AndrewAAgamer (Allies) vs. Germany (Ragnell804)

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

How do you determine or play by avg dice?

Average Dice show the average number of hits based on the number of targeted units available. For example, 2 3’s plus 6 1’s are attacking 6 units. Average Dice say this is 2 hits. However, reduce the target units to 2 and the average dice changes to 1.6. You can easily represent this by putting the battle into a Battle Calculator and choosing 1 combat roll of dice. The result is average dice. Using this method we capture the average results in every battle based on all possible outcomes.

The issue with Average Dice is it overrepresents misses in small battles. Take that same battle as above and put in 1 target unit and the result will be 0.92 unit. Due to the chance of ANY miss Average dice will never give you 1 hit based on 1 target unit since there is always a chance the dice will miss.

Since in DDay there are a lot of 1 unit defensive battles, due to Fighters and AAA, we shouldn’t use average dice in those battles. Instead, the way to accommodate this issue is to use a targeted percentage of what constitutes an average hit. Using the Bell Curve we know that 68.2% of all results fall into 1 Standard Deviation. Since we are testing we want any result to at least cover that percentage. To achieve at least a 68.2% percentage for 1’s we need to adjust it to 7 rolls equals 1 hit (72%).

There are details as to how to implement this methodology for testing and if you are interested I will post them too before we begin.

@AndrewAAGamer

All understood, however when applying losses do we just round the Average Hits to the nearest whole? If consistent rounding up or down is applied then that creates the possibility of one side gaining an advantage over the other, however I assume you have a way to take that into account.

One game is fine, I am curious to see how the game will go with average dice. However regardless of the outcome it will not convince me of anything. A game will never be completely average, there will always be some up and downs for both sides in some cases and that also has an effect on the balance. For example, the Allies could be more susceptible to bad rolls than the Germans. And not to forget, risk also takes part in this. It can have a large impact if you already know what the final result of a battle will be before it takes place. It changes playstyle and strategy. Only a large number of games with standard rules will convince me.

Yes, please share the details of your methodology, thanks. However I think it’s best if you that in a separate thread.

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

However regardless of the outcome it will not convince me of anything. A game will never be completely average, there will always be some up and downs for both sides in some cases and that also has an effect on the balance.

Oh YES! Don’t think for even a second I am thinking games will be average. In fact, we KNOW they will not. Therefore, with even Dice, the Allies HAVE to win, otherwise the game is definitely unbalanced in favor of the Axis.

Just like Global 1940 the Allies have to win more than the Axis. In Global 1940 the Allies have to win on BOTH sides of the board; whereas the Axis only one to win on ONE side of the board. Thus, in Global 1940, for the game to be even, the Axis can only have a 37% chance of winning on either side. (37% plus 23% = 50%)

It is even worse in DDay. For me, I think there are 4 parts:

• Early game (Rounds 1, 2 and 3)
• Cherbourg
• St. Lo
• Caen

The Allies have to win in all 4 parts, the Germans only have to win in one. BTW I think an argument could be made that Caen and St Lo might be 1.5 instead of 2 due to they are kind of close but only tanks can move back and forth so I like to count it as two separate areas.

Therefore, the question is how much bad luck can the Allies take and still win? That is what the testing is for.

For example: Let’s assume the Allies win 100% of the time when they get fair dice. But they lose 20% of the time when they get bad dice in one area and they lose 60% of the time when they get very bad dice in any one area.

Looking at the Bell Curve = 15% low, 70% even, and 15% high. If we define Bad dice as getting less than your opponent and Very Bad dice as getting 2 levels of dice below your opponent then using this matrix we get:

Bad Dice = 10.5% + 2.25% +10.5% = 23.25% x 20% = 4.65%
Very Bad Dice = 2.25% = 2.25% x 60% = 1.35%
4.65% + 1.35% = 6%
Times four areas = 24% of the time the Axis wins.

