Method for Estimating the Outcomes of Large Battles

For reference, here where I get the Punch formula:
@taamvan:

Nice presentation sir!

I think that odds calculators (novel or traditional) are a bit of a crutch, also, they are ruthlessly accurate but accuracy does not reflect all the special rules or anomalous outcomes that occur in a wargame vs a flat probabilities system.   I personally do not use them, permit them to be used in hosted games, and they are not allowed in tournaments.

Just as you propose, I therefore need a way to determine odds for large battles.   I much prefer to sketch this out rather than even reducing the odds to a series of estimates the reason for this is pretty basic;

A formal system of analysis may give you a rough estimate, but since luck has an overwhelming influence when you are rolling a few dice, it will not really advise optimal commits.   1 man and 1 tank should beat 1 man most of the time but you really should send at least 3 ground units against 1 to ensure a take no matter how crap your odds…there are also situations where you can “win” a battle when you really “lost” it, such as when the attacker kills a big stack, and then retreats leaving you with like 1 tank or 1 fighter.   He did not “win” or take the territory, but it was a huge attritional win for him within the context of the whole game.  An example of a failed “win” is one where the enemy kills all your warships but is in turn killed by you and therefore your transports survive.   These are examples of non-binary outcomes, which the game permits (often) but the calculator cannot necessarily account for or counsel for.

One important thing to remember is that “regression to the mean” has a bigger effect the more dice you roll.  that means that the smaller editions of this game (1941) where the average dice rolled per battle and total are smaller than global (for example) are actually more subject to luck than the bigger ones.   This is also true of larger battles vs smaller ones;  a really big battle you are rolling 30+ dice per round and so crazy anomalies (like rolling 3 6s with just 3 dice) are less likely to happen in a way that affects you catastrophically.   The odds of rolling triple boxcars on any 3 dice remain the same…but if you only have 3 units rolling trip boxcars is devastating whereas if you have 30 units, you just missed with some and hopefully hit with others since you’re rolling all those dice.

**Anyways, the best system for me is usually just adding up all

(Attacker HP + total attack pips) = total attack power
(Defender HP + total defense pips) = total defense power**
compare the two gross numbers, if they are roughly equal, so are your odds.   If one exceeds the other by 10 or more, then the odds are probably closer to 60% or worse.

You still have to analyze whether and which units you can afford to lose in every situation (ground vs air) based on whether you must take that zone (and or block it) or not in order to know what the optimal commit is.   For this reason, I consider reliance on the calculator to be misguided (except where you are jamming the odds for big battles, and then its not misguided, its just a crutch lol)

And moreover, sometimes you just have to say #$.   Even when the odds are against you, you may still need to do a risky attack in order to win.   If you are discouraged by the odds and wait (never tell me the odds!), you are guaranteed to lose the game because you relied on a calculator rather than your moxy.

Finally, I have found that while luck matters very much, the rules for the attacker in this game (attack as much as you please, retreat whenever, maneuver wherever) mean that most offensive battles are intentional blowouts.  It is only those few battles where risks must be taken that determine the outcome of the game (not the minibattles picking off 1 infantry).   You can trade risk for time by waiting to attack, the odds on some subsequent turn may be better as more of your units coalesce into that zone.

The quintessence of the game is therefore knowing when to attack now at great risk (but to speed things up) vs wait a turn or two for the odds to become more blowout-like.   The Axis especially cannot just wait for premium odds and 95% victory chances as the Allies power grows over time…

no calculator can tell you when to seize the day ;)

OK, I found the correct Stack formula when there is A0 or D0 unit from AAA or Carrier or Battleship:

MetaPower= (number of Hits) (Punch: sum all individuals to hit number)*

MetaPower= (number of 1 Hit units with combat value) (Punch: sum all individuals to hit number) +
1.62 (number of units with no combat value)* (Punch: sum all individuals to hit number)**

For instance, what would be the outcomes of 1 Inf+2 Art + 1 Tank vs 5 AAAs + 2 Infs ?
Punch says: A9 and 4 hits vs D4 and 7 hits,
9+4 = 13 points vs 4+7 = 11 points
So, the attacker might win according to Punch formula.

