Actually, a d4 only had an expected value of 2.5, so the expected damage output from the senate should be 2.5600.55 = 82.5.
Sounds impressive, but more interesting is the actual chance of success of killing Caesar. Each senator has a 0.45 chance to miss and a 0.55/4 chance of doing 1-4 damage respectively, for an expected value of 1.375 and variance of ~2.23. Formally modelling the distribution of the sum of 60 of these variables requires a 60 fold convolution which is too difficult. Instead, we can approximate the sum of total damage as a normal variable with an expected value of 601.375 = 82.5 and variance 602.23 = 134.06.
The probability that this is less than 60 is around ~0.43, so Brutus’ plan had a less than 60% chance of succeeding. That’s… rather terrible for an assassination plan. The addition of sneak attack rolls wouldn’t help much, given that the variance of dice rolls is just so high.
EDIT: Forgot to take the square root of the variance in calcs. This takes Brutus’ chance of success to a much more respectable 97%. Truly a big brain conspirator.
Actually, a d4 only had an expected value of 2.5, so the expected damage output from the senate should be 2.5600.55 = 82.5.
Sounds impressive, but more interesting is the actual chance of success of killing Caesar. Each senator has a 0.45 chance to miss and a 0.55/4 chance of doing 1-4 damage respectively, for an expected value of 1.375 and variance of ~2.23. Formally modelling the distribution of the sum of 60 of these variables requires a 60 fold convolution which is too difficult. Instead, we can approximate the sum of total damage as a normal variable with an expected value of 601.375 = 82.5 and variance 602.23 = 134.06.
The probability that this is less than 60 is around ~0.43, so Brutus’ plan had a less than 60% chance of succeeding. That’s… rather terrible for an assassination plan. The addition of sneak attack rolls wouldn’t help much, given that the variance of dice rolls is just so high.
EDIT: Forgot to take the square root of the variance in calcs. This takes Brutus’ chance of success to a much more respectable 97%. Truly a big brain conspirator.