2-TRN, each with $4 Cargo … $7.20
Note these are the same as the case for 2 Bmrs & 1 Ftr
One Bomber and 4-Fighters vs. one DD and 2-TRN with no cargo … $4.19
One Bomber and 4-Fighters vs. one DD and 2-TRN, one with $2 Cargo … $4.93
One Bomber and 4-Fighters vs. one DD and 2-TRN, one with $4 Cargo … $5.66
One Bomber and 4-Fighters vs. one DD and 2-TRN, one with $4 and other with $2 Cargo … $6.40
One Bomber and 4-Fighters vs. one DD and 2-TRN, each with $4 Cargo … $7.14
One Bomber and 4-Fighters vs. one DD with $2 Cargo and 2-TRN, each with $4 Cargo … $8.84
Note these are the same as the case for 2 Bmrs & 2 Ftrs

One Bomber                vs. 2-DD with no cargo … -$1.74
One Bomber                vs. 2-DD, one with $2 Cargo … -$1.44
One Bomber                vs. 2-DD, each with $2 Cargo … -$1.15
One Bomber and one Fighter vs. 2-DD with no Cargo … $0.35
One Bomber and one Fighter vs. 2-DD, one with $2 Cargo … $1.07
One Bomber and one Fighter vs. 2-DD, each with $2 Cargo … $2.19
One Bomber and 2-Fighters vs. 2-DD with no cargo … $1.79
One Bomber and 2-Fighters vs. 2-DD, one with $2 Cargo … $2.83
One Bomber and 2-Fighters vs. 2-DD, each with $2 Cargo … $4.29

One Bomber and one Fighter vs. 2-DD and one TRN with no cargo … $0.36
One Bomber and one Fighter vs. 2-DD and one TRN with $2 Cargo … $0.37
One Bomber and one Fighter vs. 2-DD and one TRN with $4 Cargo … $0.37
One Bomber and one Fighter vs. 2-DD, one with $2 Cargo and one TRN with $4 Cargo … $1.10
One Bomber and one Fighter vs. 2-DD, each with $2 Cargo and one TRN with $4 Cargo … $1.82
One Bomber and 2-Fighters vs. 2-DD and one TRN with no cargo … $1.83
One Bomber and 2-Fighters vs. 2-DD and one TRN with $2 Cargo … $1.87
One Bomber and 2-Fighters vs. 2-DD and one TRN with $4 Cargo … $1.91
One Bomber and 2-Fighters vs. 2-DD, one with $2 Cargo and one TRN with $4 Cargo … $2.95
One Bomber and 2-Fighters vs. 2-DD, each with $2 Cargo and one TRN with $4 Cargo … $3.99
One Bomber and 3-Fighters vs. 2-DD and one TRN with no cargo … $2.73
One Bomber and 3-Fighters vs. 2-DD and one TRN with $2 Cargo … $3.07
One Bomber and 3-Fighters vs. 2-DD and one TRN with $4 Cargo … $3.42
One Bomber and 3-Fighters vs. 2-DD, one with $2 Cargo and one TRN with $4 Cargo … $4.60
One Bomber and 3-Fighters vs. 2-DD, each with $2 Cargo and one TRN with $4 Cargo … $5.79
One Bomber and 4-Fighters vs. 2-DD and one TRN with no cargo … $3.58
One Bomber and 4-Fighters vs. 2-DD and one TRN with $2 Cargo … $4.25
One Bomber and 4-Fighters vs. 2-DD and one TRN with $4 Cargo … $4.92
One Bomber and 4-Fighters vs. 2-DD, one with $2 Cargo and one TRN with $4 Cargo … $6.22
One Bomber and 4-Fighters vs. 2-DD, each with $2 Cargo and one TRN with $4 Cargo … $7.48
Note these are the same as the case for 2 Bmrs & 2 Ftrs

