# SBR's with D8 D10 dice

• Has this been discussed in the past ?

I want the Bomber instead of rolling a D6 for damage would like to try a D8 die instead.

For H Bomber I would like to use a D10 and not use +1, +2 or +3 added to a D6 die.

Wouldn’t your odds/% go down and up higher the more sides you have on dies. I know the ave of each die is but if your only SBRing a couple of times a game at least get a chance of being rewarded for being  accurate with a higher die roll. I’ve been testing numbers and the D8 and D10 do come out with lower and higher numbers than a D6 which should but I would like risk factor. Just some thoughts. Maybe Baron can crunch some numbers. Look out now !

Thinking it could take out Russia to fast. But the German risk is low rolls and maybe US UK increase bombing runs ?

• Just for comparison,
D6 = avg 3.5 and standard deviation (SD)= 1.87
D6+2= range 3-8 with average 5.5, but max is 8 and SD is 1.87
1D8 = average 4.5, but max is 8 and SD is 2.45
1D10 = average 5.5, but max is higher: 10, SD= 3.028
1D6+3= range 4-9, avg 6.5, but max is 9, SD= 1.87
1D12 = average 6.5, but max is 12, SD= 3.6055
2D6= average 7, max is 12, SD= 2.44949

IDK how to compare this increase range with standard deviation.
And IDK how this increase in standard deviation (SD) somehow change level of SBR damage per raid.

• @Baron:

Just for comparison,
D6 = avg 3.5 and standard deviation (SD)= 1.87
D6+2= range 3-8 with average 5.5, but max is 8 and SD is 1.87
1D8 = average 4.5, but max is 8 and SD is 2.45
1D10 = average 5.5, but max is higher: 10, SD= 3.028
1D6+3= 4-9, avg 6.5, but max is 9, SD= 1.87
1D12 = average 6.5, but max is 12, SD= 3.6055
2D6= average 7, max is 12, SD= 6

IDK how to compare this increase range with standard deviation.
And IDK how this increase in standard deviation (SD) somehow change level of SBR damage per raid.

Baron Munchhausen

How in the world do you calculate range with dice, and how do you get your SB numbers, and what is a SBR???

One more thing, what is a OOB???

• OOB means Out Of the Box.
SBR: Strategic Bombing Raid
It is the usual odds when 1 St bomber bomb an IC but must submit to AAgun.
5/6 to survive then damage roll, G40 is D6+2, which is an avg of 5.5 (3+8=11 /2)
5/65.5 = 4.583 - 1/612 IPCs lost (cost of StB) = 2.583 avg IPCs dmg per raid or SBR.

Range is simply a way to show the gap between lowest and highest number.
Nothing specific about it, 1D8 is from 1 to 8.
SD or standard deviation was provided by a calc on line which also explains how to do it yourself.

No matter the bonus (+1, +2, +3), if you use D6, it is the same SD: 1.87.
Which is the square roots of variance: 3.5

It is calculated based on sum of all differences between avg and the given number then squared and this number is divided by n-1.
For instance, 1-3.5 = -2.5^2 = 6.25
2- 3.5 = -1.5^2 = 2.25
3- 3.5= -0.5^2 = 0.25
4- 3.5= 0.5^2 = 0.25
5- 3.5 = 1.5^2 = 2.25
6- 3.5 = 2.5^2 = 6.25
Sum: 17.5
n-1 = 5
Variance : 17.5 /5 = 3.5
SD : 1.87082…

• @SS:

Has this been discussed in the past ?

I want the Bomber instead of rolling a D6 for damage would like to try a D8 die instead.

For H Bomber I would like to use a D10 and not use +1, +2 or +3 added to a D6 die.

Wouldn’t your odds/% go down and up higher the more sides you have on dies. I know the ave of each die is but if your only SBRing a couple of times a game at least get a chance of being rewarded for being  accurate with a higher die roll. I’ve been testing numbers and the D8 and D10 do come out with lower and higher numbers than a D6 which should but I would like risk factor. Just some thoughts. Maybe Baron can crunch some numbers. Look out now !

Thinking it could take out Russia to fast. But the German risk is low rolls and maybe US UK increase bombing runs ?

@Baron:

Just for comparison,
D6 = avg 3.5 and standard deviation (SD)= 1.87
D6+2= range 3-8 with average 5.5, but max is 8 and SD is 1.87
1D8 = average 4.5, but max is 8 and SD is 2.45
1D10 = average 5.5, but max is higher: 10, SD= 3.028
1D6+3= range 4-9, avg 6.5, but max is 9, SD= 1.87
1D12 = average 6.5, but max is 12, SD= 3.6055
2D6= average 7, max is 12, SD= 2.44949

IDK how to compare this increase range with standard deviation.
And IDK how this increase in standard deviation (SD) somehow change level of SBR damage per raid.

So, if you use D10, you will get same avg 5.5 than D6+2, with more deviation from the mean near + -3 compared to near + -2 with OOB.
D10 is what your regular bomber should roll, not D8.

