Lucky Little Fin

[Sir Derf]

Yes, you need to win bonus SF fewer times using the 71 Ring than using the 31 Ring. Yes, you need to win bonus SF 2.62 times with the 31 Ring to be on par with one win of 71.

Which leads to the question - how often do you expect to win with the 31 Ring compared to the 71 ring? 12% vs 4%. Which is 3 times. Which is more than 2.62 times.

The 31 Ring naturally, without luck, wins bonus SF 3 times more often than the 71 Ring, and thus your position falls apart.

Equally lucky is not both of us getting one extra win. Equally lucky is both of us seeing the same percent improvement. The 71 Ring picker is 25% luckier, wins 25% more often, and the 31 Ring picker is 25% luckier, wins 25% more often. 71 Ring wins 5 instead of 4 out of 100, 31 Ring wins 15 instead of 12 out of 100. And, as you've already agreed, a single extra 71 Ring win is slightly worse than three extra 31 Ring wins..


And as to your but again, I respond with and again, you keep ignoring what happens when the other side gets equally as lucky as you. I'm using averages everywhere else, because you set the terms by saying that you are wishing for lucky outcomes with winning bonus SF, so I'm comparing the results of equally unlikely bonus SF outcomes and assuming that everything else is average. If you want to apply luck to other aspects of the computations, then I'll apply the equal luck to the same aspects of the computations for both sides.

 

[Silly Bubbles]

@Sir Derf We start going in circles again and repeating the same arguments again so this is it from me. I'll stick to my strategy as it's my full right and you can do whatever you want to do as it's your right. I just hope that others will pick what makes more sense to them rather than what is sold most frequently and loudest.

 

[SkyRider99]

It grows towards infinity faster.

To infinity, and beyond!

 

[Sir Derf]

Yup, it's your right (well, less right, and more available option or free will, but ok) to stick to your strategy.
And I can do whatever I want.

And yes, people will pick what makes sense to them. And hopefully they won't pick based on popular opinion because it is popular opinion. They should pick what "makes sense" because, well, it's rational, and logical, and has supporting information and stuff.

Everyone is welcome to their opinion. It's just when your opinion peanut-butter gets all over your support-reason chocolate that I draw the line.


It's fine to prefer muscle cars. It's fine to try to convince others that they should prefer muscle cars. It's, let's say, unfortunate, to think that they are fuel-efficient because they can go further on a tank of gas, without realizing that they have larger gas tanks, and fuel-efficiency is based on miles/gallon and not miles/tank. It's, let's say, bad if you try to convince others that they should prefer muscle cars because they are fuel-efficient. (I don't know that they have larger tanks, but it's the best analogy I could come up with on short notice.)

Perfectly fine to prefer taking what you think is a "riskier" approach towards a potentially "superior" reward. And to describe your preference to others. It's, let's say, unfortunate, that it appears that preference is based on an incorrect assessment of risk, or reward, or unequal comparison; on an incomplete/inaccurate computation of the likelihood (or even the existence) of an eventually superior potential reward that could be received by the proposed approach, or an apples-to-oranges evaluation, granting your side more liberties or tying the opposition's hands behind their backs. It's, let's say, bad if you try to convince others that they should prefer this approach on the basis of flawed reasoning.


Why does this matter? End of the day, it's only a game, right?. People can do what they want. People can have opinions that explain the "Whys?" for what they do. But, if those reasons are trying to be based on reason, on fact, on concrete comparisons that use measurements and computations to distill the choice down to two numbers and picking the maximum, well, then you should bother to actually use proper reason, use actual (and not alternative) facts, and if attempting to make a concrete comparison to use the correct measurements and the correct computations to arrive at the correct two numbers and pick the correct maximum, otherwise it's all just a lie. And the more you work on the right computations in the game, the more you will work on the right computations in life.

Sure, making the less-efficient decision in the game might mean you get fewer free prizes in the game, no harm, no foul. But making less efficient decisions in life can cause harm and foul. Properly combining ring cost, bonus odds, bonus payouts and Daily odds let's you optimize your chances at the rewards of your choice; computational mistakes give fewer free rewards, oh well. Sticking with my auto analogy, there's fuel-efficiency, repair costs, sticker prices, guesses on future fuel prices, available cash, different terms on auto loans, prospects on future employment; all can have a big impact on long-term financial outcome. Many more factors involved here than in a silly game. And long term consequences even a year out from that decision that dwarf the impact on a city in the next chapter based on the number of high-mana-producing buildings you do or don't win.

 

[Silly Bubbles]

@Sir Derf Maybe I feel sorry for you because I proved you wrong so many times and want to give you a break. Unfortunately, you keep asking for more. Maybe try a little bit harder to actually understand others, I know that you do have the ability to do it if you stopped supporting your position at any cost even after I showed you the mistakes you do.

I agree that 31 ring is the safest ring as it gives you highest chance of getting average result. But if you want better than average result you need to risk more and 71 ring gives you that because in less turns it can give 3 times more SF than 31 ring if you’re lucky. You need to win 3x on 31 ring to get to the same result as one win using 71 ring.

This is what happens when you start with 1000 SF and have maximum luck:

Ring value​	Possible SF win​	Possible turns for 1000 SF​	Possible max SF win​
31​	50​	32.26​	1,612.90​
71​	300​	14.08​	4,225.35​

As you can see, you can get much more out of your lucky streak using 71 ring.

If you still don’t understand then I can’t help you, sorry.

 

[Sir Derf]

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...

