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#1488199

redvers
21054xp
Cult of Games Member

The probability of rolling a 12 on a d12 is 1 in 12, or 1/12th. To roll a 12 a second time would be 1/12th * 1/12th = 1/144.

For your problem, you’ve already rolled a critical hit so the chance of rolling on the first crit table is 1 (you’re going to do it). A roll of a twelve will get you to roll on the second crit table, so the chance of this is 1/12. Now rolling on the second crit table, the chance of rolling a twelve is 1/12 but you need to multiply that by the previous probabilities to get to where you are, so 1/12 * 1/12 is 1/144. If you do it, to roll another 12 on the 3rd crit table is 1/12 * 1/144 and so on. So to get to roll on the 5th table, the probability is 1/20736 or put another way, on average you should do this just once in every 20,736 attempts. So not very likely.

To be really accurate, you would also need to factor in the probability of rolling a critical hit in the first place to have the chance to roll on the 5th Critical hit table. If we assume you had to roll a 12 on a d12 to get a critical in the first plae, then it would be 1/12 * 1/20736 which is 1/248832 or just less than 1 in a quarter million chance. If you use a d20 for the roll to hit and a critical is on a 20, then it’s even worse at 1/20 * 1/20736 = 1/414720.

For RPGs, you don’t tend to roll lots of dice, so even probabilities at 1 in 200 or 1 in 300 rarely happen at the table but are an event when they do. If you think of your average RPG night, the total number of rolls by all players and GM might not reach 100, so this already means that extreme probability events won’t ever happen – even rolling a natural 20 on a d20 is cause for celebration for me! As an example, I still play 2nd Edition AD&D and when rolling up your character stats, you use 3d6 with 18 being the best score. Probability of getting just one stat score of 18 is 1 in 216. I can’t think of any characters I played in many, many years that had a natural stat of 18, had a couple of 17’s (1 in 108 chance).

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