Maths problem: fatigue vs critical hits

[MaxWilson]

Cleveland. Nice work. Small correction, though: a critical hit happens if a DRN is _less_ than fatigue/15, rounded down. There's a .97 probability that a DRN is < 2, which means there's a .03 probability that it's >= 2, which means there's a 3% chance of critical hit when your fatigue/15 is 3. Thus, the table needs to shift by two rows. Chance of critical hit from fatigue 0-29 is 0%, 30-44 is 3%, etc.

-Max

Edit: poetic justice. There's a .97 probability that it's > 2, and .03 that it's <= 2. This is the opposite of what I typed.

[cleveland]

Max,

You're absolutely right that the table needs to be shifted, but upon closer inspection of the mechanic, it seems that the shift only needs to be by one row.

This is because a critical hit is scored when the DRN - Fatigue/15 is LESS THAN 2.

For example, let's say Stay Puft, Hero of Alexandria, swings at Gromulos, The Contemptuous Cyclops. Gromulos has 20 fatigue already, so Stay Puft gets a bonus of 20/15 = 1.33 --> 1 to his critical hit roll. Since Stay Puft is particularly good at smiting villains, his DRN = 2 (which had a 1/6*1/6 = 2.8% chance); subtracting the fatigue bonus of 1, his final critical hit roll is 2 - 1 = 1. Since 1 < 2 (the threshold for a critical hit), he scores yet another devastating smash on Gromulos, one of a presumed series of such blows.

So yes, the table needs to be shifted, but only by 1 row, as there is a 2.8% chance of a critical hit when the opponent has 20 fatigue.

Again, I encourage all to double-check my logic. I've only had 1/2 cup of coffee so far.

[MaxWilson]

cleveland said:
Max,

You're absolutely right that the table needs to be shifted, but upon closer inspection of the mechanic, it seems that the shift only needs to be by one row.

Yeah, you're right. Serves me right for misremembering the mechanic.

-Max