I cannot say, from a statistical POV, if your D10 odds of damage is greater or lower compared to the OOB SBR rule D6+2.
Maybe Larrymarx or Kreuzfeld might chimed in?

In this case, Heavy bomber should roll 2D6, if you like avg numbers, since it follow a normal bell curve.
Avg 7 + - 2.45 = 4.5 to 9.5 main variations.
If you like more variations, then use D12 for damage.
Avg 6.5+ - 3.6 = 3 or 10 main variations.

• From a statistical point of view, the bombers have a greater chance of dealing damage that is farther from the expected average if you go with D10 instead of D6+2.

These tables illustrate the chances of achieving a certain rate of damage per bomber rolling a given amount of dice. As you can see, the D6+2 method causes the chances to converge on a 5.5 average sooner than the D10 method. This is because you are allowing new possible ranges of outcomes for average damage: 1 through 3 and 8 through 10. Neither of those ranges are possible in D6+2, so of course some of the probability is going to get “diverted” and allocated to those new ranges.

The average damage is still the same, the odds of dealing more damage have gone up, and the odds of dealing less damage have also gone up.

D6+2
–--------------------------------------------
DMG   x1   x2   x3
3.0-3.5 16.67% 8.33%  1.85%
3.5-4.5 16.67% 19.44% 12.50%
4.5-5.5 16.67% 22.22% 35.65%
5.5-6.5 16.67% 22.22% 35.65%
6.5-7.5 16.67% 19.44% 12.50%
7.5-8.0 16.67% 8.33%  1.85%

## D10

DMG   x1   x2   x3
1.0-1.5 10.00% 2.00%  0.40%
1.5-2.5 10.00% 6.00%  3.10%
2.5-3.5 10.00% 10.00% 8.50%
3.5-4.5 10.00% 14.00% 16.30%
4.5-5.5 10.00% 18.00% 21.70%
5.5-6.5 10.00% 18.00% 21.70%
6.5-7.5 10.00% 14.00% 16.30%
7.5-8.5 10.00% 10.00% 8.50%
8.5-9.5 10.00% 6.00%  3.10%
9.5-10 10.00% 2.00%  0.40%

• Thank you very much Larrymarx.
For the issue at end, it would means that assuming a few SBRs in game, there is more randomness but the longer the game and the higher number of SBRs the more likely the sum of it will tend toward average results.

Maybe SS you can find some reason like interception or long range travel to increase randomness, while escorted might reduced interception effect.
Example, D6+2 when no opposition. Avg 5.5
D8 when interception occurs. Avg 4.5, 1 to 8 range
D10 when both escort and interceptor are present. Avg 5.5 but more random results, range from 1 to 10.

Being escorted, StB may have a different flight plan, being at lower altitude, escorts being targeted by AA too.
IDK, just looking for some rationalization to explain higher results (9 or 10).

• From a statistical point of view, the bombers have a greater chance of dealing damage that is farther from the expected average if you go with D10 instead of D6+2.

These tables illustrate the chances of achieving a certain rate of damage per bomber rolling a given amount of dice. As you can see, the D6+2 method causes the chances to converge on a 5.5 average sooner than the D10 method. This is because you are allowing new possible ranges of outcomes for average damage: 1 through 3 and 8 through 10. Neither of those ranges are possible in D6+2, so of course some of the probability is going to get “diverted” and allocated to those new ranges.

The average damage is still the same, the odds of dealing more damage have gone up, and the odds of dealing less damage have also gone up.

D6+2
–--------------------------------------------
DMG   x1   x2   x3
3.0-3.5 16.67% 8.33%  1.85%
3.5-4.5 16.67% 19.44% 12.50%
4.5-5.5 16.67% 22.22% 35.65%
5.5-6.5 16.67% 22.22% 35.65%
6.5-7.5 16.67% 19.44% 12.50%
7.5-8.0 16.67% 8.33%  1.85%

## D10

DMG   x1   x2   x3
1.0-1.5 10.00% 2.00%  0.40%
1.5-2.5 10.00% 6.00%  3.10%
2.5-3.5 10.00% 10.00% 8.50%
3.5-4.5 10.00% 14.00% 16.30%
4.5-5.5 10.00% 18.00% 21.70%
5.5-6.5 10.00% 18.00% 21.70%
6.5-7.5 10.00% 14.00% 16.30%
7.5-8.5 10.00% 10.00% 8.50%
8.5-9.5 10.00% 6.00%  3.10%
9.5-10 10.00% 2.00%  0.40%

Thank You Larrymarx. I already new the ave numbers and the odds would go up for low damage and higher damage but needed to see some numbers to confirm or at least get an idea.

Baron,

I got to choose an option here. It may change. Plus max damage on Capital factory’s is 16 in my 40 game.

1. Bomber     D8 = 1-8  4.5 ave  2 bombers = 9.0 ave  max dam 16  low dam 1
H Bomber  D10 = 1-10 5.5 ave  2 bombers = 11.0 ave  max dam 20  low dam 1

2. Bomber    D8+2 = 1-10 5.5 ave 2 bombers = 11.0 ave  max dam 20  low dam 3
H Bomber  D10+1 = 1-11 6.5 ave  2 bombers = 12.0 ave  max dam 22  low d 2
This would give you a bit less low risk and higher reward for accuracy.

