I recently played a Warhammer 40k adaption using the Savage Worlds game system by the Pinnacle Entertainment Group, and they had an interesting game mechanic that I had not run into before – the Savage Worlds Ace system. I was attempting to optimize my character’s combat performance, and my knee-jerk reaction was that Trademark weapon (which provides a flat +1 bonus) was less useful than increasing the die type. However, there were two factors that I hadn’t dealt with before in RPG’s that made it an interesting challenge to optimize.
First, the aforementioned Savage Worlds Ace system. A dice that rolls its maximum value is rolled again and this new roll is added to the total. Second, player characters (PCs) gain a Wild Die (d6) which they roll along with their appropriate die and they can use the result of either.
Let’s do some math.
Starting with a d6 in a skill, is it better to increase die type it to a d8, or add +1 (d8 or d6 vs d6+1 or d6+1)?
Acronyms and Keywords:
dX – Die with X amount of sides.
Ace – Occurs when a player rolls the maximum value on a die. The player is allowed to reroll the die in question and add this new value to their previous roll.
Raise – Occurs when a player beats a TN by 4. Each increment of 4 is an additional raise (i.e. beat by 8 is 2 raises, etc).
TN – Target Number – The number the player needs to roll for an action to succeed.
X R – Shorthand for dX is rolled and the desired value occurs. For example, P(6 R) for a raise (+4 on top of the TN) where the TN = 4 is shorthand for calculating the probability that a player gets a total of 8 or more when rolling a d6.
Success % (TN = 4) = [ 1 – 3/8 * ( 3/6 ) ] * 100% = 81.25%
Raise % (TN = 4) = P(8 R) + P(6 R) – P(8 & 6 R) = P(8 R) + P(6 R) – P(8 R) P(6 R) = [ ( 1/8 ) + ( 5/36 ) – ( 1/8 ) ( 5/36 ) ] * 100% = 24.6%
2 Raises % (TN = 4) = 10.4%
Success % (TN = 4) = [ 1 – 2/6 * ( 2/6 ) ] * 100% = 88.9%
Raise % (TN = 4) = P(6+1 R) + P(6+1 R) – P(6+1 R)P(6+1 R) = [ ( 1/6 ) + ( 1/6 ) – ( 1/6 )( 1/6 ) ] * 100% = 30.1%
2 Raises % (TN = 4) = 10.8 %
Success % (TN = 4) = [ 1 – 3/6 * ( 3/6 ) ] * 100% = 75%
Raise % (TN = 4) = P(6 R) + P(6 R) – P(6 R)P(6 R) = [( 5/36 ) + ( 5/36 ) – ( 5/36 )( 5/36 )] * 100% = 25.8%
2 Raises % (TN = 4) = 5.4%
For those of you who don’t care about the math or to sort through it, this means the following:
A +1 bonus is almost always better than a die type increase, at least for straight success / raise considerations (it might change at 3 raises and beyond, I’ve not done the math there).
The ace system makes lower die (d4, d6) types much stronger at getting raises than marginal die increases (d8)
The wild die really messes with probabilities of die types around d4-d8, due to the d6 being very strong in comparison
This goes back to another concern I had, in that increasing your die type actually decreases your chance for high single digit numbers, in this case, raises go down slightly for a die type increase compared to baseline. This is very counter-intuitive; a sniper that raises their Shooting from d6 to d8 actually decreases their chance at hitting at long range (TN = 8)!
I’m not suggesting that the Savage Worlds Ace system is necessarily problematic, although I doubt it was intended that increasing your die type can reduce your chance of success in specific situations. I’m also wondering if the game designers knew this and it was simply an artifact of the system they couldn’t / didn’t want to remove.