One Bomber and 2-Fighters vs. 2-DD and 2-TRN with no cargo … $1.83
One Bomber and 2-Fighters vs. 2-DD and 2-TRN, one with $2 Cargo … $1.86
One Bomber and 2-Fighters vs. 2-DD and 2-TRN, one with $4 Cargo … $1.88
One Bomber and 2-Fighters vs. 2-DD and 2-TRN, one with $4 and other with $2 Cargo … $1.90
One Bomber and 2-Fighters vs. 2-DD and 2-TRN, each with $4 Cargo … $1.92
One Bomber and 2-Fighters vs. 2-DD, one with $2 Cargo and 2-TRN, each with $4 Cargo … $2.96
One Bomber and 2-Fighters vs. 2-DD, each with $2 Cargo and 2-TRN, each with $4 Cargo … $4.00
One Bomber and 3-Fighters vs. 2-DD and 2-TRN with no cargo … $
One Bomber and 3-Fighters vs. 2-DD and 2-TRN, one with $2 Cargo … $
One Bomber and 3-Fighters vs. 2-DD and 2-TRN, one with $4 Cargo … $
One Bomber and 3-Fighters vs. 2-DD and 2-TRN, one with $4 and other with $2 Cargo … $
One Bomber and 3-Fighters vs. 2-DD and 2-TRN, each with $4 Cargo … $
One Bomber and 3-Fighters vs. 2-DD, one with $2 Cargo and 2-TRN, each with $4 Cargo … $
One Bomber and 3-Fighters vs. 2-DD, each with $2 Cargo and 2-TRN, each with $4 Cargo … $
One Bomber and 4-Fighters vs. 2-DD and 2-TRN with no cargo … $
One Bomber and 4-Fighters vs. 2-DD and 2-TRN, one with $2 Cargo … $
One Bomber and 4-Fighters vs. 2-DD and 2-TRN, one with $4 Cargo … $
One Bomber and 4-Fighters vs. 2-DD and 2-TRN, one with $4 and other with $2 Cargo … $
One Bomber and 4-Fighters vs. 2-DD and 2-TRN, each with $4 Cargo … $
One Bomber and 4-Fighters vs. 2-DD, one with $2 Cargo and 2-TRN, each with $4 Cargo … $
One Bomber and 4-Fighters vs. 2-DD, each with $2 Cargo and 2-TRN, each with $4 Cargo … $
Note these are the same as the case for 2 Bmrs & 2 Ftrs

I plan to run this progression up still higher adding DD, TRN, and more bombers and fighters.  One thing I’m beginning to see is that CAP may play a bigger role than I thought before.  Aircraft used against main fleets always had to survive the AA round against the enemy CAP fighters in particular.  These engagements I analyzed have not included any participation with fighters escorting the ships.

One thing I see in the data is that it is very risky to use destroyers as transports if you think you may be attacked by aircraft and you don’t have adequate fighters to escort you.  Notice that the damage rises a bit when destroyers are hit carrying cargo.  Maybe a compromise might be to place infantry on destroyers and other cargo on the transports when you have to do this at all.

Another ‘rule of thumb’ I am beginning to develop is that it appears you should strive for at least one bomber per DD/CA and at least 75% of the opponents AA dice in fighters.  For example, if attacking a convoy of 2-CA, 2-DD, and four loaded TRNs, you should probably need at least 4 bombers and 3 fighters.  Yes, a perfect score with the opponents AA dice will risk a bomber, but the probability is not high.  (1/3)^4 = 1/81 ~ 1.25%  But you have a 56% chance with each bomber of scoring at least one hit.

Edit:  Added colored text …  And then some more …  And then some more …

As some may have noted, I am directly computing the odds of winning various engagements with small numbers of ships and aircraft.  As I slog through the permutations, I have to assign a value to the result.  Currently, I am using the ‘unit cost’ to make the final rating.  But this is not really a good ‘Battle Damage Assessment’ in AAG unless you are playing a total elimination game, which I am sure is quite fun in its own right.  But in the OOB AAG rules, the game is played on a timeline of about five or six turns.  A damaged ship in the second to last round, is essentially a kill.  A lost supply token far from your home base might take two or three turns to buy and transport to the destination, costing you two or three victory points.  Do you have any mathematical tools for measuring these situations?  I have noticed for example, that in a late round, you can sacrifice many ships for a chance to inflict damage on an enemy capitol ship, and there is little down side since losing those ships does not count against you (just don’t over expose your own capitol ships to an air attack).  Another example, since losing bombers and fighters doesn’t count against you, go ahead and send them on that suicide attack at the end of the game.  Maybe you won’t win.  But you might enjoy sinking your opponents capitol ship.  I find it a challenge to really assess the situation on the board when I am used to looking at total force levels and strategic position.  These have so much less importance in this game.  An airfield with a supply token in reserve and a stack of infantry is money in the bank.  Add an AA gun or two and your opponent is probably going to wince at the thought of sending an airstrike your way.  What do you think?

