Hit Points

Roll 4d6, drop lowest die. Table of all 6^4 = 1296 possible outcomes.

	1, 1	1, 2	1, 3	1, 4	1, 5	1, 6	2, 1	2, 2	2, 3	2, 4	2, 5	2, 6	3, 1	3, 2	3, 3	3, 4	3, 5	3, 6	4, 1	4, 2	4, 3	4, 4	4, 5	4, 6	5, 1	5, 2	5, 3	5, 4	5, 5	5, 6	6, 1	6, 2	6, 3	6, 4	6, 5	6, 6
1, 1	03	04	05	06	07	08	04	05	06	07	08	09	05	06	07	08	09	10	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	1, 1
1, 2	04	05	06	07	08	09	05	06	07	08	09	10	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	1, 2
1, 3	05	06	07	08	09	10	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	1, 3
1, 4	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	11	12	13	14	15	16	1, 4
1, 5	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	11	12	13	14	15	16	12	13	14	15	16	17	1, 5
1, 6	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	11	12	13	14	15	16	12	13	14	15	16	17	13	14	15	16	17	18	1, 6
2, 1	04	05	06	07	08	09	05	06	07	08	09	10	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	2, 1
2, 2	05	06	07	08	09	10	06	06	07	08	09	10	07	07	08	09	10	11	08	08	09	10	11	12	09	09	10	11	12	13	10	10	11	12	13	14	2, 2
2, 3	06	07	08	09	10	11	07	07	08	09	10	11	08	08	09	10	11	12	09	09	10	11	12	13	10	10	11	12	13	14	11	11	12	13	14	15	2, 3
2, 4	07	08	09	10	11	12	08	08	09	10	11	12	09	09	10	11	12	13	10	10	11	12	13	14	11	11	12	13	14	15	12	12	13	14	15	16	2, 4
2, 5	08	09	10	11	12	13	09	09	10	11	12	13	10	10	11	12	13	14	11	11	12	13	14	15	12	12	13	14	15	16	13	13	14	15	16	17	2, 5
2, 6	09	10	11	12	13	14	10	10	11	12	13	14	11	11	12	13	14	15	12	12	13	14	15	16	13	13	14	15	16	17	14	14	15	16	17	18	2, 6
3, 1	05	06	07	08	09	10	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	3, 1
3, 2	06	07	08	09	10	11	07	07	08	09	10	11	08	08	09	10	11	12	09	09	10	11	12	13	10	10	11	12	13	14	11	11	12	13	14	15	3, 2
3, 3	07	08	09	10	11	12	08	08	09	10	11	12	09	09	09	10	11	12	10	10	10	11	12	13	11	11	11	12	13	14	12	12	12	13	14	15	3, 3
3, 4	08	09	10	11	12	13	09	09	10	11	12	13	10	10	10	11	12	13	11	11	11	12	13	14	12	12	12	13	14	15	13	13	13	14	15	16	3, 4
3, 5	09	10	11	12	13	14	10	10	11	12	13	14	11	11	11	12	13	14	12	12	12	13	14	15	13	13	13	14	15	16	14	14	14	15	16	17	3, 5
3, 6	10	11	12	13	14	15	11	11	12	13	14	15	12	12	12	13	14	15	13	13	13	14	15	16	14	14	14	15	16	17	15	15	15	16	17	18	3, 6
4, 1	06	07	08	09	10	11	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	11	12	13	14	15	16	4, 1
4, 2	07	08	09	10	11	12	08	08	09	10	11	12	09	09	10	11	12	13	10	10	11	12	13	14	11	11	12	13	14	15	12	12	13	14	15	16	4, 2
4, 3	08	09	10	11	12	13	09	09	10	11	12	13	10	10	10	11	12	13	11	11	11	12	13	14	12	12	12	13	14	15	13	13	13	14	15	16	4, 3
4, 4	09	10	11	12	13	14	10	10	11	12	13	14	11	11	11	12	13	14	12	12	12	12	13	14	13	13	13	13	14	15	14	14	14	14	15	16	4, 4
4, 5	10	11	12	13	14	15	11	11	12	13	14	15	12	12	12	13	14	15	13	13	13	13	14	15	14	14	14	14	15	16	15	15	15	15	16	17	4, 5
4, 6	11	12	13	14	15	16	12	12	13	14	15	16	13	13	13	14	15	16	14	14	14	14	15	16	15	15	15	15	16	17	16	16	16	16	17	18	4, 6
5, 1	07	08	09	10	11	12	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	11	12	13	14	15	16	12	13	14	15	16	17	5, 1
5, 2	08	09	10	11	12	13	09	09	10	11	12	13	10	10	11	12	13	14	11	11	12	13	14	15	12	12	13	14	15	16	13	13	14	15	16	17	5, 2
5, 3	09	10	11	12	13	14	10	10	11	12	13	14	11	11	11	12	13	14	12	12	12	13	14	15	13	13	13	14	15	16	14	14	14	15	16	17	5, 3
5, 4	10	11	12	13	14	15	11	11	12	13	14	15	12	12	12	13	14	15	13	13	13	13	14	15	14	14	14	14	15	16	15	15	15	15	16	17	5, 4
5, 5	11	12	13	14	15	16	12	12	13	14	15	16	13	13	13	14	15	16	14	14	14	14	15	16	15	15	15	15	15	16	16	16	16	16	16	17	5, 5
5, 6	12	13	14	15	16	17	13	13	14	15	16	17	14	14	14	15	16	17	15	15	15	15	16	17	16	16	16	16	16	17	17	17	17	17	17	18	5, 6
6, 1	08	09	10	11	12	13	09	10	11	12	13	14	10	11	12	13	14	15	11	12	13	14	15	16	12	13	14	15	16	17	13	14	15	16	17	18	6, 1
6, 2	09	10	11	12	13	14	10	10	11	12	13	14	11	11	12	13	14	15	12	12	13	14	15	16	13	13	14	15	16	17	14	14	15	16	17	18	6, 2
6, 3	10	11	12	13	14	15	11	11	12	13	14	15	12	12	12	13	14	15	13	13	13	14	15	16	14	14	14	15	16	17	15	15	15	16	17	18	6, 3
6, 4	11	12	13	14	15	16	12	12	13	14	15	16	13	13	13	14	15	16	14	14	14	14	15	16	15	15	15	15	16	17	16	16	16	16	17	18	6, 4
6, 5	12	13	14	15	16	17	13	13	14	15	16	17	14	14	14	15	16	17	15	15	15	15	16	17	16	16	16	16	16	17	17	17	17	17	17	18	6, 5
6, 6	13	14	15	16	17	18	14	14	15	16	17	18	15	15	15	16	17	18	16	16	16	16	17	18	17	17	17	17	17	18	18	18	18	18	18	18	6, 6
	1, 1	1, 2	1, 3	1, 4	1, 5	1, 6	2, 1	2, 2	2, 3	2, 4	2, 5	2, 6	3, 1	3, 2	3, 3	3, 4	3, 5	3, 6	4, 1	4, 2	4, 3	4, 4	4, 5	4, 6	5, 1	5, 2	5, 3	5, 4	5, 5	5, 6	6, 1	6, 2	6, 3	6, 4	6, 5	6, 6

