Fireball half damage on save

At the table

In D&D 5e, Fireball deals 8d6 fire damage on a failed Dexterity saving throw. On a success, the target takes half that damage, rounded down (same as halving each possible total with floor division).

Try it

In the playground, open this recipe in the playground and click Run. Output shows the full-damage distribution and the succeeded-save distribution side by side.

The script

↗output("failed_save", 8d6)
output("succeeded_save", 8d6 // 2)

failed_save · DieRoll · mean 28.000

outcome	%	frac	X
8	0.00	0	0.000
9	0.00	0.000	0.000
10	0.00	0.000	0.000
11	0.01	0.000	0.000
12	0.02	1/5064	0.000
13	0.05	1/2117	0.000
14	0.10	1/983	0.001
15	0.20	2/997	0.002
16	0.37	4/1093	0.004
17	0.62	4/641	0.006
18	1.00	13/1299	0.010
19	1.52	10/659	0.015
20	2.18	23/1053	0.022
21	2.99	5/167	0.030
22	3.92	44/1123	0.039
23	4.90	49/999	0.049
24	5.88	424/7207	0.059
25	6.77	84/1241	0.068
26	7.48	115/1538	0.075
27	7.94	128/1613	0.079
28	8.09	48/593	0.081
29	7.94	128/1613	0.079
30	7.48	115/1538	0.075
31	6.77	84/1241	0.068
32	5.88	424/7207	0.059
33	4.90	49/999	0.049
34	3.92	44/1123	0.039
35	2.99	5/167	0.030
36	2.18	23/1053	0.022
37	1.52	10/659	0.015
38	1.00	13/1299	0.010
39	0.62	4/641	0.006
40	0.37	4/1093	0.004
41	0.20	2/997	0.002
42	0.10	1/983	0.001
43	0.05	1/2117	0.000
44	0.02	1/5064	0.000
45	0.01	0.000	0.000
46	0.00	0.000	0.000
47	0.00	0.000	0.000
48	0.00	0	0.000

succeeded_save · DieRoll · mean 13.750

outcome	%	frac	X
4	0.00	0.000	0.000
5	0.01	0.000	0.000
6	0.07	1/1495	0.001
7	0.30	1/331	0.003
8	0.99	37/3738	0.010
9	2.52	31/1231	0.025
10	5.18	45/869	0.052
11	8.82	395/4477	0.088
12	12.7	125/988	0.127
13	15.4	84/545	0.154
14	16.0	193/1204	0.160
15	14.2	51/358	0.142
16	10.8	115/1066	0.108
17	6.91	77/1114	0.069
18	3.70	69/1864	0.037
19	1.62	20/1231	0.016
20	0.57	2/353	0.006
21	0.15	1/672	0.001
22	0.03	1/3719	0.000
23	0.00	0.000	0.000
24	0.00	0	0.000