Well, I’m just glad to hear I’m not talking to myself.  These things take a bit of time and I don’t want to wear myself out over nothing.

One Bomber and two fighters going after two DD carrying no cargo …
0.1111 chance both fighters die in the AA round
0.4444 chance one fighter dies in the AA round
0.0278 chance bomber kills both DD if fighters killed by AA
0.0556 chance bomber kills one DD and damages second DD if fighters killed by AA
0.0278 chance bomber damages both DD if fighters killed by AA
0.2222 chance bomber kills only one DD if fighters killed by AA
0.2222 chance bomber damages only one DD if fighters killed by AA
0.0833 chance airplanes kill both DD if one fighter killed by AA
0.1204 chance airplanes kill one DD and damage second DD if one fighter killed by AA
0.0556 chance airplanes damage both DD if one fighter killed by AA
0.2222 chance airplanes kill only one DD if one fighter killed by AA
0.2222 chance airplanes damage only one DD if one fighter killed by AA
0.1605 chance airplanes kill both DD if no planes killed by AA
0.1728 chance airplanes kill one DD and damage second DD if no planes killed by AA
0.0741 chance airplanes damage both DD if no planes killed by AA
0.1975 chance airplanes kill only one DD if no planes killed by AA
0.1975 chance airplanes damage only one DD if no planes killed by AA
(-$6) x 0.1111 + (-$3) x 0.4444 + ($10) x 0.1111 x 0.0278 + ($7) x 0.1111 x 0.0556 + ($4) x 0.1111 x 0.0278 + ($5) x 0.1111 x 0.2222 + ($2) x 0.1111 x 0.2222 + ($10) x 0.4444 x 0.0833 + ($7) x 0.4444 x 0.1204 + ($4) x 0.4444 x 0.0556 + ($5) x 0.4444 x 0.2222 + ($2) x 0.4444 x 0.2222 + ($10) x 0.4444 x 0.1605 + ($7) x 0.4444 x 0.1728 + ($4) x 0.4444 x 0.0.0741 + ($5) x 0.4444 x 0.1975 + ($2) x 0.4444 x 0.1975 = $1.79

One bomber and two fighters going after one DD carrying $2 Cargo and a second DD carrying no cargo … $2.83

One bomber and two fighters going after two DD each carrying $2 Cargo … $4.29

Things are starting to shape up as we approach a supply convoy with meaningful size.  I should compare this to the ‘value’ of attacking a sub with a few aircraft.

Here are the first few combinations regarding two destroyers

One bomber going after two DD carying no cargo …
0.5556 chance bomber dies in the AA round
0.0278 chance bomber kills both DD if it survives AA
0.0556 chance bomber kills one DD and damages the second DD if it survives AA
0.0278 chance bomber damages both DD if it survives AA
0.2222 chance bomber kills only one DD if it survives AA
0.2222 chance bomber damages only one DD if it survives AA
(-$5) x 0.5556 + ($10) x 0.4444 x 0.0278 + ($7) x 0.4444 x 0.0556 + ($4) x 0.4444 x 0.0278 + ($5) x 0.4444 x 0.2222 + ($2) x 0.4444 x 0.2222 = -$1.74

One bomber going after one DD carying $2 Cargo and a second DD carrying no cargo … -$1.44