According to stack formula:
4 hitsPunch A9 = 36 points vs (2 hitsD4 = 8 points) + (1.625 hitsD4= 32.4 ) = 40.4
Considering skew, we can add 5% to attacker stack: 36*1.05 = 37.8

No Distribution (all attacking/defending at same number): no bonus
Slight Distribution (equal 1s and 2s, or equal 2s and 3s): 5% bonus
Equal Distribution (equal 1s and 3s, equal 1s, 2s, 3s, and 4s): 10% bonus
Fodder Distribution (equal 1s and 4s): 15% bonus

But still, defender will win on average according to Stack formula (based on Lanchester’s laws).

AACalc: Overall %*: A. survives: 41% D. survives: 55.1% No one survives: 3.9%
http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=3&aCru=1&aCar=&aBat=&adBat=&dInf=&dArt=&dArm=&dFig=&dBom=&dTra=5&dSub=&dDes=2&dCru=&dCar=&dBat=&ddBat=&ool_att=Bat-Inf-Art-AArt-Arm-Sub-SSub-Des-Fig-JFig-Cru-Bom-HBom-Car-dBat-Tra&ool_def=Bat-Inf-Art-AArt-Arm-Bom-HBom-Tra-Sub-SSub-Des-Car-Cru-Fig-JFig-dBat&battle=Run&rounds=&reps=10000&luck=pure&ruleset=AA1942&territory=&round=1&pbem=

Another example, what would be the outcomes of 1 Inf+1 Art + 2 Tank vs 5 AAAs + 2 Infs ?
Punch says: A10 and 4 hits vs D4 and 7 hits,
10+4 = 14 points vs 4+7 = 11 points
So, again here, the attacker might win according to Punch formula.

According to Stack formula:
4 hitsPunch A10 = 40 points vs (2 hitsD4 = 8 points) + (1.625 hitsD4= 32.4 ) = 40.4
Again the skew might be considered for attacker’s stack (+5%) : 40 * 1.05 = 42

So, again, even on average according to Stack formula (based on Lanchester’s laws), it remains very similar.
And the AACalc results are according to the formula:
AACalc: Overall %*: A. survives: 49% D. survives: 46.9% No one survives: 4.1%
http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=2&aCru=2&aCar=&aBat=&adBat=&dInf=&dArt=&dArm=&dFig=&dBom=&dTra=5&dSub=&dDes=2&dCru=&dCar=&dBat=&ddBat=&ool_att=Bat-Inf-Art-AArt-Arm-Sub-SSub-Des-Fig-JFig-Cru-Bom-HBom-Car-dBat-Tra&ool_def=Bat-Inf-Art-AArt-Arm-Bom-HBom-Tra-Sub-SSub-Des-Car-Cru-Fig-JFig-dBat&battle=Run&rounds=&reps=10000&luck=pure&ruleset=AA1942&territory=&round=1&pbem=

Played a fair amount of games during confinement and quite often my opponents had poor ratios of land units for the big battles.

Ive played more with artillery and the system is not that different from what ive post 3 years ago.
(assuming tanks cost 5$)

1- do not lose art or tanks in the first 2 rounds
2- have as less as possible infantry alive after the first 2 rounds.
3- between 1 & 2 give rule 1 the priority***.
4- number of artillery should be as close as possible of the number of infantry that survive round 1, aim for more rather than less. (having not enough art hurt more than having too much of them wich implies less tanks***)
5- rest are tanks if they cost 5$.

ex
60inf to kill. you estimate they are going to make 20 hits on R1 (you will make at least 15) so hopefully they will make 35 hits or less in the first 2 rounds. So you need around 35i and 15a (35-20)
cost of total units 211$

35 inf+14 art+10 tanks(211$) = above 52% & close to 80% for LL.
34i + 11a + 13t = above 48.5% and slightly under 46% for LL (not enough art)
33i + 13a + 12t = slighty under 51% and 74% for LL.
36i + 12a + 11t = 50.5% and under 56% for LL
36i + 17a + 7t = 54.5% & 90.7% for LL
36i + 22a +3t = 55.5% and 85% for LL

210$
34i+12a+12t = 48% and under 39% for LL
35i+15a+9t = 51% and under 71% for LL

• ***There is a small “bonus” for having more units especially when the stacks make less than 25 hits on the first round.