A math-y question
Mantis37
Member Posts: 1,177
So... I was tiring a little of rerolling till I get a 90 or just doing ctrl-8 and selecting some stats for my Bhaalspawn, and wanted to try a system more akin to p&p. However, when doing SCS no-reload runs one really needs some decent stats. So I was thinking of doing the following system.
First I will roll 3d6 in order, unto the way prescribed by the Great Gygax. And select an appropriate class- though would allow someone with decent charisma to 'grow into' being a Paladin etc. via the magic of EE Keeper.
These will be the stats at level 1.
However... each level up (for single class characters obviously, multis would have xp thresholds instead) one would roll a d20 for each attribute. (Optionally you may choose to roll d20+1 for two main stats, a plain d20 for two regular stats, and d20-1 for two weaker stats. This will stop the stats from getting samey.)
If you roll under the stat nothing happens.
If you roll the stat exactly then you lose 1 point in that stat.
If you roll over the stat then you gain 1 point in that stat.
If you roll a 20 then you gain 2 points, but then no further rolls are made for that stat.
This would mean that your Bhaalspawn grew in attributes as well as in levels, and give a decent power progression if you don't get eaten by a wolf early on. But I was wondering... how would this likely work in practice? Anyone care to give me some pointers on the probability curve for how stats might change over BG1 & 2?
First I will roll 3d6 in order, unto the way prescribed by the Great Gygax. And select an appropriate class- though would allow someone with decent charisma to 'grow into' being a Paladin etc. via the magic of EE Keeper.
These will be the stats at level 1.
However... each level up (for single class characters obviously, multis would have xp thresholds instead) one would roll a d20 for each attribute. (Optionally you may choose to roll d20+1 for two main stats, a plain d20 for two regular stats, and d20-1 for two weaker stats. This will stop the stats from getting samey.)
If you roll under the stat nothing happens.
If you roll the stat exactly then you lose 1 point in that stat.
If you roll over the stat then you gain 1 point in that stat.
If you roll a 20 then you gain 2 points, but then no further rolls are made for that stat.
This would mean that your Bhaalspawn grew in attributes as well as in levels, and give a decent power progression if you don't get eaten by a wolf early on. But I was wondering... how would this likely work in practice? Anyone care to give me some pointers on the probability curve for how stats might change over BG1 & 2?
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Say you start with a 3. You would have an 85% of raising the stat on level up including a 5% chance of raising it by 2 against a 5% chance of lowering it to 2. For a stat of 18 you'd have a 10% chance of raising it by one or two against a 5% chance of lowering it by one.
The dynamic of not being able to re-roll after a 20 is difficult to work into the equation. It's kind of a wildcard preventing Godhood before ascension...
Assuming it just stays at 1, and assuming I knew what I was doing, these are the results I got at level 20, using an initial 3d6 and then d20 at every level: Or, given a known starting value, the chance to end up at a given stat (by level 20): (all 0.00% are just less than 0.01%)
The other end that needs clarification - if your current stat is a 20 and you roll a 20, do you drop back to 19 or go up to 22 and stop rolling?
I've built it in a spreadsheet myself, on the assumption that you can drop to zero and die and also that rolling a 20 when you already have 20 drops you to 19. My level 20 results:
No noticeable differences there. If we have any differences in our assumptions, they're only in extremely rare border cases.
I also ran it all the way out to level 40. Here are the numbers for that:
You can't get to 20 with another roll left. If you start at 19 and roll a 20 you go to 21 and stop. If you roll a 20 at 18 you go to 20 and stop.
The behavior here is dominated by the absorbing states in the long run, but the second most important component is the decay of the non-absorbing states. The dominant eigenvector for that part looks like the power series for e, with an eigenvalue of almost exactly 0.95. After (very) many rounds of this process, if you haven't rolled a 20 to stop things yet, the current value of the stat will be 19 with probability approximately 1/e, 18 with probability approximately 1/e, 17 with probability approximately 1/2e, 16 with probability approximately 1/6e, and so on.
Starting at level 1 with a random 3d6, level 40 is just far enough in this process that a non-final 18 is more likely than a non-final 17. A non-final 19 is still only half as likely as those two.
So an average stat of 10 has about a 50/50 chance of reaching a 15 by level 20.... Hm, that seems like it might be slightly on the low side for an aspiring demigod so I suppose I shall tweak the system slightly.