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Here are three tables, one for each method, listing the average value and probability of achieving each roll, for the various hit dice.

Normal. Most gamers know this one, but it's good for reference. Probability of achieving each roll.

Hit die	Average	1	2	3	4	5	6	7	8	9	10	11	12
d4	2.5000	0.2500	0.2500	0.2500	0.2500	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
d6	3.5000	0.1667	0.1667	0.1667	0.1667	0.1667	0.1667	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
d8	4.5000	0.1250	0.1250	0.1250	0.1250	0.1250	0.1250	0.1250	0.1250	0.0000	0.0000	0.0000	0.0000
d10	5.5000	0.1000	0.1000	0.1000	0.1000	0.1000	0.1000	0.1000	0.1000	0.1000	0.1000	0.0000	0.0000
d12	6.5000	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833

Variant 1. Roll one die. If below half, roll again and take the second roll. Probability of achieving each roll.

Hit die	Average	1	2	3	4	5	6	7	8	9	10	11	12
d4	3.0000	0.1250	0.1250	0.3750	0.3750	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
d6	4.2500	0.0833	0.0833	0.0833	0.2500	0.2500	0.2500	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
d8	5.5000	0.0625	0.0625	0.0625	0.0625	0.1875	0.1875	0.1875	0.1875	0.0000	0.0000	0.0000	0.0000
d10	6.75000	0.0500	0.0500	0.0500	0.0500	0.0500	0.1500	0.1500	0.1500	0.1500	0.1500	0.0000	0.0000
d12	8.0000	0.0417	0.0417	0.0417	0.0417	0.0417	0.0417	0.1247	0.1247	0.1247	0.1247	0.1247	0.1247

Variant 2. Roll two hit dice, take the larger of the two. Probability of achieving each roll.

