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# What dice pool balances a 20 point buy?

Dice Pool:
Each character has a pool of 24d6 to assign to his statistics. Before the dice are rolled, the player selects the number of dice to roll for each score, with a minimum of 3d6 for each ability. Once the dice have been assigned, the player rolls each group and totals the result of the three highest dice. For more high-powered games, the GM should increase the total number of dice to 28. This method generates characters of a similar power to the Standard method.

http://paizo.com/pathfinderRPG/prd/gettingStarted.html

What is the appropriate dice pool to balance a 20 point buy? Would you recommend any changes to the standard dice pool concept instead?

I'm looking at either increasing the number of dice in the pool to 28d6 (following the Paizo prescription), staying at 24d6 and rerolling ones or staying at 24d6 allowing the player to switch out one roll for a six and another for a four.

Has anyone done some math HW on this?

Just use point buy. Offer players the option to play at lower than 20 points.

Only reason left for anyone to want to roll is that 20 points isn't enough for them / greediness.

Although I say that somewhat facetiously, as 20 PB isn't particularly high and is rough on the MAD classes; I would never offer lower than 25. PB of 15 is enough for a Wizard to have 20 Int and and ~+2 Dex and Con, so anything beyond that is just helping out the weak classes.

The 20 point buy is pretty close to the average you would get with the "standard" method (4d6 drop the lowest). That means that a straight 24d6 pool is probably your best bet.

That depends on allocation of the point buy.

For example, I could, with my 20 point buy allocate ability scores as 18, 13, 10, 10, 10, 10, which is an average of 11.83.

I could also allocate as 14, 14, 14, 14, 10, 10, for an average of 12.67.

The "optimal" allocation in terms of high ability score average is (I think) 14, 13 (x5), for an average of 13.17.

So there's a pretty large spread of averages dependent on point-buy allocation, but each certainly exceeds 3d6 (which yields an average of 10.5) by a large margin.

4d6-drop-the-lowest (which is equivalent to your 24d6 pool) will give average ability scores of 12.24, which is pretty close to the middle allocation. Note, though, that probabilities for at-most and at-least results can vary between statistical ensembles with identical averages.

Now, it's worth noting that, in the point buy method, a 7 (10-3) costs -4 points, while a 13 (10+3) costs 3 - that is, there's a cost asymmetry favoring better scores, which suggests some dice rolls which impose a similar high/low asymmetry, such as 4d4+2 (average of 12, min/max of 6 and 18) or 2d6+6 (average 13, min/max 8 and 18), which give similar averages but constrain the lower-bound and make "heroic" ability scores more likely.

Going old-school: if you're old enough to have read the original AD&D Dungeon Master's Guide, Gary Gygax explained that the "reasoning" behind "3d6" is that it yields a normal distribution of ability scores. Generally, the modern gamer doesn't want this (imagine playing with a 3 or 4 in an ability score!), so it's probably worth shifting curve area "to the right", hence my suggestion of randomization plus a fixed value: it's a compromise between "rolling" and "point buy".

Role I'm a luck sack get incredible die rolls take a chance guys.

4d6 to be specific lol.

Well... to attempt to approach the average, what you need is more dice rolls.

To this end, I like 4d6 (Drop lowest)
Roll 8 times, drop the lowest score and the highest score.
Keeps stats more toward the center of the curve.

StreamOfTheSky wrote:

Just use point buy. Offer players the option to play at lower than 20 points.

Only reason left for anyone to want to roll is that 20 points isn't enough for them / greediness.

Agreed -- random dice merely guarantees that there will be a wide disparity between the "totals" of the best and worst rolls of the player (usually such that the worst player is still behind even if +2s to three or four stats are factored in).

If there isn't a disparity, then the die-rolling wasn't any different than point-buy in the first place.

Meanwhile, 20pts put into the 15,14,14,14,12,07 array, with the highest stat racial+4th boosted to an 18, represents +11 in positive stat bonuses -- and you are very unlikely to duplicate that with die-rolling (because you're more likely to end up with a lot of "waste" in odd-numbered stats you don't want to raise).

StreamOfTheSky wrote:

Just use point buy. Offer players the option to play at lower than 20 points.

Only reason left for anyone to want to roll is that 20 points isn't enough for them / greediness.

Although I say that somewhat facetiously, as 20 PB isn't particularly high and is rough on the MAD classes; I would never offer lower than 25. PB of 15 is enough for a Wizard to have 20 Int and and ~+2 Dex and Con, so anything beyond that is just helping out the weak classes.

Pathfinder Roleplaying Game Subscriber
Lord_Malkov wrote:

4d6 (Drop lowest)

Roll 8 times, drop the lowest score and the highest score.
Keeps stats more toward the center of the curve.

I like this! * rolls of 4d6 each, dropping the extremes would probably work.

As for no high/no low scores, use averaging dice, if you can find them.

I just finished a highly suspect test, but the problem David Haller points out (no point value below 7) is kicking my results. Continuing the downward progression (6 sets of best 3 of 4) comes to 18.73 or 20.94, subject to my crappy math. I went with increasing the points for the low stat by 1 on even, 2 on the odd down to 3 (a 1/1296 chance, btw). Then, I cheated and used a previous '3 keep 4' posting results I had stashed, so my results might be skewed. Heck, they are, two differing results from the same math?