3. Bomber    D10 = 1-10 5.5 ave  2 bombers = 11.0 ave  max dam 20  low dam 1
H Bomber  D12 = 1-12 6.5 ave  2 bombers = 13.0 ave  max dam 24  low dam 1
This option will give you the max in risk and higher reward.

OOB - Bomber D6+2 = 5.5 ave   2 bombers = 11.0 ave  max dam 16   low dam 3

G39 game - Bomber 2D6 = 7.0 ave   2 bombers = 14.0 ave  max dam 24  low d 2

Will this give you more SBR attacks in game ? You would think so with option 2 and 3.
Is this an other option to the C5 bomber ? I will need to choose an option by Sat. for another test game. Maybe this is to far out there but just some thoughts going on.

• I’d like to point out that increased randomness in both directions is not beneficial from most players’ points of view because players tend to send enough force to ensure good results. An attack is considered good if it has 80% chance or more of success. With D6+2, players should send 4 bombers to achieve this 80% threshold for maximum damage on a major industrial complex. With D10, players would still need to send 4 bombers, so the chance for additional damage in the upper probability band doesn’t matter because you are already expecting to deal maximum damage, but the chance for less damage in the lower probability band does matter because there is no minimum bound on damage. So when you speak in actual game terms, I think the odds of dealing less damage have gone up.

• I’d like to point out that increased randomness in both directions is not beneficial from most players’ points of view because players tend to send enough force to ensure good results. An attack is considered good if it has 80% chance or more of success. With D6+2, players should send 4 bombers to achieve this 80% threshold for maximum damage on a major industrial complex. With D10, players would still need to send 4 bombers, so the chance for additional damage in the upper probability band doesn’t matter because you are already expecting to deal maximum damage, but the chance for less damage in the lower probability band does matter because there is no minimum bound on damage. So when you speak in actual game terms, I think the odds of dealing less damage have gone up.

Yes I agree. Then I’ll go with option 2. 3 bombers still can do close to ave on max damage on a factory of 16 in my game and take the risk of sending 2 bombers and still get max damage with a good roll.  Just trying to increase SBR runs while not changing the cost and maybe get more 2 bomber raids instead 3 or 4 bombers.

• May try this.

Bomber    D12-2 = 1-10 5.5 ave  max dam 10  low damage 3
HBomber  D12 = 1-12 6.5 ave  max dam 12  low damage 3

Any roll of a 2 or less = 3 damage for lowest.
Example a roll of 1=3  roll of 2=3  roll of 3=3  roll of 4=4  roll of 5=5 and so on.

• 2. Bomber    D8+2 = 1-10 6.5 ave 2 bombers = 11.0 ave  max dam 20  low dam 3
H Bomber  D10+1 = 1-11 6.5 ave  2 bombers = 12.0 ave  max dam 22  low d 2
This would give you a bit less low risk and higher reward for accuracy

You have to check in a few calc when doubling up minimal dmg, should be 6 and 4.

If max dmg is only 16, you have a deterrent.

You loose simplicity if you add number to the dice roll…

If you want around 16 dmg, you can make bomber deal 2D6.
For 2 StBs: avg 14 dmg, max 24, min 4.
And it will get more avg dmg and less extreme, but still keep all random.
No +x bonus to warrant higher low dmg.

Heavy might rise to 2D8.
For 2 Hvy Bombers: avg 18 dmg, max 32, min. 4

C5 bomber is already good at D6, maybe heavy C8 rise to D8 or D10…

• I’m trying to stay away from the D6 dies. Will have to work it out. I just want to raise the reward a bit.

• This is what we have in game now.

Bombers C10
H Bombers C12

Bomber     D6  1-6  3.5 ave  6 max dam 1 lowest dam

H Bomber  D6+2  1-8  4.5 ave   8 max dam  3 lowest dam

This is the change I’m putting in next game.

Bomber    D8  1-8   4.5 ave    8 max dam  1 lowest dam

H Bomber  D10  1-10  5.5 ave  10 max dam  1 lowest dam

• @SS:

This is what we have in game now.

Bombers C10
H Bombers C12

Bomber     D6  1-6  3.5 ave  6 max dam 1 lowest dam

H Bomber  D6+2  1-8  4.5 ave   8 max dam  3 lowest dam

This is the change I’m putting in next game.

Bomber    D8  1-8   4.5 ave    8 max dam  1 lowest dam

H Bomber  D10  1-10  5.5 ave  10 max dam  1 lowest dam

Nice +1 dmg increase.
To your game, it fit perfectly well with no bonus, only 1 dice to roll.

I like the fact that heavy bomber get a wider range from 1 to 10.
I don’t think heavy (high altitude bomber) were more accurate than bomber.
Probably due to the high altitude of bombing.

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