Mana Comparison

👉 This page compares the starting mana and mana growth of all character classes and races in GnollHack.

🔮 Mana by Character Class

Character Class	Starting Mana	Mana Per Level	Avg. Int	Avg. Wis	Starting Stat Bonus	Per Level Stat Bonus
Archaeologist	1d4+3 (avg. 5.5)	+1d3+1 (avg. 3)	14	14	+8	+2.17
Barbarian	1d2 (avg. 1.5)	+1d2 (avg. 1.5)	7	8	+4	+1.06
Caveman	1d6+1 (avg. 4.5)	+1d2+1 (avg. 2.5)	8	13	+5	+1.44
Healer	1d3+6 (avg. 8)	+1d3+2 (avg. 4)	14	14	+8	+2.17
Knight	1d4+2 (avg. 4.5)	+1d2+1 (avg. 2.5)	7	13	+5	+1.33
Monk	1d4+4 (avg. 6.5)	+1d2+2 (avg. 3.5)	9	14	+6	+1.61
Priest	1d3+6 (avg. 8)	+1d3+2 (avg. 4)	10	18	+7	+1.94
Ranger	1d2+3 (avg. 4.5)	+1d2+1 (avg. 2.5)	9	10	+5	+1.39
Rogue	1d2+3 (avg. 4.5)	+1d2+1 (avg. 2.5)	10	10	+6	+1.50
Samurai	1d3 (avg. 2)	+1d2 (avg. 1.5)	10	8	+5	+1.39
Tourist	1d4+3 (avg. 5.5)	+1d3+1 (avg. 3)	13	9	+7	+1.78
Valkyrie	1d2 (avg. 1.5)	+1d2 (avg. 1.5)	9	9	+5	+1.33
Wizard	1d3+8 (avg. 10)	+1d5+2 (avg. 5)	18	10	+9	+2.39

🧬 Mana by Race

Race	Starting Mana	Mana Per Level	Int Modifier	Wis Modifier
Human	1d3+2 (avg. 4)	+1d2 (avg. 1.5)	+0	+0
Elf	1d6+6 (avg. 9.5)	+1d2+1 (avg. 2.5)	+2	+2
Dwarf	1d2 (avg. 1.5)	+1d2-1 (avg. 0.5)	-2	-2
Gnoll	1d3+1 (avg. 3)	+1 (avg. 1)	-2	-2
Orc	1d3+1 (avg. 3)	+1 (avg. 1)	-2	-2

📈 Mana Progression by Character Class

🏺 Archaeologist

Mana Per Level by Race:

Race	Human	Dwarf
Mana Per Level	+6.67	+5.33

Level	Human	Dwarf
1	17.5	14
2	24	19.5
3	31.5	25
4	38	29.5
5	44.5	35
6	51	40.5
7	57.5	46
8	64	51.5
9	71.5	57
10	78	61.5
11	84.5	67
12	91	72.5
13	97.5	78
14	104	83.5
15	111.5	89
16	118	93.5
17	124.5	99
18	131	104.5
19	137.5	110
20	144	115.5

🪓 Barbarian

Mana Per Level by Race:

Race	Human	Gnoll	Orc
Mana Per Level	+4.06	+3.22	+3.22

Level	Human	Gnoll	Orc
1	9.5	6.5	6.5
2	13.5	10	10
3	17.5	13.5	13.5
4	21.5	17	17
5	25.5	19.5	19.5
6	29.5	23	23
7	33.5	26.5	26.5
8	37.5	29	29
9	41.5	32.5	32.5
10	45.5	36	36
11	49.5	39.5	39.5
12	53.5	42	42
13	57.5	45.5	45.5
14	61.5	49	49
15	66.5	52.5	52.5
16	70.5	55	55
17	74.5	58.5	58.5
18	78.5	62	62
19	82.5	64.5	64.5
20	86.5	68	68

🦴 Caveman

Mana Per Level by Race:

Race	Human	Dwarf	Gnoll
Mana Per Level	+5.44	+4.11	+4.61

Level	Human	Dwarf	Gnoll
1	13.5	10	11.5
2	19.5	14	16
3	24.5	18	20.5
4	30.5	22	25
5	35.5	26	29.5
6	41.5	31	35
7	46.5	35	39.5
8	51.5	39	44
9	57.5	43	48.5
10	62.5	47	53
11	68.5	51	57.5
12	73.5	55	62
13	79.5	59	66.5
14	84.5	63	71
15	90.5	68	76.5
16	95.5	72	81
17	100.5	76	85.5
18	106.5	80	90
19	111.5	84	94.5
20	117.5	88	99

🧪 Healer

Mana Per Level by Race:

