Chaos Bolt

Level 1st	Casting Time 1 action	Range/Area 60 ft	Components v, s
Duration instantaneous	School evocation	Attack/Save ranged	Damage/Effect fire cold ...

When you cast this spell, crackling prismatic energy leaps from you to a creature within range. Make a ranged spell attack against the target. On a hit, the target takes 10 (3d6) damage. To determine the damage type, choose one of the dice rolled and look it up on the table below.

d6	Damage Type
1	Fire
2	Cold
3	Poison
4	Thunder
5	Lightning
6	Psychic

If any pair of the damage dice show the same value, the spell leaps to a new creature within range of the first target. Make a new attack roll against the target, but roll one less d6 every time the spell chains. Extra dice, such as from a critical hit, do not count, and the spell cannot leap to a target it has already hit.

At higher levels: When you cast this spell using a spell slot of 2nd level or higher, the spell deals an additional d6 of damage to the first target for each slot level above 1st.

The odds of the spell leaping, as a function of the number of dice rolled:

P(leap) = 1 - (product([6, 5, 4, 3, 2, 1, 0][:x]) / 6**x)

This is the inverse probability of rolling all different numbers on the dice. Importantly, for 7+ dice, the probability becomes 100%, due to the pigeonhole principle.

Number of dice	Probability of leaping
1	0%
2	16.6%
3	44.4%
4	72.2%
5	90.7%
6	98.4%
7+	100%

Spell Level	Expected damage (95% hit, no crits)	Expected total damage (65% hit, no crits)
1	4.4 d6	2.6 d6
2	7.6 d6	4.1 d6
3	11.8 d6	5.9 d6
4	16.9 d6	7.7 d6
5	22.7 d6	9.5 d6
6	29.2 d6	11.4 d6
7	36.3 d6	13.2 d6
8	44.0 d6	15.1 d6
9	52.2 d6	16.9 d6

The spell is extremely affected by gaining blanket advantage, such as from being invisible. With a normal hit chance, the average damage is not particularily impressive, although it is always capable of huge spikes.

sorcerer