One bomber going after two DD each carrying $2 Cargo … -$1.15

One bomber and one fighter going after two DD carrying no cargo …
0.1111 chance both aircraft die in AA round
0.4444 chance the fighter dies in the AA round
0.0278 chance bomber kills both DD if ftr killed by AA
0.0556 chance bomber kills one DD and damages the second DD if ftr killed by AA
0.0278 chance bomber damages both DD if ftr killed by AA
0.2222 chance bomber kills only one DD if ftr killed by AA
0.2222 chance bomber damages only one DD if ftr killed by AA
0.0833 chance airplanes kill both DD if they both survive AA
0.1204 chance airplanes kill one DD and damage the other DD if they both survive AA
0.0556 chance airplanes damage both DD if they both survive AA
0.2222 chance airplanes kill only one DD if they both survive AA
0.2222 chance airplanes damage only one DD if they both survive AA
(-$8) x 0.1111 + (-$3) x 0.4444 + ($10) x 0.4444 x 0.0278 + ($7) x 0.4444 x 0.0556 + ($4) x 0.4444 x 0.0278 + ($5) x 0.4444 x 0.2222 + ($2) x 0.4444 x 0.2222 + ($10) x 0.4444 x 0.0833 + ($7) x 0.4444 x 0.1204 + ($4) x 0.4444 x 0.0556 + ($5) x 0.4444 x 0.2222 + ($2) x 0.4444 x 0.2222 = $0.35

One bomber and one fighter going after one DD carrying $2 Cargo and a second DD carrying no cargo … $1.07

One bomber and one fighter going after two DD each carrying $2 Cargo … $2.19

More to come, should anyone care.

I don’t recall seeing anything besides the Russian girl thing and the A&A shirts.

Well, as promised, I have a set of scenarios including a transport …

One bomber going after a DD and one TRN carrying no cargo …
0.3333 chance the bomber dies in the AA round
0.0556 chance the bmr kills the DD and the TRN if it survives AA
0.2778 chance the bmr kills the DD if it survives AA
0.2222 chance the bmr damages the DD if it survives AA
(-$5) x 0.3333 + ($7) x 0.6667 x 0.0556 + ($5) x 0.6667 x 0.2778 + ($2) x 0.6667 x 0.2222 = -$0.185

One bomber vs. one DD and one TRN carrying $2 Cargo … -$0.111

One bomber vs. one DD and one TRN carrying $4 Cargo … -$0.037

One bomber vs. one DD carrying $2 Cargo and one TRN carrying $4 Cargo … $0.630

One bomber and one fighter going after a DD and one TRN carrying no cargo …
0.3333 chance the fighter dies in the AA round
0.0556 chance the bmr kills the DD and the TRN if ftr killed in AA
0.2778 chance the bmr kills the DD if ftr killed in AA
0.2222 chance the bmr damages the DD if ftr killed in AA
0.1481 chance the airplanes kill the DD and TRN if they all survive the AA
0.3333 chance the airplanes kill the DD if they all survive AA
0.2222 chance the airplanes damage the DD if they all survive AA
(-$3) x 0.3333 + ($7) x 0.3333 x 0.0556 + ($5) x 0.3333 x 0.2778 + ($2) x 0.3333 x 0.2222 + ($7) x 0.6667 x 0.1481 + ($5) x 0.6667 x 0.3333 + ($2) x 0.6667 x 0.2222 = $1.850

One bomber and one fighter vs. one DD and one TRN carrying $2 Cargo … $2.074

One bomber and one fighter vs. one DD and one TRN carrying $4 Cargo … $2.309

One bomber and one fighter vs. one DD carrying $2 Cargo and one TRN carrying $4 Cargo … $3.617

One bomber and two fighters going after a DD and one TRN carrying no cargo …
0.3333 chance a fighter dies in the AA round
0.1481 chance the airplanes kill the DD and the TRN if a ftr killed in AA
0.3333 chance the airplanes kill the DD if a ftr killed in AA
0.2222 chance the airplanes damage the DD if a ftr killed in AA
0.2593 chance the airplanes kill the DD and TRN if they all survive the AA
0.3457 chance the airplanes kill the DD if they all survive AA
0.1975 chance the airplanes damage the DD if they all survive AA
(-$3) x 0.3333 + ($7) x 0.3333 x 0.1481 + ($5) x 0.3333 x 0.3333 + ($2) x 0.3333 x 0.2222 + ($7) x 0.6667 x 0.2593 + ($5) x 0.6667 x 0.3457 + ($2) x 0.6667 x 0.1975 = $2.675

One bomber and two fighters vs. one DD and one TRN carrying $2 Cargo … $3.119

One bomber and two fighters vs. one DD and one TRN carrying $4 Cargo … $3.564

One bomber and two fighters vs. one DD carrying $2 Cargo and one TRN carrying $4 Cargo … $5.103

Since it is clear that one bomber alone is not good, one fighter and one bomber derive a positive benefit and adding fighters makes the score rise rapidly, there is no reason to explore other combinations of aircraft in this case.  The next set of statistics will be prepared for aircraft against two destroyers.  Then I will add transports to that case also.

