What is the chance of a Pokemon being frozen for ten turns in a row?

Question

I was just playing some Doubles OU when my kingdra got a freeze on my opponents volcanion. WHICH PROCEDED TO BE FROZEN FOR 10 TURNS IN A ROW!!! What is the chance of this happening?

Comments

Btw he "unfroze" bc he died.

Answer 1

Since the Frozen status condition has a 20% chance each turn to thaw you out, (Assuming no Fire moves were used), you have an 80% chance to stay frozen. 80% can be represented as the decimal 0.8, so 10 turns in a row means that the probability is 0.8^10. Math:

0.8^10 = 0.1073741824 = 10.73741824%

So the probability of being frozen for 10 turns is about 10.7%. However, this is just the probability of being frozen for 10 turns, and it assumes that the freezing is guaranteed to happen, which is not true without very specific setup of Serene Grace, Rainbow, and Snow, with Secret Power.

Assuming you used Ice Beam or Blizzard, which have a 10% chance to freeze, that makes the calculation this:

0.1(0.8^10) = 0.01073741824 = 1.073741824%

So your specific scenario has a 1.073741824% chance to happen. Hope I helped.

Comments

Notably, as of Pokemon Champions, Freeze was reworked to have a 25% unfreeze chance each turn, and will always unfreeze on the third turn if it didn't unfreeze earlier. But Doubles OU at this time still uses SV mechanics, so your answer is still correct for the asker's scenario.