Mana Comparison

👉 Starting mana and mana growth in GnollHack depend on your character class, your race, and your Intelligence and Wisdom.

🔮 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

Starting Mana

Starting mana is set when the character is created. The class and the race each give a fixed amount and roll a die, and the Intelligence and Wisdom bonus for level 1 is added on top:

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

Class Initial Mana and Race Initial Mana are the class's and the race's fixed starting mana, and the two rolls are their random starting mana. In the class and race tables above, Archaeologist's 1d4+3 means 3 fixed mana and a roll of a four-sided die. Each roll is a number from 1 to the size of the die, (size + 1) / 2 on average. A class or race with no starting die adds nothing random.

Intelligence and Wisdom Mana Bonus

At every experience level, including level 1, Intelligence and Wisdom add this bonus:

$\text{Stat Mana Bonus}(L) = \lfloor \frac{\max\left(0, \frac{2 \times \text{Int} + \text{Wis}}{3} - 1\right) \times (L + 3)}{6} \rfloor$

Int and Wis are the character's current Intelligence and Wisdom, and L is the experience level. Intelligence counts twice as much as Wisdom, and the bonus is never negative.

Mana Gained Per Level

Each new level, from level 2 up to level 50, adds the class's and the race's fixed mana per level and one roll of each one's mana die:

$\text{Mana Gain} = \text{Class Fixed Gain} + \text{Race Fixed Gain} + \text{Class Roll} + \text{Race Roll}$

A class or race with no die adds only its fixed gain. When both have a die, the average gain per level, with Class Die and Race Die as the sizes of the two dice, is:

$\text{Gain}_{\text{avg}} = \text{Class Fixed Gain} + \text{Race Fixed Gain} + \frac{\text{Class Die} + \text{Race Die}}{2} + 1$

⚠️ Note on UI Display: The game UI shows the class and race gain as one combined die: +1d(Class Die + Race Die + 1) + (Class Fixed Gain + Race Fixed Gain - 1). It has the same maximum as the two real rolls, but a lower minimum, and its average is 1 lower than the real average gain (0.5 lower when only one of them has a die).

Total Expected Mana at Level L

The progression tables above give the expected maximum mana at levels 1 to 20:

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

Starting Mana avg is the class's and the race's fixed starting mana plus the average of both starting dice, and Gain avg is the average gain per level. The stat bonus uses the average Intelligence and Wisdom of the class and race, limited by the race's attribute maximums.