Probabilties in KEY battles: LC, Norway...

[Codename Condor]

Ive read some posts and i think people misjudge the probablities involved in some KEY attacks. For example, the german attack on LC. Its far from 99% of sucess. Lets see it.

1.Usual logistics:

- 3 AFs 0-2 each (odds: AL/DL)

- 1 tank 0-3

- 1 army 0-3

Adding up: 12 points of damage in average, and we only need 10 to kill the coprs defending Brussels.

HC implemented the +1/-1 randomness in the dice roll, so damage can vary in this range: from 7 to 17. (17+7)/2 = 12 ,as we already knew, this is the average.

posib: 7 8 9 | 10 11 12 13 14 15 16 17

probab:1/11 1/11 1/11|...

Sucess: 8 bullets (10,11,...,17)

Failure: 3 bullets (7,8,9)

Sucess probabilty = 8/11 = 0.7272 = 72.7% and LC is taken in 1 turn. Far from 99%.

With this same analysis u can guess the exact probabilty to other KEY atacks such as LC gambit (allies attackin), Norway,...

Almost everybody uses those units to attack LC, i dont.

2.Logistics:

- 3 AFs 0-2 each (odds: AL/DL)

- 1 army 0-4

- 1 corps 0-2

Note: u can only get those odds if u tranfer Rundsted (rating 7) instead of Bock (rating 6), army and corps both in cities.

Easy now: 7+17/2 = 12, same as before!!!!, and obviosly same sucess probability, 72.7%.

Advantages: u r using the two tanks in poland in turn 1, very interesting to get some exp., and take poland quickly. U dont risk the tank in a french counterattack (with Billote that tank could be killed).

Disadvantages: I cant see any!!, maybe the fact that u spend 8 MMPs more in the transfers.

Im using this all the time as u, people, has noticed.

[ November 07, 2003, 06:13 PM: Message edited by: Codename Condor ]

[zappsweden]

Condor, the way you are calculating is evenly distributed probabilities.

If you roll one die you get 1, 2, 3, 4, 5, 6

i.e 1/6 chance for every outcome.

Say we roll 5 dies instead, do u think that getting 5 (1+1+1+1+1) has the same chance as getting say 15???

No, ofcourse not.

The same way is in SC. You attack with 5 units independantly (it would be as you said if you could attack with units simultaneously instead of one at the time) so the chances are much higher getting something around the average (the 12 point damage u showed us).

So, it is quite hard calculating it. In fact, in the end of the battle the low readiness of a nearly dead corps might affect the expected losses in Axis favour.

[ November 07, 2003, 08:05 PM: Message edited by: zappsweden ]

[Codename Condor]

I do think its higher than 72%, from experience id say more than 90%, and i know i didnt take into account the low readiness of the defending corps, i didnt cos if u test it u see u get the same odds, even if u have a corps with 3 points of strenght left u still get the 0-2 odd(and that is what really counts, i dont care about readiness) cos now its a more experience corps or whatever, so i think that doesnt count in the end.

But yes, u r right, u have to take into account previous results and so u have to multiply the probabilities, that way u should get the >90%.

I should edit my previous post and just say that the 2 options have the same probability.

[ November 07, 2003, 08:37 PM: Message edited by: Codename Condor ]

[Terif]

My 2 cents, LC turn 2 as Axis:

Condor: if you place your units right, you can have with Bock (he is marching, not operating):

3 AF 0-2

2 Army/Tank 0-3

1 Corps 0-1 (from the river)

In total a damage of 13 (Brussel Corps at full strength), not only 12 .

For the calculation of the probability the events are independent from each other as Zapp already mentioned. There are some formulas to calculate the exact probability. I had them during my study, but I am too lazy at the moment to search after them and translate it in english .

Anyhow, from experience I can also say, the probability should be somewhere between 90-98%. I guess its over ~95% since in my last ~50 games as Axis it only failed once if I remember right...