So, the testing is really to try and give us an idea of how easily the Allies win with fair luck to see how much bad luck they need to lose.

@AndrewAAGamer

How are you going to test for Bad Dice and Very Bad Dice during games? Are you going to artificially shape the combat results so that they match the areas in the Bell Curve? How will you factor in the strategic importance of a battle? Some battles are more game deciding than others and dice results should weigh differently depending on that.

Not sure what you exactly wanted to calculate at the end of your post, but the percentages of a Bad Dice/Very Bad Dice result in any of the four areas isn’t calculated by multiplying it by four, but rather by calculating the chance that it doesn’t happen and raising it to the fourth power.

Bad Dice for Allies in one area = 23.25%
No Bad Dice for Allies in one area = 100% - 23.25% = 76.25%
No Bad Dice for Allies in all four areas= (76.25)^4 = 34.70%
Bad Dice for Allies in at least one area = 100% - 34.70% = 65,30%

With the same logic for Very Bad Dice
Very Bad Dice for Allies in at least one area = 8.70%

Still I don’t understand how one game is going to be more representative than ten however if it suits your needs that is fine with me.

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

@AndrewAAGamer

How are you going to test for Bad Dice and Very Bad Dice during games? Are you going to artificially shape the combat results so that they match the areas in the Bell Curve? How will you factor in the strategic importance of a battle? Some battles are more game deciding than others and dice results should weigh differently depending on that.

Not sure what you exactly wanted to calculate at the end of your post, but the percentages of a Bad Dice/Very Bad Dice result in any of the four areas isn’t calculated by multiplying it by four, but rather by calculating the chance that it doesn’t happen and raising it to the fourth power.

Bad Dice for Allies in one area = 23.25%
No Bad Dice for Allies in one area = 100% - 23.25% = 76.25%
No Bad Dice for Allies in all four areas= (76.25)^4 = 34.70%
Bad Dice for Allies in at least one area = 100% - 34.70% = 65,30%

With the same logic for Very Bad Dice
Very Bad Dice for Allies in at least one area = 8.70%

Still I don’t understand how one game is going to be more representative than ten however if it suits your needs that is fine with me.

Sweet! Someone who is good at math! Mind if I use your abilities?

I am a little confused.

You are saying that 65.3% of the time their will be bad dice in at least one area.

Are you also saying there will be Very Bad dice in at least one area 8.7% of the time?

Would you be able to calculate when we get Bad dice or Very Bad dice in two or more areas? That should be important too.

In my game with Ragnell804 there were two areas that had very bad dice. It would be nice to know what that percentage, 2 or more areas are, to calculate in 100% wins for the Axis.

Regarding the bad luck, no I am not testing for that. All I want to test for is IF the Allies get fair dice would they win every time. Then, subjectively, looking at the board and trying to determine how much bad dice they can take and still win. Right now I am guessing they can take bad dice in 1-2 areas or very bad dice in 1 area and still do fairly well and their performance would drop off from there. But, all of that comes after we know they win every time with no bad luck. If that isn’t the case, the game is unbalanced for sure.

@AndrewAAGamer

I was considered to be the “math nerd” in high school lol. Probabilities isn’t necessarily my strong point although I do know how to calculate basic stuff.

Are you also saying there will be Very Bad dice in at least one area 8.7% of the time?

Yes. The logic behind this is as follows. Suppose you make a probability tree of this. Let’s say there are only two areas for clarity.

Sorry for the bad handwriting, this was just a quick sketch to illustrate my explanation.

BD = Bad Dice
Encircled are the paths in which at least one area has BD for the Allies. To calculate the probabilty of an entire series of nodes to occur, you multiply the percentages of the entire path.

So then we get this.
BD EG + BD CAEN = 23% * 23% = 5.3%
BD EG + No BD CAEN = 23% * 77% = 17.7%
No BD EG + BD CAEN = 77% * 23% = 17.7%
Thus, the Allies have 5.3% + 17.7% + 17.7% = 40.7% to get Bad Dice in at least one area.