Well here is another small installation:

One Bomber and two fighters going after a destroyer carrying no cargo …
0.3333 chance a fighter dies in AA round
0.6049 chance the airplanes kill the DD if they all survive th AA round
0.1975 chance the airplanes damage the DD if they all survive the AA round
0.4815 chance the airplanes kill the DD if the DD kills a fighter
0.2222 chance the airplanes damage the DD if the DD kills a fighter
(-$3) x 0.3333 + $5 x 0.6667 x 0.6049 + $2 x 0.6667 x 0.1975 + $5 x 0.3333 x 0.4815 + $2 x 0.3333 x 0.2222 = $2.230

One bomber and two fighters going after one destroyer carrying $2 cargo … $3.770

The situation becomes much more complex when you have more than one variety of ship in play.  I’ll give you the tranny one tomorrow.

My brother is in the area.  He hasn’t been introduced to Axis and Allies in a substantive way yet.  Contact me with a pm and I’ll let you know when I’m headed that way to visit him.

My big rub is that historically subs are the real terror of the sea (at least through WWII era).  The curious thing about subs is that the US employed theirs to attack mainly Japanese supply but the Japanese employed theirs to attack US capitol ships.  From a gaming perspective, subs can deny the use of the seas to the other player.  This can make the game less fun because the game could take on a two phase feel; first obtain an overwhelming advantage in subs, then fight the enemy.  A game like this would not be fun at all.  If the sub were given its true potential, something would have to be done to limit their numbers in the game.  On the other hand, I don’t recall if subs played a key roll in Guadalcanal, possibly because of operational commitments elsewhere in the Pacific.  I still prefer my proposal for a submarine phase to capture the flavor of the stealth of the submarine.  However, I have not play tested my proposal so it could alter the fun of the game for the worse.

I’m trying to come up with a similar rule for aircraft, but it could be that they are much more nearly modeled than I am giving credit.  On the one hand, I know the Japanese and US forces had carrier groups operating near Guadalcanal but I don’t recall a significant carrier group battle such as Midway or Coral Sea during the Solomon Islands campaign.  And it could be that I am thinking too much of the significance of aircraft in the Battle of Midway, which may have less statistical significance than I might give it.

Legion3,

I think I’ll take up that challenge, although it will take a little time.  First off, I doubt the numbers will look good for aircraft going after a fleet of any real size.  But I think small supply excursions can be more vulnerable than you may think.  Lets look at some smaller engagements.

One bomber going after one destroyer carrying no cargo …
0.3333 chance the bomber dies in AA round
0.3333 chance the bomber kills the DD if it survives to take the shot
0.2222 chance the bomber damages the DD if it survives to take the shot
(-$5) x 0.3333 + ($5) x 0.3333 x 0.6667 + ($2) x 0.2222 x 0.6667 = -$0.2593

One bomber going after one destroyer carrying $2 of cargo … +$0.4815

One bomber and one fighter going after one destroyer carrying no cargo …
0.3333 chance the fighter dies in AA round
0.4815 chance the airplanes kill the DD if they survive to take the shot
0.2222 chance the airplanes damage the DD if they survive to take the shot
0.3333 chance the bomber kills the DD if fighter is killed
0.2222 chance the bomber damages the DD if fighter is killed
(-$3) x 0.3333 + ($5) x 0.4815 x 0.6667 + ($2) x 0.2222 x 0.6667 + ($5) x 0.3333 x 0.3333 + ($2) x 0.2222 x 0.3333 = +$1.605

One bomber and one fighter going after one destroyer carrying $2 of cargo … +$2.914

Give me a little more time and I’ll take a look at adding a tranny before I add destroyers.  BTW, notice that a cruiser is no better than a destroyer in this battle so using a cruiser rather than a destroyer only increases the risk (in dollars) to the supply convoy.  Tell me you are not a bit surprised with these numbers.(?)

