AndrewAAGamer Solo Test

dicebot

1d1000<=1: 571; Hits: 0
1d1000<=1: 631; Hits: 0
1d1000<=1: 888; Hits: 0

AndrewAAGamer

TripleA Manual Gamesave Post: AlliedFighters round 9

TripleA Manual Gamesave Post for game: D-Day 2 fix

Game History

Round: 9

    Movement Reset - AlliedFighters
        AlliedFighters collect 0 PUs; end with 0 PUs

Combat Hit Differential Summary :

Savegame

VictoryFirst

@AndrewAAGamer said in AndrewAAgamer (Allies) vs. Germany (Ragnell804):

Odds of at least 1 area area with Bad dice

65.30%

Odds of at least 2 areas with Bad dice

This is slightly more complicated to do. We have to add up percentages of all different possibilities that include this result. Let’s write some of them out. We have four areas, EG - CAEN - St. Lo - Cherbourg. A 1 means bad dice in the area, a 0 means no bad dice. Let’s look at bad dice in two areas first.
EG - CAEN - St. Lo - Cherbourg
1 - 1 - 0 - 0 = 23% * 23% * 77% * 77% = 3.13%
1 - 0 - 1 - 0 = 23% * 77% * 23% * 77% = same calculation = 3.13%
1 - 0 - 0 - 1 = …
0 - 1 - 1 -0 = …
0 - 1 - 0 - 1 = …
0 - 0 - 1 - 1 = …
As you can see, we just have the same calculation 6 times. The 6 comes from the total number of combinations of two numbers out of a total of four numbers. This can be calculated directly on a calculator using the Combination Formula, which is defined as follows.

Most calculators have a built-in function to calculate this (i.e. you can type in 4C2 instead of the longer expression on the right side)

And not to forget, we also have to include the possibilities that have bad dice in three or four areas, because those are also included from the wording “at least two areas”.
I am not going to write out the combinations for that, now we can simply use the Combination Formula.
4C3 = 4 and 4C4 = 1 (and 4C2 = 6)

The entire calculation is as follows.

(23% * 23% * 77% * 77%) * 4C2 + (23% * 23% * 23% * 77%)*4C3 + (23%^4)*4C4 = 22.84%

Odds of at least 1 area with Very Bad dice

8.70%

Odds of at least 2 areas of Very Bad dice

Same logic, however the percentages change to 2.25% and 97.75%
(2.25% * 2.25% * 97.75% * 97.75%) * 6 + (2.25% * 2.25% * 2.25% * 97.75%) * 4 + (2.25%^4)*1= 0.3%

You can even create a general formula for this if you want, however for now this will do I think.

VictoryFirst

And by the way, the matrix thing you did was clever. That way you would indeed find the probabilities of bad dice and very bad dice in the first place ^^

VictoryFirst

@AndrewAAGamer said in AndrewAAgamer (Allies) vs. Germany (Ragnell804):

BTW if you did that it would be awesome if you used 16% / 68% /16% as the low, normal and high parameters.

I missed this. Currently the calculation are based on 15% - 70% - 15%. Is that a big deal? Where do the 16% and 68% come from? They seem familiar but I can’t put my finger on it. It had to with the standard deviations I believe.

crockett36

Is the purpose of this tactical, strategic or mathematical?

AndrewAAGamer

@VictoryFirst

LOL - that’s me. I can be clever with math but I am not good with math formulas.

AndrewAAGamer

@VictoryFirst said in AndrewAAGamer Solo Test:

@AndrewAAGamer said in AndrewAAgamer (Allies) vs. Germany (Ragnell804):

BTW if you did that it would be awesome if you used 16% / 68% /16% as the low, normal and high parameters.

I missed this. Currently the calculation are based on 15% - 70% - 15%. Is that a big deal? Where do the 16% and 68% come from? They seem familiar but I can’t put my finger on it. It had to with the standard deviations I believe.

You are quite correct. 68.2% is the standard deviation of the Bell Curve.

AndrewAAGamer

@crockett36 said in AndrewAAGamer Solo Test:

Is the purpose of this tactical, strategic or mathematical?

Both strategic and mathematical. Their is a broad discussion among a few of us, both on and off this site, as to how balanced DDay is, so some of us on this site are doing some testing to determine if it is balanced and if not how badly out of balance it is.

Originally some said it was as bad as 10% Allies vs 90% Axis or 20% Allies vs 80% Axis while I was saying 50% vs 50%. But based on the testing I am doing now it appears I was wrong - it does not appear to be 50-50. Not sure how much out of whack yet, still trying to figure that out. My current guess is 30-70 based on some of the numbers VictoryFirst is showing.