However, this is also equal to 100% minus the chance there is no BD for the Allies in either two areas.
100% - 77% * 77% = 100% - 59.3% = 40.7%

So the latter method is essentially a much quicker way to calculate this. Instead of three calculations, we are making one. In cases of many possibilities, this will save a lot of comptutation time while basically achieving the same thing.

I will take a deep look at your game with Ragnell.

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

Would you be able to calculate when we get Bad dice or Very Bad dice in two or more areas? That should be important too.

I think what will be difficult here is defining what territories belong which areas. For example a battle in G28, should you include it under Caen or St. Lo? Units there can go either way. An approach like this is almost impossible.

All I want to test for is IF the Allies get fair dice would they win every time.

Alright, that sounds logical, taking one step at a time. My first guess they wouldn’t but I am going to play a solo game first with this. I want to see what effect the average dice will have on the game. After that we can play.

@AndrewAAGamer

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

a) I am calm, I am addressing the point presented by Ragnell804 in a logical manner so not sure where that is coming from. b) It does not matter what you expressed in your strategy video. Ragnell804 said he has never seen Omaha Beach bombarded in his tests game which means your test games are flawed.

I misspoke earlier. I personally never went after Omaha Beach. @The_Good_Captain used that against me several times upon reviewing some of our game files. This was my first time playing D-Day in over EIGHT months, with about 50 games crammed in between; sorry, my memory was a little fuzzy. Ironically, though, one of the few Allied wins came from my game when I saved the UK tanks on turn 1. So his testing is not flawed; just my memory of the games was.

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

@AndrewAAGamer

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

a) I am calm, I am addressing the point presented by Ragnell804 in a logical manner so not sure where that is coming from. b) It does not matter what you expressed in your strategy video. Ragnell804 said he has never seen Omaha Beach bombarded in his tests game which means your test games are flawed.

I misspoke earlier. I personally never went after Omaha Beach. @The_Good_Captain used that against me several times upon reviewing some of our game files. This was my first time playing D-Day in over EIGHT months, with about 50 games crammed in between; sorry, my memory was a little fuzzy. Ironically, though, one of the few Allied wins came from my game when I saved the UK tanks on turn 1. So his testing is not flawed; just my memory of the games was.

That is good to know. At least some of your test games used the appropriate opener.

I do appreciate the game. I was able to confirm what I suspected was your German strategy based on the videos and with that information I can work on testing.

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

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

Would you be able to calculate when we get Bad dice or Very Bad dice in two or more areas? That should be important too.

I think what will be difficult here is defining what territories belong which areas. For example a battle in G28, should you include it under Caen or St. Lo? Units there can go either way. An approach like this is almost impossible.

I guess I wasn’t clear. I am not looking for you to peruse the game I just had and figure out what the dice variable was. I was hoping, if possible, due to your math skills, if sometime in the near future you would be able to tell me certain odds like you just did. For example:

• Odds of at least 1 area area with Bad dice
• Odds of at least 2 areas with Bad dice
• Odds of at least 1 area with Very Bad dice
• Odds of at least 2 areas of Very Bad dice

That way, once, and if, we can confirm the Allies win 100% of the time with even dice, or dice favorable to the Allies we could assign percentages to the varies bad dice and come up with some estimate of how often the Germans would win. BTW if you did that it would be awesome if you used 16% / 68% /16% as the low, normal and high parameters.

All I want to test for is IF the Allies get fair dice would they win every time.

Alright, that sounds logical, taking one step at a time. My first guess they wouldn’t but I am going to play a solo game first with this. I want to see what effect the average dice will have on the game. After that we can play.

Here is a link to a solo test I started. I will place the methodology instructions there that I am using for the testing.

https://www.axisandallies.org/forums/topic/41401/andrewaagamer-solo-test?_=1733436170864