A Deductive Moral Argument for Helping Those Who Fail

My buddies and I are doing a
Harn
campaign right now and one of the mechanics involves accruing stat “checks”
over time. Every five stat checks you get allows you to roll a single d6. So
if you have 15 checks you get to roll 3d6.

The goal is to roll over your stat, which will raise it by one.

So the question of, “when is the best place to roll?” came up. We all know
that having more dice makes it more likely, but we wanted to know
exactly how much more likely in order to make an informed decision.

Not being overly strong in statistics, I put together the following Ruby
code to arrive at the answer using experiment instead of theory.

 # Define the sum class
class Array; def sum; inject( nil ) { |sum,x| sum ? sum+x : x }; end; end
 # Define the experiment parameters
number_of_d6=9
number_of_runs = 100000
goal = 19
successes = 0
failures = 0
 # Program logic
number_of_runs.times do
rolls = [ ]
number_of_d6.times do
rolls.push rand(6)+1
end
if rolls.sum >= goal
successes += 1
else
failures += 1
end
end
 # Output
print "You ran the experiment #{number_of_runs} times using #{number_of_d6} d6."
print "n"
print "You succeeded #{successes} times."
print "n"
print "You failed #{failures} times."
print "n"
successrate = successes / 1000
print "Your success rate is #{successrate}%."

There is an additional considering that I’m thinking of adding later, which
is that when you miss your attempt you lose half the checks you put into it.
So it becomes something of an EV equation.

Anyway, if anyone has any comment on how to do this statistically I’d love
to hear from you. ::