Hit die	Average	1	2	3	4	5	6	7	8	9	10	11	12
d4	3.1250	0.0625	0.1875	0.3125	0.4375	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
d6	4.4722	0.0278	0.0833	0.1389	0.1944	0.2500	0.3056	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
d8	5.8125	0.0156	0.0469	0.0781	0.1094	0.1406	0.1719	0.2031	0.2344	0.0000	0.0000	0.0000	0.0000
d10	7.1500	0.0100	0.0300	0.0500	0.0700	0.0900	0.1100	0.1300	0.1500	0.1700	0.1900	0.0000	0.0000
d12	8.4861	0.0069	0.0208	0.0347	0.0486	0.0625	0.0764	0.0903	0.1042	0.1181	0.1319	0.1458	0.1597

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The left column is the Attack Difficulty. Although there is of course no -10 on a d20, it may be that your opponent's total AC bonuses minus your total attack bonuses is a negative number. The probabilities take into account auto-miss on a 1 and auto-hit on a 20 and assume a 19-20/x2 crit range.

The four columns under each heading (Full Attack, Manyshot, and Manyshot cost) are for the case when you are firing 2, 3, 4, or 5 arrows. These correspond to a base-attack bonus of 6-10, 11-15, 16-20, and 21-25. The data in each column is the expected number of arrows to hit the target for the Full Attack Action and Using Manyshot Feat groups; under Cost to Use Manyshot the numbers represent the number of arrows expected to miss because of the use of Manyshot. Negative numbers indicate that the Manyshot feat will actually cause you to hit more often than using a full attack action.

	Full Attack Action				Using Manyshot Feat				Cost to Use Manyshot
AD	2	3	4	5	2	3	4	5	2	3	4	5
-10	1.90	2.85	3.65	4.20	1.90	2.85	3.80	4.75	0.00	0.00	-0.15	-0.55
-9	1.90	2.85	3.60	4.10	1.90	2.85	3.80	4.75	0.00	0.00	-0.20	-0.65
-8	1.90	2.85	3.55	4.00	1.90	2.85	3.80	4.75	0.00	0.00	-0.25	-0.75
-7	1.90	2.80	3.45	3.85	1.90	2.85	3.80	4.50	0.00	-0.05	-0.35	-0.65
-6	1.90	2.75	3.35	3.70	1.90	2.85	3.80	4.25	0.00	-0.10	-0.45	-0.55
-5	1.90	2.70	3.25	3.55	1.90	2.85	3.60	4.00	0.00	-0.15	-0.35	-0.45
-4	1.90	2.65	3.15	3.40	1.90	2.85	3.40	3.75	0.00	-0.20	-0.25	-0.35
-3	1.90	2.60	3.05	3.25	1.90	2.70	3.20	3.50	0.00	-0.10	-0.15	-0.25
-2	1.85	2.50	2.90	3.05	1.90	2.55	3.00	3.25	-0.05	-0.05	-0.10	-0.20
-1	1.80	2.40	2.75	2.85	1.80	2.40	2.80	3.00	0.00	0.00	-0.05	-0.15
0	1.75	2.30	2.60	2.65	1.70	2.25	2.60	2.75	0.05	0.05	0.00	-0.10
1	1.70	2.20	2.45	2.50	1.60	2.10	2.40	2.50	0.10	0.10	0.05	0.00
2	1.65	2.10	2.30	2.35	1.50	1.95	2.20	2.25	0.15	0.15	0.10	0.10
3	1.55	1.95	2.10	2.15	1.40	1.80	2.00	2.00	0.15	0.15	0.10	0.15
4	1.45	1.8	1.90	1.95	1.30	1.65	1.80	1.75	0.15	0.15	0.10	0.20
5	1.35	1.65	1.70	1.75	1.20	1.50	1.60	1.50	0.15	0.15	0.10	0.25
6	1.25	1.50	1.55	1.60	1.10	1.35	1.40	1.25	0.15	0.15	0.15	0.35
7	1.15	1.35	1.40	1.45	1.00	1.20	1.20	1.00	0.15	0.15	0.20	0.45
8	1.05	1.20	1.25	1.30	0.90	1.05	1.00	0.75	0.15	0.15	0.25	0.55
9	0.95	1.05	1.10	1.15	0.80	0.90	0.80	0.50	0.15	0.15	0.30	0.65
10	0.85	0.90	0.95	1.00	0.70	0.75	0.60	0.25	0.15	0.15	0.35	0.75
11	0.75	0.80	0.85	0.90	0.60	0.60	0.40	0.25	0.15	0.20	0.45	0.65
12	0.65	0.70	0.75	0.80	0.50	0.45	0.20	0.25	0.15	0.25	0.55	0.55
13	0.55	0.60	0.65	0.70	0.40	0.30	0.20	0.25	0.15	0.30	0.45	0.45
14	0.45	0.50	0.55	0.60	0.30	0.15	0.20	0.25	0.15	0.35	0.35	0.35
15	0.35	0.40	0.45	0.50	0.20	0.15	0.20	0.25	0.15	0.25	0.25	0.25
16	0.30	0.35	0.40	0.45	0.10	0.15	0.20	0.25	0.20	0.20	0.20	0.20
17	0.25	0.30	0.35	0.40	0.10	0.15	0.20	0.25	0.15	0.15	0.15	0.15
18	0.20	0.25	0.30	0.35	0.10	0.15	0.20	0.25	0.10	0.10	0.10	0.10
19	0.15	0.20	0.25	0.30	0.10	0.15	0.20	0.25	0.05	0.05	0.05	0.05
20	0.10	0.15	0.20	0.25	0.10	0.15	0.20	0.25	0.00	0.00	0.00	0.00
AD	2	3	4	5	2	3	4	5	2	3	4	5
	Full Attack Action				Using Manyshot Feat				Cost to Use Manyshot

