I am trying to understand the Original Research rules (in True Lineages), and what is the optimal strategy for a magus using them: what strategy will deliver the most progress towards the Breakthrough. It's giving me a headache, the rules are very confused, so I want your advice.
In this I am following the errated version, the one that says the risk modifier affects the results of the Extraordinary Result Chart as normal, but in addition may now be added or subtracted from this result to achieve a Discovery. The example is rolling an 8 on the dice, which with a +3 risk modifier translates to 11 (Modified Effect), which affects the spell but in addition a -1 is applied to it for an added result of 10 â€“ Discovery.
I believe this is very quirky. The change in the rules also makes the paragraphs below it strange and inexplicable. What does â€œHaving deciding how you will use your risk modifier in a previous season, you must continue to use it in the same manner for consecutive seasonsâ€ mean now? At any rate the example on page 28 no longer agrees with the rules on page 27, and should be errated as well.
Seeking the Unknown
The first stage of Original Research is Seeking the Unknown: inventing a new spell or enchanting a new item. Great. When does it fail?
The rules (TL p. 27) say â€œYou may accrue odd and weird results as your research progresses, but may continue to experiment provided you don't receive a Complete Failure or Disaster resultâ€. This is not how experimentation usually works, in Complete Failure â€œyour season is wastedâ€, and even in Disaster you may still have a project left if for example you roll 0 or less (â€œYour season is still wasted; see Complete Failureâ€). Of course both Complete Failure and Disaster can bring to failing the entire project, wasting all prior investment and seasons in it.
By the rules as written, it seems TL implies that both Complete Failure and Disaster always bring experimentation in the course of Original Research to a grinding halt on this stage, leaving the maga to begin the project anew (or abandon it). If any of those occur, you may no longer experiment and hence no longer pursue the current experiment/project.
Really, I think the whole thing is just not well written, but the (post-errata) rules as written seem to be this: you must successfully invent a spell or enchant an item using the normal experimentation rules, but with the Risk Modifier subject to a limit of Magic Theory/5 (up to +3), and furthermore on at least one season gain a result of Discovery or at most Risk Modifier removed from it, and if you get a Complete Failure or Disaster even once the entire attempt fails. Fine.
I think a better, more consistent rule, would have been that you simply invent the spell or enchant the item as usual under the usual experimentation rules, and not mentioning a stop in case of a Complete Failure or Disaster unless this is already implied by said rules. I also like the way the original TL rules worked with the Discovery entry, allowing you some leeway in controlling the results of the experimentation, rather than providing an â€œin additionâ€ process on top of normal experimentation. And I really thing the whole thing could be written much clearer. But lets move on.
Stabilizing the Unknown
The second stage of Original Research is stabilizing the discovery. I find this section even more confusing.
I think the intention is that you attempt to stabilize your experiment by repeating it season by season, using the exact Lab Total and Risk Modifier as in the original experiment. As soon as one season yields a non harmful result (anything except Disaster, No Benefit, or Complete Failure) you stabilized your discovery, and need proceed no further with this stage. This interpretation is supported by â€œAs long as you do not roll a harmful effect, you stabilize your discoveryâ€ and â€œIf your stabilization attempt fails, you may spend another season and try it again. You may continue to stabilize your discovery until you succeed...â€. It is contradicted by â€œYou must repeat the experimentation, continuing for the same number of seasons...â€
(Again, the part about adding the risk modifier in the same way you did before is very unclear post-errata.)
Again, none of these results imply loss of a project under normal experimentation rules, but TL says â€œyou have lost the chance to stabilize that Discoveryâ€. Yet it also goes on to say â€œYou may continue to stabilize your discovery until you succeed...â€. Given the core ArM5 rules on experimentation and the supportive quote, I am inclined to say that you lost your chance to stabilize that Discovery this season. Yeesh.
Again, I'd recommend rewording the entire section so it doesn't contradict itself.
Optimal Risk Modifier
All that out of the way, let us turn to optimization.
Let us assume that the maga has a Magic Theory score of 11 (or 8+2 with a fitting specialty), allowing her up to a +3 Risk Modifier. For simplicity, let us assume that through a combination of low aura, Careful Sorcerer, a strong familiar golden cord, and perhaps a specialized lab (I don't have Covenants yet) the maga has zero botch dice even with a +3 Risk Modifier. What Risk Modifier should she choose?
A Discovery result is a 10.
With a +0 risk modifier, a stress die a roll of 1,5 will result in10 - a 0.01 probability.
