Re: [GZG] Opposed roll randomness (Was: [SG3]: What if?)

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basic calculations:

Opposed die roll calculations

Player A vs. Player B

D6 vs D6

Player A has 41% chance of winning an opposed die roll (15 wins, 15
losses,
6 ties)

D8 vs D6

Player A has 56% chance of winning an opposed die roll (27 wins, 15
losses,
6 ties)

D10 vs D6

Player A has 65% chance of winning an opposed die roll (39 wins, 15
losses,
6 ties)

D12 vs D6

Player A has 71% chance of winning an opposed die roll (51 wins, 15
losses,
6 ties)

Overall the statistics look ok as a D12 unit should win at a ratio of
almost
3:1 compared to a d6 unit which will win at less than the rate of 1:1.
Which
makes the d12 unit roughly 3 times more effective than the d6 unit.

If you ignore ties, the numbers increase slightly:

Opposed die roll calculations

Player A vs. Player B

D6 vs D6

Player A has 50% chance of winning an opposed die roll (15 wins, 15
losses,
6 ties)

D8 vs D6

Player A has 64% chance of winning an opposed die roll (27 wins, 15
losses,
6 ties)

D10 vs D6

Player A has 72% chance of winning an opposed die roll (39 wins, 15
losses,
6 ties)

D12 vs D6

Player A has 77% chance of winning an opposed die roll (51 wins, 15
losses,
6 ties)

Overall the statistics look ok as a D12 unit should win at a ratio of
3:1
compared to a d6 unit which will win at the rate of 1:1.

Using this as a baseline, you would then need to determine if a d12 unit
is
3 times better than a d6 unit and price them accordingly.
--Binhan

On 2/1/08, Allan Goodall <agoodall@hyperbear.com> wrote:
>
> On Feb 1, 2008 7:12 AM, The Sutherlands <nishawn@charter.net> wrote:
> > Do get the the result of poor troops have to do very well to beat
good
> > troops who have done very poorly can you just add a modifier to the
base
> > roll for quality?
>
> Therein lies the issue that Oerjan et al have been saying. That's
> entirely the _wrong_ way to look at it.
>
> People are assigning a worth to each roll of the dice on both sides.
> One side rolls good while the other side rolls bad, or one side rolls
> bad and the other side rolls terrible. It's natural, of course, but
> that's not how you should look at it.
>
> You should look at the overall odds of success, period. It's the end
> result that you need to worry about it, not the individual dice rolls
> that you took to get there.
>
> As Stephen pointed out, there's a 1.3% chance for a Green to beat an
> elite. If you had a big chart that said "Green defeating Elite: 1 on a
> D100" and a Green unit rolled a 01, we wouldn't be having this
> conversation.
>
> --
> Allan Goodall 	   http://www.hyperbear.com
> agoodall@hyperbear.com
> awgoodall@gmail.com
>
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