Krieghund, thanks for coming to my defense.  I must apologize for not being more careful.  However, I am very often accused of being tiresome when I spell out every single thought necessary to make my point.  Although, it appears in my haste to edit my own post, I made a mistake.  I fear that if I make the whole of my case I will be considered tiresome.  So, in brief let me say …

Yes my main point is that with fighters, bombers enjoy a special one-third protection in general.  With small numbers of aircraft, which would most likely be used against only small numbers of AA dice, the benefit is often even better.  In my example with one fighter and one bomber, against one die, the bomber is of course immune to AA.  Against two AA dice, the bomber is only at risk 11.1% of the time.  Against three AA dice, the bomber is only at risk 7/27 of the time, still less than one-third.  Against four dice the odds put the bomber at risk 33/81 of the time, which is now slightly more than one-third.  Against five dice, the odds for the bomber drop quickly because now the bomber has a direct chance of getting stung by the fifth die.  And six dice is only worse.  But regardless of the number of dice, the chances of a bomber getting whacked drops substantially, even if you add only one fighter.  More fighters only makes things better.

My point is that fighters clearly improve the effectiveness of bombers to deliver damage on the enemy.  In general, the battle box indicates this to be a drop to about one-third the chances of getting eaten by AA, but specific numbers of attack dice and fighter escorts will have some effect on the real odds in a particular battle.

I recognize the names of the folks in this thread as notable contributors to the forum.  I hope I have not given offense while defending my thesis on the merits of using fighters in conjunction with bombers.

edit:  After reading the questioned post, I feel I was clearer than I was credited.  I did state, and was later highlighted in italics, that you need to kill the fighter first when rolling less than five dice.  This is exactly what others went on to illustrate in their challenges, that two hits would kill the bomber, which is what I said in my own words.

I play (AAR & AAG) and I travel to NC occasionally.  Where are you (nearest city)?

Well, I consider fighters as bomber escorts for the following reason: With fighters the chances to lose a bomber is reduced by two-thirds.  The battle box has four slots for fighters and then two for bombers.  Yes, a direct hit on a bomber does kill it and the fighters didn’t change that, but, consider that with only one fighter and one bomber, the attacker has to roll a hit on his fifth or sixth die to score that (direct) hit.  Heck he even has to roll at least five dice to get that chance (of scoring a direct hit).  If he rolls four or less, he can’t hit an escorted bomber without killing the fighter first.  The odds are much improved for bombers when fighters are sent as escorts.  Just don’t send them at a fleet alone.

Just to make sure I got the right spin, there are six islands in the game, right?  Or are there eight (counting the two base islands)?

I have to say if you want a quick game Guadalcanal has to be considered.  It takes about five turns and the first turn will go very quickly once you learn the game.  One of my frustrations with other variants is that folks can buy a stack of infantry or trannies to “protect” their high value assets.  In Guadalcanal, this is very different.  If you get tired of the basic game, you can play a longer game of elimination if you have the time.  And you get a bunch of cruisers you can modify other variants of A&A with.  Enjoy and Good Luck!

Historically, subs and aircrft were much more leathal than they are in AAG.  I suspect the game would not be as much fun if they were.  But can anyone direct me to variants that change this?  I’d like to give it a try.  I can’t just jack their hit probabilities because it would likely mess up the play balance.  This is why I am asking you folks 'cause you know there is more to it than just the hit probability table.  At least, I think you do.

I had one idea about subs.  In addition to the problem of stealth, they are too vulnerable after they exercise their attack.  Subs did not attack with surface fleets backing them up.  But in AAG this seems necessary to keep them alive.  What if there were a new attack round for submarines just like aircraft.  But only subs and destroyers could attack in this phase.  There might be a detection dice roll, followed by either the subs first strike and the destroyers counter strike, or the sub withdraws before attacking, or the destroyer gets to attack before the sub gets to counter only against the destroyer.

I think this could be used for both AAG and even AAR if given some study.  It probably doesn’t work quite the way I described it, but it sounds much more realistic.  I just bristle at the idea of battleships and aircraft carriers attacking subs.  Remember, some of us grew up thinking there were two kinds of navy ships … subs and targets.

You could also play AAG as a conquer game, but forget about the two hours time if you do that.  It should take another hour or two at least if you go all the way.  If you really want to stay with the feel of an AAR game, go with Pacific.  But if you are ready for a different experience, go with AAG.