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The left column is the Attack Difficulty. Although there is of course no -10 on a d20, it may be that your opponent's total AC bonuses minus your total attack bonuses is a negative number. The probabilities take into account auto-miss on a 1 and auto-hit on a 20, and assume a 19-20/x2 crit range. The first main data columns are the expected number of arrows to hit with the AD (of the first arrow fired) to the left and attacker's base attack (implying number of arrows fired) at the top. The second set of columns repeats the calculation, this time taking Rapid Shot into account.

	Full Attack action					With Rapid Shot
AD	1-5	6-10	11-15	16-20	21-25	1-5	6-10	11-15	16-20	21-25
-10	1.00	2.00	2.99	3.83	4.41	2.00	2.99	3.99	4.73	5.2
-9	1.00	2.00	2.99	3.78	4.31	2.00	2.99	3.94	4.62	5.04
-8	1.00	2.00	2.99	3.73	4.20	2.00	2.99	3.89	4.52	4.88
-7	1.00	2.00	2.94	3.62	4.04	2.00	2.99	3.83	4.41	4.73
-6	1.00	2.00	2.89	3.52	3.89	2.00	2.99	3.78	4.31	4.57
-5	1.00	2.00	2.84	3.41	3.73	2.00	2.99	3.73	4.20	4.41
-4	1.00	2.00	2.78	3.31	3.57	2.00	2.94	3.62	4.04	4.20
-3	1.00	2.00	2.73	3.20	3.41	2.00	2.89	3.52	3.89	3.99
-2	1.00	1.94	2.63	3.05	3.20	2.00	2.84	3.41	3.73	3.78
-1	1.00	1.89	2.52	2.89	2.99	2.00	2.78	3.31	3.57	3.62
0	1.00	1.84	2.42	2.73	2.78	2.00	2.73	3.20	3.41	3.47
1	1.00	1.79	2.31	2.57	2.63	1.89	2.57	2.99	3.15	3.20
2	1.00	1.73	2.21	2.42	2.47	1.79	2.42	2.78	2.89	2.94
3	0.95	1.63	2.05	2.21	2.26	1.68	2.26	2.57	2.63	2.68
4	0.89	1.52	1.89	2.00	2.05	1.58	2.10	2.36	2.42	2.47
5	0.84	1.42	1.73	1.79	1.84	1.47	1.94	2.15	2.21	2.26
6	0.79	1.31	1.58	1.63	1.68	1.37	1.79	1.94	2.00	2.05
7	0.74	1.21	1.42	1.47	1.52	1.26	1.63	1.73	1.79	1.84
8	0.68	1.10	1.26	1.31	1.37	1.16	1.47	1.52	1.58	1.63
9	0.63	1.00	1.10	1.16	1.21	1.05	1.31	1.37	1.42	1.47
10	0.58	0.89	0.95	1.00	1.05	0.95	1.16	1.21	1.26	1.31
11	0.53	0.79	0.84	0.89	0.95	0.84	1.00	1.05	1.10	1.16
12	0.47	0.68	0.74	0.79	0.84	0.74	0.84	0.89	0.95	1.00
13	0.42	0.58	0.63	0.68	0.74	0.63	0.68	0.74	0.79	0.84
14	0.37	0.47	0.53	0.58	0.63	0.53	0.58	0.63	0.68	0.74
15	0.32	0.37	0.42	0.47	0.53	0.42	0.47	0.53	0.58	0.63
16	0.26	0.32	0.37	0.42	0.47	0.32	0.37	0.42	0.47	0.53
17	0.21	0.26	0.32	0.37	0.42	0.21	0.26	0.32	0.37	0.42
18	0.16	0.21	0.26	0.32	0.37	0.11	0.16	0.21	0.26	0.32
19	0.11	0.16	0.21	0.26	0.32	0.11	0.16	0.21	0.26	0.32
20	0.05	0.11	0.16	0.21	0.26	0.11	0.16	0.21	0.26	0.32
AD	1-5	6-10	11-15	16-20	21-25	1-5	6-10	11-15	16-20	21-25
	Full Attack action					With Rapid Shot