With a +1 risk modifier a roll of 8 or 1,4 will result it 9 hence 10; a roll of 9 will result in 10 directly; a 1,5 will result in 11 hence 10; in total, a 0.22 probability.
With a +2 risk modifier a roll of 6 will result in 8 hence a Complete Failure; a roll of 7 will result in 9 hence 10; a roll of 8 or 1,4 will result in 10; a roll of 9 will result 11 hence 10; in total, a 0.31 probability.
With a +3 risk modifier a roll of 4 or 1,4 will result in 7 hence 10; a roll of 5 will result in 8 a Complete Failure; a roll of 6 or 1,3 will result in 9 hence 10; a roll of 7 will result in 10; a roll of 8 or 1,4 will result in 11 hence 10; a roll of 9 will result in 12 hence 10 plus a 0.2 chance of Complete Failure; in total a probability of 0.53 plus a probability of 0.12 for Complete Failure.
(Edit: forgot a 0.01 from 1,5; I won't correct the math for it.)
It seems most lucrative to take the +3 Risk Modifier, as is to be expected as its main downside is the extra botch dice which are not considering.
When attempting to stabilize the effect of the Risk Modifier is null: on a Complete Failure or No Benefit it fails, and that's roughly a 0.2 probability regardless of Risk Modifier. So the above conclusion holds.
Optimal Project Length
The key choice is the project length â€“ should one pursue a one-season project? two seasons? Intuitively, it seems dividing things into many seasons just asks for trouble as the chance that at least one will get Complete Failure and fail rise up while the increase in benefit (magnitudes of stabilized discovery) crawls to a standstill as it approaches the full Lab Total â€“ clearly, immensely long projects are not worthwhile but it isn't clear whether one season is the optimum.
It is, when all is said and done. See below.
It's also simplest â€“ many of the above problems just don't come into play.
Let us consider a one-season long project, say inventing a spell of 0.5 Lab Total.
The probability for a Discovery with a +3 Risk Modifier is 0.53, so on average one would need 1.89 seasons to achieve one.
The probability for Stabilizing the discovery is 0.8 each season, so on average one would need 1.25 seasons to stabilize the discovery.
In total, we gained 0.5 Lab Total in 3.14 seasons, for a rate of 0.16 Lab Totals per season.
Let us consider a two-seasons long project, gaining 2/3 Lab Total.
The probability for a Discovery in at least one season of two is 0.78, requiring 1.28 attempts i.e. 2.56 seasons on average. This neglects the 0.12 chance for a Complete Failure on each season causing the addition of one or two seasons; I'll take this into account by adding 0.12*(1+2) to the total implying it takes 2.92 seasons to complete the 2-season project with a Discovery. I'll neglect rarer complications.
Stabilization is still 0.8 likely per season, requiring 1.25 seasons to stabilize the discovery.
In total, we gained 2/3 Lab Total in 4.17 seasons, for a rate of 0.16 Lab Total.
Let us now consider a three-seasons long project, gaining 3/4 Lab Total.
The probability for a Discovery in at least one season of three is 0.9, requiring 1.11 attempts or 3.33 seasons on average. I'll add to that 0.12*(1+2+3), or 0.72, for 4.05 seasons on average.
Stabilization still requires but 1.25 seasons on average.
In total we gained 3/4 Lab Total in 5.3 seasons, for a rate of 0.14 Lab Total.
I won't go into more seasons; the addition of ever-increasing chances for Complete Failure on at least one season plus ever diminishing returns from fraction of Lab Total stabilized will tend, I think, to diminish the rate from here on end.
The result of all of this is that one should pick one- or two-season length projects for Original Research.
And If We Botch
All this assumed we don't botch, having enough tricks to offset the botch dice. If this is not the case, we have a small chance to botch on each season â€“ no more than 0.065 probability per season, really. Since it's per season, and can ruin multi-season projects much like Complete Failure on the invention stage, it would tend to favor shorter projects.
Even with such a huge chance to botch, I believe the cost benefit analysis will be in favor of taking the +3 Risk Modifier, except perhaps in the case of having very few botch dice (like 0 or possibly 1) without it; this is because each additional botch dice increases the chance for a botch by less than the one before it. Then there is the chances for Twilight to consider, but that is such a rare occurance (less than 0.1x 0.1 x 0.2 = 0.002, or 0.2 %) that it's all but negligible, as ironic as that sounds.
I think this tips the scale in favor of one-season long projects.
I won't do the math for this. Way too complicated.
The optimal strategy seems to be taking the +3 Risk Modifier and conducting research into small (one-season long) projects of as close to 1/2 Lab Total as you can get.
The rules are also quite a mess.