Race	Human	Gnoll
Mana Per Level	+7.67	+6.83

Level	Human	Gnoll
1	20	18
2	27.5	25
3	36	32
4	43.5	38
5	51	45
6	58.5	52
7	66	59
8	73.5	66
9	82	73
10	89.5	79
11	97	86
12	104.5	93
13	112	100
14	119.5	107
15	128	114
16	135.5	120
17	143	127
18	150.5	134
19	158	141
20	165.5	148

🛡️ Knight

Mana Per Level by Race:

Race	Human	Dwarf
Mana Per Level	+5.33	+4.00

Level	Human	Dwarf
1	13.5	10
2	18.5	14
3	24.5	18
4	29.5	22
5	34.5	26
6	40.5	30
7	45.5	34
8	50.5	38
9	56.5	42
10	61.5	46
11	66.5	50
12	72.5	54
13	77.5	58
14	82.5	62
15	88.5	66
16	93.5	70
17	98.5	74
18	104.5	78
19	109.5	82
20	114.5	86

🥋 Monk

Mana Per Level by Race:

Race	Human
Mana Per Level	+6.61

Level	Human
1	16.5
2	23.5
3	29.5
4	36.5
5	42.5
6	49.5
7	56.5
8	62.5
9	69.5
10	75.5
11	82.5
12	89.5
13	95.5
14	102.5
15	109.5
16	115.5
17	122.5
18	128.5
19	135.5
20	142.5

⛪ Priest

Mana Per Level by Race:

Race	Human	Elf	Gnoll
Mana Per Level	+7.44	+8.78	+6.61

Level	Human	Elf	Gnoll
1	19	26.5	17
2	26.5	35	24
3	34	43.5	30
4	41.5	52	37
5	49	61.5	43
6	56.5	70	50
7	64	78.5	57
8	71.5	88	63
9	79	96.5	70
10	86.5	105	76
11	94	113.5	83
12	101.5	123	90
13	109	131.5	96
14	116.5	140	103
15	124	149.5	110
16	130.5	158	116
17	138	166.5	123
18	145.5	175	129
19	153	184.5	136
20	160.5	193	143

🏹 Ranger

Mana Per Level by Race:

Race	Human	Elf	Gnoll	Orc
Mana Per Level	+5.39	+6.72	+4.56	+4.56

Level	Human	Elf	Gnoll	Orc
1	13.5	20	11.5	11.5
2	18.5	27	16	16
3	24.5	34	20.5	20.5
4	29.5	41	25	25
5	35.5	47	29.5	29.5
6	40.5	54	34	34
7	45.5	61	38.5	38.5
8	51.5	67	43	43
9	56.5	74	47.5	47.5
10	62.5	81	52	52
11	67.5	88	56.5	56.5
12	72.5	94	61	61
13	78.5	101	65.5	65.5
14	83.5	108	70	70
15	89.5	115	75.5	75.5
16	94.5	121	80	80
17	99.5	128	84.5	84.5
18	105.5	135	89	89
19	110.5	141	93.5	93.5
20	115.5	148	98	98

🗡️ Rogue

Mana Per Level by Race:

Race	Human	Gnoll	Orc
Mana Per Level	+5.50	+4.67	+4.67

Level	Human	Gnoll	Orc
1	14.5	11.5	11.5
2	19.5	16	16
3	25.5	21.5	21.5
4	30.5	26	26
5	36.5	30.5	30.5
6	41.5	35	35
7	47.5	39.5	39.5
8	52.5	44	44
9	58.5	49.5	49.5
10	63.5	54	54
11	69.5	58.5	58.5
12	74.5	63	63
13	80.5	67.5	67.5
14	85.5	72	72
15	91.5	77.5	77.5
16	96.5	82	82
17	102.5	86.5	86.5
18	107.5	91	91
19	113.5	95.5	95.5
20	118.5	100	100

⚔️ Samurai

Mana Per Level by Race:

Race	Human
Mana Per Level	+4.39

Level	Human
1	11
2	15
3	20
4	24
5	29
6	33
7	37
8	42
9	46
10	51
11	55
12	59
13	64
14	68
15	73
16	77
17	81
18	86
19	90
20	94

📸 Tourist

Mana Per Level by Race:

Race	Human
Mana Per Level	+6.28

Level	Human
1	16.5
2	22
3	28.5
4	35
5	41.5
6	48
7	53.5
8	60
9	66.5
10	73
11	78.5
12	85
13	91.5
14	98
15	104.5
16	110
17	116.5
18	123
19	129.5
20	135

⚡ Valkyrie

Mana Per Level by Race:

Race	Human	Dwarf
Mana Per Level	+4.33	+3.00

Level	Human	Dwarf
1	10.5	7
2	14.5	10
3	19.5	13
4	23.5	16
5	27.5	19
6	32.5	22
7	36.5	25
8	40.5	28
9	45.5	31
10	49.5	34
11	53.5	37
12	58.5	40
13	62.5	43
14	66.5	46
15	71.5	49
16	75.5	52
17	79.5	55
18	84.5	58
19	88.5	61
20	92.5	64

