4.2.3.2 Low odds attack (Full Version)

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Angeldust2 -> 4.2.3.2 Low odds attack (1/29/2022 11:56:09 AM)

Please see the combat results attached.
If combat values of 7:7 would yield a +2, then 6:7 should yield a +1,2 , but not 5:7. What am I missing?
And why is the failed fractional odds shown as -1, instead of 0?
And even if the fractional odds = -1 would be correct, why is the net drm then not -2, instead of -1?



[image]local://upfiles/71407/C230031CDBC7489F83B612A91803B366.jpg[/image]



Orm -> RE: 4.2.3.2 Low odds attack (1/29/2022 1:35:44 PM)

Assuming the odds modifier is correct in giving the attack to +1.2 then it follows to me:

+1.2 in odds
-2 in ARM bonus
Gives -0.8 as final odds
-0.8 is rounded to -1
With a fractional odds roll that if it succeeds would change the attack to +0
And since the fractional odds roll failed the attack is at -1

Does that make it any clearer? [&:] [:)]

Making another post about the fractional odds.



Orm -> RE: 4.2.3.2 Low odds attack (1/29/2022 1:39:53 PM)

It does however seem inconsistent with how the fractional odds is displayed with higher odds. It should, in my humble opinion, be shown as +1 is the fractional roll is a success, or a +0 if it is a failure.

Graphic bug maybe?



Orm -> RE: 4.2.3.2 Low odds attack (1/29/2022 1:43:20 PM)

I have trouble calculating fractional odds below 1:1 with the 2d10 table because 2:3 gives a +1 modifier, and 1:2 gives +0. The modifier is not linear here. [:(]



Orm -> RE: 4.2.3.2 Low odds attack (1/29/2022 1:57:59 PM)

5:7 rounds to 2:3 in odds which gives +1. The attacker then has 0.33 in spare factors. Attack Factors needed for reaching 1:1 (or 7:7) is 2.33.

So shouldn't the fractional odds be 0.33:2.33 which is 0.14?

0.14 is not that far from 0.2 shown as fractional odds. Wonder if it is some rounding error somewhere? [&:]



paulderynck -> RE: 4.2.3.2 Low odds attack (1/29/2022 6:02:41 PM)

2D10 DRMs are linear from odds of 1:6 on up. You have to take into account that each half odds increment is a difference of 1 DRM.

1:2 gives 0
2:3 = 1:1.5 gives +1
1:1 gives +2
1.5:1 gives +3 etc.

so 1:2.5 gives -1
1:3 gives -2
1:3.5 gives -3 etc.

People disagree on how to interpolate between the DRMs to produce the "chance" (i.e. the fractional probability) of going up by one DRM from the one you are at if there were no fractional odds in play.



ACMW -> RE: 4.2.3.2 Low odds attack (1/29/2022 9:15:06 PM)

This is also my calculation. I would therefore agree with your implication that the Fractional Odds should be 0.1 not 0.2. If it was the case that 1:1 was +O, you could kind of imagine that fractional rounding below that might go the other way: rounding towards the '0' both positive and negative. I wonder if, in the implementation, Shannon might have done the calculations that way and then added +2 to correct for that offset. Not sure how he'd deal with the non-linearities with that schema, but maybe.

Cheers

Adrian



paulderynck -> RE: 4.2.3.2 Low odds attack (1/30/2022 3:21:31 AM)

The mathematically correct calculation is this:

To get 1:1.5 odds against 7 requires 4.66667 factors. So base DRM before fractions and mods (since rounding is always in favor of the defender) is +1. With fractional odds, there is some chance to get the attack to a DRM of +2. The attacker has 5 minus 4.66667 = 0.33333 "spare" factors to try to bridge the gap between 4.66667 and 7, which is 2.333333. Therefore the fraction is 0.33333/2.33333 = .1428

The armor mod makes the attack a -1 instead of a +1 and there should be a 14.28% chance of it being a straight up zero DRM.

You could also express the DRMs including fractionals as = 1.1428 - 2 = -0.8572 or an 85.72% chance of being a minus 1.



Draconis -> RE: 4.2.3.2 Low odds attack (2/1/2022 2:04:55 AM)

Trying to figure out the derivation of the 1.20 combat ratio (0.200 fractional).

The half odds are the key I think. (Not considering the Armor modifier in the below analysis).

2:3 is 1:1.5 in half odds with a DRM of +1
1:1 is 1:1.0 in half odds with a DRM of +2

The reference battle is 5:7 which is 1:1.4 in half odds

Spread from the above DRM levels in half odds is 1.5 to 1.0 = 0.5
The battle is 0.1 on it way to the higher DRM or 0.1/0.5 or 20%

Is that how the 1.20 combat ratio and 20% fractional is derived?
That’s the only thing I could figure that yields the fractional.



Shannon V. OKeets -> RE: 4.2.3.2 Low odds attack (2/1/2022 7:10:11 PM)


quote:

ORIGINAL: Draconis

Trying to figure out the derivation of the 1.20 combat ratio (0.200 fractional).

The half odds are the key I think. (Not considering the Armor modifier in the below analysis).

2:3 is 1:1.5 in half odds with a DRM of +1
1:1 is 1:1.0 in half odds with a DRM of +2

The reference battle is 5:7 which is 1:1.4 in half odds

Spread from the above DRM levels in half odds is 1.5 to 1.0 = 0.5
The battle is 0.1 on it way to the higher DRM or 0.1/0.5 or 20%

Is that how the 1.20 combat ratio and 20% fractional is derived?
That’s the only thing I could figure that yields the fractional.

Without looking at the code, that seems right to me.

The key element is to determine how many more points are needed to reach the next odds level. That value is then divided into how far towards achieving that amount the current odds have. The resulting fraction is the probability of the fractional odds die roll succeeding.

I know I did something comparable for negative odds - but that was many years ago and it was a pain to figure out.



paulderynck -> RE: 4.2.3.2 Low odds attack (2/3/2022 2:42:00 AM)

quote:

ORIGINAL: paulderynck

People disagree on how to interpolate between the DRMs to produce the "chance" (i.e. the fractional probability) of going up by one DRM from the one you are at if there were no fractional odds in play.




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