AndrewAAGamer

@VictoryFirst

In my test I found that there were a few land combat battles that had a 90% plus hit against 1 unit that I did not take the hit unless there was carry over from a previous battle. I found this to be rather disturbing as quite a few times there was no hit. With a 90% hit chance I am thinking it is better to take the hit, only a 10% difference, rather than missing, a 90% difference. So ONLY if their is 1 targeted unit left and the rolling side gets 90% plus I am taking it as a hit every time going forward.

VictoryFirst

@AndrewAAGamer said in AndrewAAGamer Solo Test:

You are quite correct. 68.2% is the standard deviation of the Bell Curve.

What Bell Curve exactly? Please elaborate on this.

VictoryFirst

@AndrewAAGamer said in AndrewAAGamer Solo Test:

In my test I found that there were a few land combat battles that had a 90% plus hit against 1 unit that I did not take the hit unless there was carry over from a previous battle. I found this to be rather disturbing as quite a few times there was no hit. With a 90% hit chance I am thinking it is better to take the hit, only a 10% difference, rather than missing, a 90% difference. So ONLY if their is 1 targeted unit left and the rolling side gets 90% plus I am taking it as a hit every time going forward.

Optionally what you could do is round up once it is 70%, round down if it is 30% and keep track of the difference. For the cases between 40%-60%, you try to minimize the differential at all times.

AndrewAAGamer

@VictoryFirst said in AndrewAAGamer Solo Test:

@AndrewAAGamer said in AndrewAAGamer Solo Test:

You are quite correct. 68.2% is the standard deviation of the Bell Curve.

What Bell Curve exactly? Please elaborate on this.

AndrewAAGamer

@VictoryFirst said in AndrewAAGamer Solo Test:

Optionally what you could do is round up once it is 70%, round down if it is 30% and keep track of the difference. For the cases between 40%-60%, you try to minimize the differential at all times.

Now THAT is an interesting thought as anything over 70% or below 30% is an outlier.

So, only use the 31%-69% results as the carry over? That does mean lone attacking infantry are only going be counted if there is carry over to get them to a hit but that is not a bad thing.

VictoryFirst

@AndrewAAGamer

Yeah so if you have 1.7 hits, that will become 2 hits with a difference of -0.3. Let’s say in another battle you have 1.6 hits. Since the differential is negative and you want to keep it as close to 0 as possible, you round down this time. Now the differential become +0.3.

AndrewAAGamer

@VictoryFirst said in AndrewAAGamer Solo Test:

@AndrewAAGamer

Yeah so if you have 1.7 hits, that will become 2 hits with a difference of -0.3. Let’s say in another battle you have 1.6 hits. Since the differential is negative and you want to keep it as close to 0 as possible, you round down this time. Now the differential become +0.3.

What I was doing was taking any carry over, 2.4 = .4 and applying it to the next battle. Thus the next battle at 1.2 becomes 1.6 and carry over .6. Then the next battle is 1.8 and all .6 is applied for a hit and then start over at 0 again.

Are you saying track all differences as a running total? For example, 1.3 becomes 1 hit with .3, then 1.9 becomes 2 hits, with .2 and then 2.7 is is 3 hits with -.1?

VictoryFirst

@AndrewAAGamer

Yes, I don’t think carrying overs are a good idea. When the battle calc says 2.4 hits, it should be 2.4 hits. However because you can only get a whole number of hits, the real number of hits are always off from the ideal number. You want to keep that difference to a minimum. So yes, I would suggest keeping track over an overall differential. Also - although it is just a feeling - I think you can’t just add leftovers from other battles without breaking the odds of the current battle.

VictoryFirst

@AndrewAAGamer said in AndrewAAGamer Solo Test:

Are you saying track all differences as a running total? For example, 1.3 becomes 1 hit with .3, then 1.9 becomes 2 hits, with .2 and then 2.7 is is 3 hits with -.1?

And to confirm, yes that is what I meant. It’s not perfect, although I think in the end it will work better than carrying over stuff. Although it deserves to be said that the “overall differential” method basically does the same thing as carrying over, it will negatively influence battles when the previous battle went positively and vice versa, however with this method you can more specifically make sure the overall difference stays as low as possible.

AndrewAAGamer

10 [dice 1d1000<=1]
11 [dice 1d1000<=1]
17 [dice 1d1000<=1]

dicebot

1d1000<=1: 708; Hits: 0
1d1000<=1: 894; Hits: 0
1d1000<=1: 195; Hits: 0

AndrewAAGamer Solo Test

TripleA Manual Gamesave Post: AlliedFighters round 9

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