Re: [DS] Hidden units and detection, including Recon by Fire

Alexander Williams wrote:

> >DS II already does this (kinda), with a second die.	But a second die
does
> >not increase your highest possible result, which a die value increase
DOES
> >do.	I think I like Mr. Martin's suggestion better.
>
>No, it doesn't increase the highest possible result, but it does
>decrease the chance of the /lowest/ possible result significantly, and
>since the only question is whether or not you beat the opposing roll,
>the stats actually work out much more smoothly.

Not really. If you use an "ideal" D14 (D16, D18 etc) as the norm your 
system gives better results than AM's if the opposing die is small
(D4-D6), 
they're about equally good against D8s, and AM's system is better if the

opposing die is a D10 or larger.

>If you're rolling
>d12,d4 and your opponant is d4, you are roughly twice as likely to
>succeed as you would have been without the Bonus.  If he is d6,
>roughly 1+2/3 as likely, etc.

Err... either you have a different definition of "success" than I have,
or 
you have a different definition of "twice" and "1+2/3" than I have. I'm
not 
quite sure which though :-/

In the above examples, I get the following probabilities (rounded to the

nearest whole %; "success" is always in terms of the attacker
succeeding):

Vs D4 opponents:

Attacker D4 vs Defender D10: 15% chance of success
Attacker D4 vs Defender D12: 13% chance of success
Going one die shift further:
"Ideal": Attacker D4 vs Defender D14 has 11% chance of success
"Martin": Attacker D4 vs Defender D12+1 has 6% chance of success
"Williams": Attacker D4 vs Defender D12, D4 has 7% chance of success

Attacker D10 vs Defender D4: 75% chance of success
Attacker D12 vs Defender D4: 79% chance of success
Going one die shift further:
"Ideal": Attacker D14 vs Defender D4: 82% chance of success
"Martin": Attacker D12+1 vs Defender D4: 88% chance of success
"Williams": Attacker D12, D4 vs Defender D4: 84% chance of success

And for D6 opponents:

Attacker D6 vs Defender D10: 25% chance of success
Attacker D6 vs Defender D12: 21% chance of success
Going one die shift further:
"Ideal": Attacker D6 vs Defender D14 has 18% chance of success
"Martin": Attacker D6 vs Defender D12+1 has 14% chance of success
"Williams": Attacker D6 vs Defender D12, D4 has 17% chance of success

Attacker D10 vs Defender D6: 65% chance of success
Attacker D12 vs Defender D6: 71% chance of success
Going one die shift further:
"Ideal": Attacker D14 vs Defender D6: 75% chance of success
"Martin": Attacker D12+1 vs Defender D6: 79% chance of success
"Williams": Attacker D12, D4 vs Defender D6: 74% chance of success

Dunno about you, but I usually don't consider 82% to be "roughly twice"
as 
much as 79%, nor would I say that 74% is "roughly 1+2/3" as much as
71%...

***

One important thing to remember here is that just because one side has
its 
success probability halved it doesn't automatically follow that the
other 
side has *its* success probability doubled. Eg., when AD4 vs DD12 is 
compared to AD4 vs DD12,DD4 the attacker's success probability drops
from 
13% to 7% (ie., it is cut roughly in half), but the defender's success
rate 
only increases from 87% to 93% - which is not *quite* a doubling :-/

Regards,

Oerjan
oerjan.ohlson@telia.com

"Life is like a sewer.
  What you get out of it, depends on what you put into it."