Dual Wield Concept Rule

[cynthialee]

A control mechanism come to mind:
If you dual wield, you must re-roll 1 White Shield on all defense rolls, until the dual wield stance is changed.
{Comment: This one sucks but it isn't a total loss of the dice. The dice may come up shield the second time, thus saving your butt. But then this does damage to the other use of dual wielding, defending. Now there is no mechanism in the official rules for such a case, but there are in many house rules. I haven't figured out the rule I like for such a situation, but I figure using the off-hand for defending reduces the opportunity for attack.
Perhaps allow those with the training and quests under their belt may use a short-sword or similar weapon in the off hand for +1 Defend and a 1 Dice Attack on the primary or a secondary target.}

[Gold Bearer]

Bit fiddly. -1 defence dice is much cleaner and it's not as much of a punishment. Losing a dice that stands a two in three chance of making no difference is nowhere near as bad as making the first successful one in three into a one in nine.

[cynthialee]

??

Say we roll three dice: Three Shields. One must be re-rolled. If it comes up a shield a second time, it works.
Say we roll two dice: Two Shields with no chance for a third shield.

Option 1 is better in the long run.

[Gold Bearer]

Instead of taking away a one in three chance of a white shield you're taking away a definite white shield (three times as bad) and replacing it with another one in three chance of a white shield.

It's twice as much of a penalty as simply removing one defence dice because it's the equivalent of removing two defence dice, a white shield (equivalent of three dice because it's a one in three chance) being replaced with a one in three chance of white shield (gives one back to make it equivalent of loosing two die instead of three) instead of one in three chance of a white shield being lost.

[Gold Bearer]

I can explain it much more simply than that.

Removing one dice before they're rolled means it's a one in three chance of removing a white shield, so removing a white shield after they're rolled is equivalent to removing three dice before they're rolled, so removing a white shield and giving another dice is equivalent to removing two dice before they're rolled, simples.

[cynthialee]

But with 2 dice the max shields possible is 2. With the above forced re-roll on a single shield there is still a chance at 3 shields being rolled.

[Anderas]

But in the long run you will need to roll an average of three dice to get one shield. So if you force the one success of three dice to be rerolled, it is like having three defense dice less. Then you roll one of them anew, totaling in the equivalent of two defense dice less.

It's hard.

[Goblin-King]

At a glance I think GB is right here. Rolling 2 dice is better than rolling 3 and re-rolling 1 successful die.
The 3 dice has the ability to actually roll higher, but with only 2/6 chance on each die it seems like the worse deal.

I'd really love to see the actual math... Anybody?

[Anderas]

Yes, GB is right. And he gave the complete math. I try to reword to make it more math-alike.

First important point:
As we don't have complex dice interactions or rules here, we can calculate with simple averages and have everything covered.

Second Point:
One die equals in average .33 shields. You can say it the other way round, you need 3 dice to have one complete shield. In Average.


This rule negates 1 successful shield and lets you then roll one die to try and get the shield back.

So as you need 3 dice for one shield and this rule negates one shield, it negates the equivalent of 3 dice.
Then it gives you one die to roll again.

That makes -3+1 = -2 dice in total.


If you have the colored dice available, Cynthia, i would prefer to exchange a white die by a black die in defense. That removes half a die.

[Gold Bearer]

First important point:
As we don't have complex dice interactions or rules here, we can calculate with simple averages and have everything covered.

Second Point:
One die equals in average .33 shields. You can say it the other way round, you need 3 dice to have one complete shield. In Average.


This rule negates 1 successful shield and lets you then roll one die to try and get the shield back.

So as you need 3 dice for one shield and this rule negates one shield, it negates the equivalent of 3 dice.
Then it gives you one die to roll again.

That makes -3+1 = -2 dice in total.

Exactly, it's that simple.

Break up into two parts. First, removing a dice before they're rolled means there's a one in three chance of removing what would have been a white shield. So we can say that removing a white shield after they've been rolled is the same as removing three dice before they're rolled. The fact that you can potentially roll more white shields by removing one after they're rolled is irrelevant, it's already taken into account by the one in three chance of rolling a white shield on the dice that's removed before they're rolled.

The second part is adding a defence dice after removing a white shield. This means you're effectively removing two defence dice and then adding one, so it's exactly equivalent (on average) to removing two defence dice before the roll is made.

Another way of coming at it is that you're replacing the first one in three chance of rolling a white shield with a one in nine chance (rolling a white shield twice is one in nine, 3x3). This means that there's a two in three chance that the number of white shields will be reduce by one because there's a one in three chance that the number of white shields rolled will be the same as as straight roll (three in nine that you'll roll a white shield again on the reroll and six in nine that you won't). So there's a two in three chance of rolling one less white shield if you rereoll one white shield and a one in three chance of rolling one less white shield if you roll one less dice to start with.