Thread: Powerstones
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Old 08-14-2009, 02:43 PM   #70
Polaris
 
Join Date: Feb 2005
Default Re: Powerstones/Getting Back on Topic

Guys,

I think we'll have to agree to disagree on bless. The wording seems clear enough to me. I will conceed the point about items though. Fred is right about disintigrate.

Regardless, it does not diminish my original point (which we've lost track of).

The point is that Charge Powerstone is a reasonable way to keep powerstones charged and with far less risk than Fred is willing to admit.

Here are the numbers (and remember that at the skill levels we are assuming for this discussion, Charge Powerstone is entitled to a cost reduction of one PP):

Assuming the Mage has 11 fatigue available (likely), it takes three castings of charge powerstone to recharge a powerstone of size 9-12 and only two to recharge a powerstone from 5-8 (the most likely starting size for a wizard of modest means).

Now, let's look at the math:

The chance of destroying a 12 pt stone per casting is 1/216 (again for the purposes of this discussion we assume the skill is 16+). That means the total chance per recharge of destroying the stone is:

(1/216)^3+3*(1/216)^2*(215/216)+3*(1/216)*(215/216)^2

This is easily approximated to first order as 3/216 or about 1.4%

That means that the expectation value for the number of recharges before destruction is 72 times which is going to be much longer than any reasonable adventure.

It is fairly easy to factor in luck to a first order approximation (since it effectively negates one of the critical failures). With luck, the first order probability is 0.0064% chance with an expectation value for the number of recharches of 1552 times. [3*(1/216)^2] Again this is far more than any reasonable length of campaign/adventure.

If you reject quirked stones, it's harsher but not overly so. In that case you replace in the above formulas 1/216 with 4/216 but otherwise the math is identical. In this case the chance of quirking your stone per recharge (for a 12pt stone) is 5.5% which means you have an expected 18 times before you quirk it. That isn't so good, and if it really bothers you, then use luck (either your own or 'bottled alchemical luck'). With luck the odds go down to 0.1% with an expected 972 recharges which is much, much better. [Again all calculations done to first order.]

This is with 9-12 point stones which are very large for starting characters. For more normal starting stones, the numbers are even better. For a 5-8pt stone, the chance of destruction per recharge is 2/216 to first order or about 0.9% with an expected number of recharges of 108. With luck this becomes 2*(1/216)^2 with an expected number of recharges of 46,656 which is obviously far more than you'll likely ever need. If you reject quirks, then again replace 1/216 with 4/216 everyone. To first order, that gives a probability of quirking per recharge of 1.9% for an expected number of recharges of 54 which isn't bad at all. If you use luck this number shoots up to 916 expected recharges or .0034% chance of quirking per recharge.

So there you have it. Fred is incorrect. Recharge powerstone is a very low risk option for the skilled wizard to recharge moderate powerstones. It's also obvious that for larger powerstones, luck makes a huge difference (and if you wanted to do it commericially, luck either by natural talent or potion) would be a good investment.

-Polaris
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