Tuesday, May 17, 2011

I recently wrote about the trouble of dice pool mechanics with large number of participants to roll for. I presented some solutions such as using a new mechanic, changing the way you roll for things (using "rerolls," for example), or just not giving mooks situational modifiers.

I think there may be a more creative way to attack this issue: allow mooks (and/or others) to combine their dice pools. One of the great things about the Septimus core mechanic is that it has diminishing returns built in. Adding new dice -- especially beyond three or four in the pool -- has fairly negligible results. It will never hurt the players to let the monsters pool their attacks.

So, say we have five goblin archers that all throw two dice in the attack. Instead of having them roll six attacks with two dice each, you could have them roll one attack with 10 dice. They're almost certain to hit (avg result of 6.648, 98% of hitting TN5, 83.84% of hitting TN6, 51.54% of hitting TN7), but will only inflict one wound. Let's compare the number of successes when (1) rolling five attacks of 2d6 and (2) rolling one attack of 10d6.

4 5 6 7 8
5x2d6 3.75 2.75 1.50 0.14 0.00
1x10d6 1.00 0.98 0.83 0.52 0.23

As you can see, the DM is much better off rolling separate attacks until the TN gets to 7. Then he's best off with one giant 10d6 dice pool to try and land a hit. That's the diminishing returns in action. The plus is that it is a "bank error in the PCs" favor. I'm generally ok with those. The downside is that there's no incentive to economize time at the table under most circumstances, and if the DM decides to screw the players he could all of a sudden land three times as much damage as they're expecting.

One way to control this is possibly through the economy of actions. Maybe the DM gets a limited number of attacks to split amongst all the monsters however he wishes, the number being based on the leadership and morale of the enemy force. If he only has three attacks, and he's got the five goblin archers, a cave troll, and a worg to play with, he'll probably want to attack once with the troll, once with the worg, then pool all the goblins together. This has the nice effect of modeling "fog and friction" and rewarding effective command and control "force multipliers." For example, say the DM could also add a non-combatant shaman that gives his force one extra attack each round. Now the PCs have a strategic choice: do they take out mooks to reduce the number of attacks getting chucked at them, target the leader-shaman to reduce the effectiveness of the enemy's dice, or hit the heavy hitters to take them out of the fight?


Another option is to let the players roll. For example, maybe instead of having monsters roll to hit a player, the player needs to roll against a fixed TN to "dodge" the monster. A very accurate monster might have a higher TN, whereas a weaker or less precise one might have a lower TN. I like putting rolls into the hands of players quite a bit, but this can lead to some wonkiness if there are players on both sides of a conflict.

It also doesn't solve the time consuming need to roll many dice pools over and over; in fact, it might make it worse (especially with a slow player!), although players might not mind slowing down the action if they throw more dice. You could introduce a rule that says that adding more monsters increases the TN. For example, maybe dodging an arrow from one goblin archer is TN4, but two is TN5, four archers in TN6, eight archers is TN7, and so on. I'd have to work out the math to see exactly how that progression should work out.

Mechanics and Efficiency

I really like the math behind my proposed core mechanic (in short: roll a pool of D6s, retain the highest, boxcars = 7). It works great for PCs and singleton foes. However, in a playtest I came up against a problem: it doesn't work well for hordes of mooks.

In traditional D&D, if you have a half dozen goblin archers you just roll six D20s to see if they hit. Likewise, if the wizard hits a squad of orcs with a fireball, you just roll a fistful of D20s to see if they save. With the dice pool mechanic, you generally have to roll one monster at a time unless they have a pool of "one;" if you color code your D6s, perhaps 2-3 at a time.

One work around would be to treat the dice pool as a "reroll." For example, say each monster has a dice pool of 2D. You could roll 1d6 for each of them and then reroll for any that failed on the first check. That is probably faster than setting up a color coded dice pool but still requires two steps. Another "solution" would be to limit situational bonuses or modifiers given to mooks; maybe part of being a mook is that you don't get modifiers to your dice pool.

I also recently thought of another simple dice mechanic that uses D6s but gives a bit more fidelity at the top of the scale: Exploding dice.
  • Roll a D6 vs. a TN.
  • If you roll a 6, roll again. If you get a 5 or a 6, then add 1 to your result. If you get another 6, roll again.
That gives an approximately 1/20 chance of getting a 7, and a 1% of getting an 8. That is, setting a TN of "7" is basically like saying, "You need a hail-mary natural 20 to hit this TN."

1 (16%)
2 (16%)
3 (16%)
4 (16%)
5 (16%)
6 (10%)
7 (5%)
8 (1%)

The problem is that it doesn't scale well with modifiers. A straight +1 modifier is fairly huge, as it doubles the chances of getting a 7 and quintuples the chance of getting an 8. You could reduce the number at which a highly skilled individual's dice "explode." For example, if you get to roll again on a 5 or a 6 then the distribution looks like this:

1 (16%)
2 (16%)
3 (16%)
4 (16%)
5 (10%)
6 (15%)
7 (5%)
8 (1%)

That leads to a somewhat wonky distribution, though, where 6 is more likely than 5.

Odds of getting a 6: .166
Odds of getting a 5 or a 6: .333
.166 * .333 = 5.5%