🪄 Wizard

Mana Per Level by Race:

Race	Human	Elf	Orc
Mana Per Level	+8.89	+10.22	+8.06

Level	Human	Elf	Orc
1	23	29.5	21
2	31.5	40	29
3	41	50.5	37
4	49.5	61	45
5	59	70.5	53
6	67.5	81	61
7	76	91.5	69
8	85.5	101	77
9	94	111.5	85
10	103.5	122	93
11	112	132.5	101
12	120.5	142	109
13	130	152.5	117
14	138.5	163	125
15	148	173.5	134
16	156.5	183	142
17	165	193.5	150
18	174.5	204	158
19	183	213.5	166
20	191.5	224	174

🧬 Mana Calculation Formulas

This section explains the formulas used by the game engine to calculate starting mana (energy) and level-up mana progression.

Starting Mana

Starting mana is determined when the character is created. It consists of fixed and random components determined by class and race, plus the stat mana bonus at level 1.

$\text{Starting Mana} = \text{Class Initial Mana} + \text{Race Initial Mana} + \text{Class Starting Random} + \text{Race Starting Random} + \text{Stat Mana Bonus}(1)$

Where:

• $\text{Class Initial Mana}$ is the starting infix field in the class's energy advancement configuration.
• $\text{Race Initial Mana}$ is the starting infix field in the race's energy advancement configuration.
• $\text{Class Starting Random}$ is rolled if inrnd is greater than 0: $\text{rnd}(\text{Class Starting Random Range})$.
• $\text{Race Starting Random}$ is rolled if inrnd is greater than 0: $\text{rnd}(\text{Race Starting Random Range})$.
• $\text{Stat Mana Bonus}(1)$ is the Intelligence and Wisdom mana bonus at level 1.
• The average starting random component for a range parameter $N \gt 0$ is $\frac{N + 1}{2.0}$.

Intelligence and Wisdom Mana Bonus

The Intelligence and Wisdom mana bonus is applied at every experience level (including level 1) and is calculated using the following formula:

$\text{Stat Mana Bonus}(L) = \lfloor \frac{\max\left(0.0, \frac{2 \times \text{Int} + \text{Wis}}{3.0} - 1.0\right) \times (L + 3)}{6.0} \rfloor$

Where:

• $\text{Int}$ is the active Intelligence score of the character.
• $\text{Wis}$ is the active Wisdom score of the character.
• $\text{L}$ is the experience level of the character.

Mana Gained Per Level

Each time the character gains a level (from level 2 to level 50), they receive a random increase in mana determined by two independent dice rolls for class and race:

$\text{Mana Gain} = \text{Class lofix} + \text{Race lofix} + \text{rnd}(\text{Class lornd}) + \text{rnd}(\text{Race lornd})$

Where:

• $\text{Class lofix}$ and $\text{Race lofix}$ are the fixed minimum increases for the class and race, respectively.
• $\text{Class lornd}$ and $\text{Race lornd}$ are the random range parameters (die sizes) for the class and race.
• $\text{rnd}(N)$ generates a random integer in the range $[1, N]$ with uniform probability. If $N \le 0$, no roll is made and the term is $0$.
• The average base gain per level is: $\text{Gain}_{\text{avg}} = \text{Class lofix} + \text{Race lofix} + \frac{\text{Class lornd} + 1}{2.0} + \frac{\text{Race lornd} + 1}{2.0} = \text{Class lofix} + \text{Race lofix} + \frac{\text{Class lornd} + \text{Race lornd}}{2.0} + 1.0$ (when both range parameters are $\gt 0$).

⚠️ Note on UI Display: In the game UI, the combined advancement is represented as a single combined die: +1d(Class lornd + Race lornd + 1) + (Class lofix + Race lofix - 1). While this single-die approximation has a slightly wider range than rolling two independent dice, it yields the same average base gain per level.

Total Expected Mana at Level L

At experience level $L$ (where $1 \le L \le 20$), the expected maximum mana is:

$\text{Expected Mana}(L) = \text{Starting Mana}_{\text{avg}} + (L - 1) \times \text{Gain}_{\text{avg}} + \text{Stat Mana Bonus}(L)$

Where:

• $\text{Starting Mana}_{\text{avg}}$ is the average starting mana of the class and race: $\text{Class Initial Mana} + \text{Race Initial Mana} + \text{Class Starting Random Average} + \text{Race Starting Random Average}$.
• $\text{Gain}_{\text{avg}}$ is the average mana gained per level.
• $\text{Stat Mana Bonus}(L)$ is computed using the average Intelligence and Wisdom scores for the class and race (subject to the race's attribute caps).