Hello,
I decided to make an odd’s calculator to determine on a 100% scale who[attacker, defender] has what odds. I found this post and dug through the info a bit. Interesting stuff. I think most people are taking different routes to attempt the same effect.
I have some idea on how I want to go about doing this but I’m not sure if it is giving the true odds. I racked my brains last night to come up with some form of an algebra formula to determine the odds. I started simple and worked my way up to AA vs Fighters, this is what I’ve come up with.
Dice:
Odds on rolling a 1 or less:
16.6%
Odds on rolling a 2 or less:
33.3%
Odds on rolling a 3 or less:
50%
Odds on rolling a 4 or less:
66.6%
Odds on rolling a 5 or less:
83.3%
So we have the first variable for the formula which would obviously correspond to the attacking unit or defending unit. So here are the other variables that I’ve thought of.
Attacker:
How many attacking units[Atk]
the reason for this number is so you can determine now many hits you can take before a loss
Odds on rolls [Atk]
Determines the odds of a hit all around for different units
How many first strike attacking units [Atk]
If I’m thinking correctly, the odd’s of this unit’s hit would come right off the top of the corresponding unit.
How many defending units [Def]
This would determine how many hits the defender could take before a loss
Odds on rolls [Def]
this would determine the odds on each unit types odds of hitting
How many first strike defending units[Def]
If I’m thinking correctly, the odd’s of this unit’s hit would come right off the top of the corresponding unit.
So for an easy example, to test out the theory we could use this setup:
Attacker:
2 Soldiers
1 tank
3 Planes
Defender:
1 AA
1 Soldier
3 Tanks
1 Plane
Beginning the battle the AA would have a shot at taking the planes out of the equation. So I think we need to look at that area first.
1 plane has a 50% chance of scoring a hit. Fighters attack on a 3. We have 3 attacking planes, which have the combined chance of 50%. So adding planes does not effect the chance, this is why I think this.
Knock the decimal over two spots and you get .05, add that three times and you get 1.5, divide that by the number of units and you get 50%. The reason for returning to 50% is that by adding more planes, your adding the chance of a hit plus the chance of a miss. So 1 plane’s odds is the same as 3 planes odds @ 50%. So it’s safe to say that 1/2 your planes will hit by the odds.
The AA unit defends by attacking each fighter separately, in effect we’ll only be looking at one because one odd is the same as 3 right? The AA unit defends on a 1 [16.6%] chance. This is where I could be wrong, but I think that you would take the AA’s odds off the fighters odds. So with an AA defending, your planes have the combined chance of 33.4%. The reason for this is because that AA would take the fighter out of the equation, by subtracting the AA’s chance off of the fighters chance we would get the true chance of that fighter, thus all of the fighters chances because the AA effects them all.
Now if there where a bomber then you would do this separate from the fighters. Bombers attack on a 4 [66.6%], having the AA unit defending [16.6%] then the bomber would have the odds of [50%]. You would calculate this separate because the bomber attacks on a different number.
So now we come to this conclusion:
Attacker:
2 Soldiers (attack on 1 [16.6%])
1 tank (attack on 3 [50%])
3 Planes (attack on 3 [50%]) coupled with the AA’s odds gives us a 33.3%
Defender:
1 AA (attack on a 1[16.6%]) Effecting Air units only and it is already calculated
1 Soldier (Defends on a 2 [33.3%])
3 Tanks (Defends on a 3 [50%])
1 Plane (Defends on a 4 [66.6%])
This is where I’m kind of stuck, I think what we would do now that we’ve figured out all the ending chances is turn those percentages into numbers by moving the decimal over two spaces or dividing the percent number by 10. So we would add all attacking numbers first.
Attacking units:
Soldiers: 16.6% / 10= .166 x 2 Soldiers = .332
Tanks: 50% / 10= .5 x 1 tank = .5
Fighters: 50% - 16.6% = 33.3% / 10 = .333 x 3 Fighters = .999
Total Attack Value (TAV)= 1.831
Defending Units:
AA’s = Already Formulated inside the Attacker’s Planes
Soldiers: 33.3% / 10= .333 x 1 soldier = .333
Tanks: 50% / 10 = .5 x 3 tanks = 1.5
Fighters: 66.6% / 10 = .666 x 1 fighter= .666
Total Def Value(TDV)= 2.499
Now add the two total values to get the dividing number for the percentage chance of victory. So this is our final formula:
[TAV/(TAV+TDV)]*10= attackers chance of success.
1.831/4.33= .422*10= 42.2%
This gives the attacker a 42.2% chance of a victory and the defender a 57.8% chance of victory.
I think this is right, but I thought I would add this in so someone could dig through and tell me if my logic for the formula is correct.
You have to remember that this is a beginning phase only calculation, you would need to redo the calculation for every complete turn. So the defender would roll for each plane, then attacker would roll for all units left, then defender would roll for his units. Then at the “attack or retreat phase” you would recalculate the odds to determine the new odds of success with the remaining units attacking and defending.
Now I’m cranking my brain to figure out the first strike bombarding stuff for battleships. Because it would only be used one time, this could be somewhat difficult to get a true chance of success. It might be easier for you not to even add the bombard into the equation, so that you can use it as a “bonus” or undefined variable.
Subs are easier, they’re basically the same as the AA units in that formula. The only difference is if there is an enemy destroyer present, then you would calculate them as a normal unit, not a first strike unit.
Battleships add to the total defense value due to having the ability of taking 2 hits. This adds a dimension to the equation that I have yet to dig into. The number of units is a variable that you could call defense that both attackers and defenders have. I need to work that into the equation somewhere and perhaps cross calculate with the possible attack values.
I think when this is all said and done, the calculator would give you a percent chance of success and the number of turns it would take to win. You would have to recalculate every full turn like I said earlyer and that would change your chances every full turn. That would give you a way of determining whether or not to retreat units that can retreat.
So for example, if your defending and your chance of success drops after the first round to 30%, then it would probably be a good idea to retreat your plane(s) and sub(s). Or if your a horrible gambler like myself, continue with your low odds lol.
I would appreciate any feedback on this negative or positive, I’m curious as hell whether or not this is correct. Yeah, curiosity killed the cat, it’s probably going to kill me too lol.