These seem like nonsensical results to me, are you abstracting rapid synth as 250% with 50% chance as being equivalent to 125% with 100% chance perhaps ?
Because you can, and will, fail it 2-4 times in a row regularly when using it without steady hands, leaving both the above results as utter disasters where you are lucky to get your materials back.
Also, the two results are contradictory - why does depth 8 use rapid and 2x basic, where depth 9 uses rapid and 1x basic ? Those can't both be true.
Well I should start by saying that one of the reasons I decided to make this in the first place is because sometimes moves which are not obvious are actually the best. Strategy is a useful tool for humans, but less so for computers which can simply compute every single state in the space to get the best result.
This program is no exception. It makes almost 0 use of strategy. Instead, it just visualizes 8-10 moves ahead, or however many you tell it, and figures out which node will lead to the best expected result
no matter how the random number generator behaves. This bolded part is important, because you point out a scenario where rapid synthesis or basic synthesis can fail N times in a row and you'll be scrounging to even save your materials. That's
exactly where something like this tool excels. In fact, I would argue that it's almost impossible (or should be, if it's working correctly) to fail a synth with this tool, because at every step it can quantify exactly how at risk you are of failing, and it uses this to make tradeoffs between risk (quality) vs safety (progress).
As for your question about using Rapid Synthesis without Steady Hands, you're right that the probability of failing without Steady Hands is high. But again, there is no strategy involved here, only reading out extremely long sequences. Because of that, it's hard to argue from a rational standpoint why it makes the decisions it does, other than simply to say "because it found that move to be best". But, if I were to try to construct my own strategy based around using Rapid Synthesis first, it's easy to think of some logical reasons as to why it might make sense.
For example, investors will tell you that when investing your money, if you're going to need the money soon then put it in bonds. But if you have many years before you need the money, put it in riskier securities. This is probably the same principle at play. It's literally the first move. Its probability of failure at this point is virtually 0. It has the luxury to take a few risks in return for potentially large gain. If it doesn't work out, it will fall back on safer measures. But over a large number of synth, that strategy will probably prove to be better. It's worth pointing out that from a purely mathematical standpoint, Rapid Synthesis is actually
better than 2 Basic Synthesis. This is because 2 Basic Synthesis will require 20 Durability, whereas 1 Rapid Synthesis requires only 10. Still though, it's difficult to understand the decisions a purely computational engine makes.
In regards to your last question, you're right that it doesn't make sense that with depth 8 it uses 1 Rapid and 2 Basic, and with Depth 9 it uses 1 Rapid and 1 Basic. It turns out that the Depth 8 was a copy/paste error, it also uses only 1 Rapid and 1 Basic. You can see this for yourself by downloading the alpha and playing through the default state by clicking Success/Normal every time.
BTW: I ran a little experiment where I found the provably optimal sequence of actions for the state that the app uses as default, and if you go through that one using all normal / succsses you end up with about 150 more quality. So that shows that the app isn't generating the absolute best possible sequence. Of course, this is expected since you're controlling how good you want the results to be with the depth factor in return for it taking less time. But I'm constantly finding improvements to the metric to make it more accurate, so my hope is that it will continue to get better.
