dice pools

Postulated: dice pools are fun. It is fun to adjust the number of dice you roll. It's scary to face a roll with fewer dice than usual, and feels great to roll a huge fistful.

Postulated: forgone conclusions are not fun. If you know before you roll the dice that there's no way to get a certain outcome, why roll?

Proposed: this is why people don't like taking sums of dice pools.

The fact that the floor of the sum of a dice pool shifts is problematic in a different way than that the peak of its bell curve shifts or than that its ceiling shifts. Look at the probability of rolling a certain sum or greater on 1-4 dice:

#	1D	2D	3D	4D
1	100.00%
2	83.30%	100.00%
3	66.70%	97.20%	100.00%
4	50.00%	91.70%	99.50%	100.00%
5	33.30%	83.30%	98.10%	99.90%
6	16.70%	72.20%	95.40%	99.60%
7		58.30%	90.70%	98.80%
8		41.70%	83.80%	97.30%
9		27.80%	74.10%	94.60%
10		16.70%	62.50%	90.30%
11		8.30%	50.00%	84.10%
12		2.80%	37.50%	76.10%
13			25.90%	66.40%
14			16.20%	55.60%
15			9.30%	44.40%
16			4.60%	33.60%
17			1.90%	23.90%
18			0.50%	15.90%
19				9.70%
20				5.40%
21				2.70%
22				1.20%
23				0.40%
24				0.10%

The floor moving is bad because it creates forgone conclusions by opening gaps in the outcome range of the smaller dice pools. It also creates them by shifting the 100% to outcomes that had previously not been 100%. We don't see either of those problems when we subtract the number of dice rolled from the sum:

#	1D	2D	3D	4D
0	100.00%	100.00%	100.00%	100.00%
1	83.30%	97.20%	99.50%	99.90%
2	66.70%	91.70%	98.10%	99.60%
3	50.00%	83.30%	95.40%	98.80%
4	33.30%	72.20%	90.70%	97.30%
5	16.70%	58.30%	83.80%	94.60%
6		41.70%	74.10%	90.30%
7		27.80%	62.50%	84.10%
8		16.70%	50.00%	76.10%
9		8.30%	37.50%	66.40%
10		2.80%	25.90%	55.60%
11			16.20%	44.40%
12			9.30%	33.60%
13			4.60%	23.90%
14			1.90%	15.90%
15			0.50%	9.70%
16				5.40%
17				2.70%
18				1.20%
19				0.40%
20				0.10%

This also makes the tiers of possible outcomes go up by 5s which is a lot easier to deal with mentally than going up by 6s (unless you're Count Rugen).

a modest proposal

Take the sixes off your dice and replace them with zeroes. Boom, done.