[zappsweden]

With Rundstedt you 0-4 on that first Infantry attack instead of 0-3.

Also, since Rundstedt gain some experience on turn one and during the initial attack, it is possible to get both the infantry and tank to 0-4 instead of 0-3.

That is a BIG gain and surely gives LC 99% chanse.

4+4+2+2+2+1=15

Very unprobable that it will be below 10.

This rounding business of battle odds degrade this to a mathematical game

[ November 08, 2003, 06:58 AM: Message edited by: zappsweden ]

[Terif]

This rounding business of battle odds degrade this to a mathematical game

Thats the good in SC: Not luck determines the winner, only the strategy and tactic. Luck normally evens out during a game. You know exactly what you have to expect. It is a pure strategy game with a very very small luck factor. Otherwise it would not be possible for me to win most games .

E.g. if you want to kill a unit and you see your first 2-3 attacks didnt do enough damage, then you can save your other 2-4 (air-)units, reposition them, reinforce or simply attack a better target...

[zappsweden]

Terif, using decimal values (to give every single increase in unit values affecting the outcome) when calculating the +1 and -1 damage would not increase the luck factor in the game.

I was not complaining that Strategy decided the game, Terif. Contrary, if I knew that higher readiness always meant better chance of inflicting damage I could come up with plans to increase my readiness in important battles.

Instead, current system encourage calculators and calculating when the values are rounded up and when they are rounded down. I could just about bring my calculator and calculate how much HQ experience and supply I need to get better odds at LC for instance. I thought that the expected losses integer was only a hint, not the exact value used.

Also, practicing opening moves are now more Chess like. You get some unlogical variations as waste products because of this i.e variations that are good just because they have this rounded value benefit.

What I DO complain about is that one unit can have 85% and the other have 88% readiness. The first one can get 0-2 and the second one 0-3.

That is very odd since ppl can practice those numbers knowing exactly when they are rounded up and when they are rounded down.

[ November 08, 2003, 08:20 AM: Message edited by: zappsweden ]

[Terif]

Zapp:

You make a problem out of a thing that is no problem. Only in the first turn of the game you can "calculate" (or simply try it out) the expected losses.

After the first turn this is simply senseless, you cant calculate it in advance (or with enough effort you could, but then you need an hour per turn... thats no fun and I cant imagine somebody doing it, including me..).

But with the rounded values everybody knows/sees what combat results he can expect (it is written at the top of the SC window). You dont need a calculator to find the best attack row (like when it would not be rounded), you just need to have a look at the monitor.

To quote Les the Sarge:

"SC is a good simple fast easy to play design with a very fast simple easy to use interface."

I can see no need to make it complicate.

[ November 08, 2003, 08:49 AM: Message edited by: Terif ]

[zappsweden]

Ok, Terif I am convinced. If not even you calculates those things I guess we do not need to worry...

[pzgndr]

Something else you guys may or may not be considering is how relative attacker/defender strengths influence combat losses. As the defender is reduced in strength, subsequent attacks become more effective. So simply comparing all the at-start estimates and then rolling in the +/- 1 random factor is not sufficient.

Orchestrating the sequence of attacks in SC is important. Do you start with low value infantry attacks and finish with higher value air and armor attacks, thus giving the kill shot to your better units and helping their experience? Or do you use those better units first to knock down the defender quicker, but probably taking some expensive losses to do so? This gets very complicated and is difficult to evaluate objectively. Sort of like war itself, yes?

[zappsweden]

Macon, I fully agree. Order of attack and stuff is the tactic in the game where the opportunity to use tactical geniousy exist. However, those tactical considerations would still exist regardless of the rounded values. How both units readiness and stuff affects the losses is written in the manual.

Having readiness using percentages seem very precise, but the preciseness gets chopped before the final result (final losses) is decided.

[ November 08, 2003, 10:11 AM: Message edited by: zappsweden ]