Yes, my math, and arguments support my position, but it isn't that I am "supporting my position at all costs." I am doing computations, mathematically correct computations as far as I know, and the end result is that they produce a conclusion, and that conclusion is my position. I'm perfectly willing to accept if, at the end of my computations, it produces an unexpected outcome. Looking back over my past posts, I was 100% willing to accept I was wrong in one of these deep-math discussions when my computations appeared to say so. I later found a math mistake, which changed the final numbers, and ended up right back with where I thought it was going to go. I also hold a position, backed by my computations, that the real optimal strategy is not that of the typical SF/Daily computation, and that there are occasions where you are sometimes better served taking a less-efficient offering out of the three being offered, to save currency for more chances at more-efficient future offerings, which is something I did not think was going to happen.
Having said that, let's look at what you are now presenting.
I 100%
agree with the information you present in the table.
I 100%
agree with your (modified to clearly express the implied) conclusion that "...you can get much more (bonus SF) out of your lucky streak using 71 ring."
I 100%
disagree that your conclusion has actually shown the conclusion we should be trying to compute, "...you can get much more Dailies out of your lucky streak using 71 ring."
And therefore, I 100%
disagree with your ultimate position, that "It is mathematically supported that it is preferrable to choose 71 Rings over 31 Rings, because 71 Rigs have the highest bonus SF amount, independent of Ring cost and bonus SF odds."
And?
First of all, now you are arguing a slightly different argument... Earlier, you said "Based on my experience whatever I do I average 20 dailies so I might at the worst risk 3 dailies to win maybe another 10, this is as far as I'm happy to go with the numbers." This is not the math of trying to reach "...another 10...", but the math of "possible max SF win", or more generally, "best case". This is a different argument. Apologies if you misstated your position and my most recent posting addressed your imprecisely worded position instead of your actual one.
So, let's talk about "best case".
Second. What you describe, or at least as far as you go in describing, isn't "best case". It's first-order best case. Why stop there? I mean, if we're talking "possible max SF wins", why are you only limiting yourself to the wins from the first 1,000 SF? Why are you stopping the analysis on Step One and declaring victory? Reinvest, and reinvest, and reinvest. You get 422% return on investment, I get 161% return on investment. On and on, up and up, and both go to infinity. The lucky streaks are both effectively, infinitely, equally rewarding. This isn't you clearly doing incrementally better; this is both of us doing infinitely better, just pausing part-way through the race to look at the partial progress and pretending that the magic stops here and the future doesn't matter
Third. So, your "maximum luck" has converted 1,000 SF into 4,225.35 SF with 71 Rings instead of 1,612.90 SF with 31 Rings. On the one hand, impressive. But..... wasn't the goal to get more Dailies? Isn't that the goal? Where are the Dailies? So, how are we going to do that? Let's continue the race from this point, and compare how we are doing when we cross the finish line, Dailies in hand.
- Do we decide to be maximally lucky with Dailies this time round? 4,225.35/71 = 59.5 Dailies for the 71 Ring, 1,612.90/31 = 52.03 Dailies. Woo-hoo for you, slightly more Dailies for the 71 Rings. But, why did we have to do this in two steps? Why couldn't we start off wanting to be maximally lucky for Dailies from the start, 1,000/71 = 14.08 Dailies for 71 Ring and 1,000/31 = 32.26 Dailies for the 31 Ring. Is there any reason that "maximally lucky" has to be "maximally lucky for bonus SF" and not "maximally lucky for Dailies"?
- Or, maybe we decide to be average with Dailies this time round? 4,225.35/71*17% = 10.12 Dailies for the 71 Ring, 1612.90/31*11% = 5.72 Dailies. Even better for you, nearly double the Dailies for the 71 Ring. But, not only do I wonder why we had to do this in two steps, starting with maximally lucky bonus SF before average odds instead of simply using average odds from the start (1,000/71*17% = 2.39 Dailies for 71 Ring vs. 1,000/71*11% = 3.55 Dailies for 31 Ring), I now also wonder why we would only consider average odds at Dailies in Round 2 and not also include average odds at bonus SF in round 2?
- So, let's consider average odds with both Dailies and bonus SF this round. 10.12 Dailies and 4,225.35/71*4%*300 = 714 bonus SF for the 71 Ring vs. 5.72 Dailies and 1612.90/31*12%*50 = 312 bonus SF for the 31 Ring. Double Dailies and Double bonus SF. But again, why did we have to do this in two steps? Why couldn't we start off with complete average behavior from the start, at which point we're back to the original, standard 347.1 vs 227.3 SF/Daily, or 2.88 vs 4.80 Dailies for 71 Ring vs. 31 Ring for our initial 1,000 SF?
Fourth. As initially expressed above, why are you hoping for better bonus SF odds? Why not hope for better Daily odds? Or picking up more currency around your city? Why must you assume better odds for your pick? Why not hope that you are choosing the better ring because the other ring might receive worse bonus SF odds, or worse Daily odds?
Fifth. Why are you hoping for maximum possible bonus SF odds? Why not a 10% better? Or 20% better? or 50% better? Building your Ring preference around requiring any specific amount of unlikely/lucky outcome is arbitrary, but to base it around the singular, most unlikely/luckiest possible outcome ignoring all others, this is the arbitrariest, most special-pleadingest explanation you could ever make.
To sum up my response to your "1612.90 vs. 4225.35 possible max SF win" explanation...
- Not the same goal. Maybe I previously misinterpreted, maybe you moved the goalposts, but some earlier discussions are completely irrelevant.
- Incorrect conclusion, due to incomplete application of your own rule. Continued analysis produces converges-on-infinity tie.
- Incomplete analysis, as the goal is being judged in Dailies, not SF. Attempts to continue the analysis and compute resultant Dailies question the appropriateness of computing "max possible SF" in the first place.
- Arbitrary choice of acceptable criteria. Hoping for the arbitrary enhancement of an arbitrary quality of a single, particular Ring, as opposed to the arbitrary increase or decrease of any other combination of any other qualities in any other Rings, which offer different results.
- Special Pleading. Hoping for injured-by-stampede-of-wild-elephants-in-your-own-house-between-3:55-and-4:00-p.m.-on-the Fourth-of-July-during-a-hailstorm-with-one-by-zebra levels of improbably lucky behavior by insisting that you will only judge based on the single, most unlikely of all possible applications of your