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

["Binhan Lin" <binhan.lin@xxxxxxxxx>]

Some 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@xxxxxxxxxxxxx> wrote:

On Feb 1, 2008 7:12 AM, The Sutherlands <nishawn@xxxxxxxxxxx> 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@xxxxxxxxxxxxx
awgoodall@xxxxxxxxx

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