1. Not the same goal. Maybe I previously misinterpreted, maybe you moved the goalposts, but some earlier discussions are completely irrelevant.
2. Incorrect conclusion, due to incomplete application of your own rule. Continued analysis produces converges-on-infinity tie.
3. 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.
4. 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.
5. 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

 

[Silly Bubbles]

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...

1. Not the same goal. Maybe I previously misinterpreted, maybe you moved the goalposts, but some earlier discussions are completely irrelevant.
2. Incorrect conclusion, due to incomplete application of your own rule. Continued analysis produces converges-on-infinity tie.
3. 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.
4. 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.
5. 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

The more SF the more dailies because you do need SF to get dailies so the more SF the more goes at getting dailies etc You can't get dailies without SF. It's really simple, it doesn't need to be done complicated way. Also, the more SF the more chances at fully evolved main prize.

 

[SkyRider99]

I simply look at the percentage chance of winning the daily prize I am after, and adjust my choice according to the associated prize-vs-rubbish that is offered with a given ring.

If that fails I suck my finger and hold it in the air to see which way the wind is blowing.

 

[Sir Derf]

The more SF the more dailies because you do need SF to get dailies so the more SF the more goes at getting dailies etc You can't get dailies without SF. It's really simple, it doesn't need to be done complicated way. Also, the more SF the more chances at fully evolved main prize.

The more SF, the more Dailies.

Step 1: Rig the game by assuming that you will get bonus SF from your chosen 71 Ring not twice as often, not thrice as often, but... they don't have a word for 25 times more frequently. Icosapental? And not because 25 was an arbitrary choice, but because it was the highest choice there was.
Step 2: Don't even bother doing additional math, because you don't care. It didn't, and still doesn't matter to you. And it shouldn't matter to anyone else, because, as I said, you've already rigged the game beyond all meaning to attempt to do further analysis.




It doesn't need to be done a complicated way.

Assuming multiverse-warping 32-out-of 32 4% chance outcomes, that, by classical computation has odds of 1 in 5.42E44... that isn't complicated? 10^44... well, that's smaller than the total number of atoms in the Solar System, which is about 10^52, so I guess that's not the big, is it?


You can't get Dailies without SF.

Except, we started with an initial amount of SF. Why do we need to get more SF first? Why not just choose the cheapest 21 Ring, and hope for possible Max Daily win of 47 Dailies from the recent initial of 1,000, or a staggering 285 Dailies from my original initial 6,000 SF? Wouldn't this be less complicated?






If there was a 10th Ring that cost 150 SF, had 4% odds for a Daily, and 1% odds at 1,000 SF, you'd probably prefer that that over the 71, since hey, 1,000/150*1,000 = 6,666 possible max SF win is better than 4,225.35, right. Or an 11th ring that costs 500 SF, had 2% odds for a Daily, and 0.25% odds at 5,000 SF, cause 1,000/500*5,000 = 10,000 possible max SF win.

And this would, of course, be better than 12th ring that costs 20 SF, had a 25% chance of a Daily, and a 20% chance at 20 SF (Who cares it would on average give 1,000/20*25% = 12.5 Dailies, it only could give a possible max SF win of 1,000). Or a 13th Ring that costs 15 SF, had a 50% chance of a Daily, and a 25% chance of 10 SF (Which would naturally give 33 Dailies, it could only give a possible max SF win of 666).





Or, consider this sequence...

1. What would you do if there was a 10th ring that also had a bonus SF of 300? Given your earlier computation, I assume you would prefer the one that costs less, since this would allow you more Rings for equal initial SF. This appears to be the limit of your considerations.
2. What if this 10th ring with an identical bonus SF of 300 also cost 71 SF? What would you then consider to determine which Ring to prefer? I guess it would be whichever had the better odds for Dailies, since if you are assuming max possible SF wins, the as stated odds for bonus SF are immaterial.
3. But them suppose this 10th ring with an identical bonus SF of 300, which also cost 71 SF, also had 17% Daily odds? I guess you now have to look at the bonus SF odds, I pick the larger of the two?

On the other hand, maybe when comparing one Ring to another, maybe you should look at all four numbers; cost, bonus SF odds, bonus SF payout, and Daily odds. I know, I know, it's sooooooo complicated to have to combine all four numbers into a meaningful single value and make a comparison that weighs all four properly. It's sooooooo easy to simply pick one or two qualities, like bonus SF amount, magnify it's importance beyond all bounds of reason, and ignore all other factors.



Oh, and lastly,,,


Also, the more SF the more chances at fully evolved main prize.

And again, let's move the goalposts and introduce yet another previously unstated success target.

Is this a secondary goal that is less important than getting 10 more Dailies, or possible max more Dailies? Or is this a newly-stated-primary goal, more important than Dailies? Does it even matter that the second goal is, if not contradictory, at least completely unrelated to the first? Sure, in a general sense, they both could benefit from more SF, but more Dailies is then influenced by choosing Rings with more efficient cost*Daily odds, while fully evolved Main Prize is instead influenced by Cost/... what are they, starfish medalions?

 

[Herodite]

I simply look at the percentage chance of winning the daily prize I am after, and adjust my choice according to the associated prize-vs-rubbish that is offered with a given ring.

If that fails I suck my finger and hold it in the air to see which way the wind is blowing.

You won't distract them @SkyRider99 they're going in hard!

 

[Laurelin]

You won't distract them @SkyRider99 [...]

@Herodite : You'd almost think we ALL need our own personal Forum in which to ramble - on whatever subjects we each deem important...

ETA : @Killiak @anonglitch

PS : I'm getting there : there's also almost more code in this post than words, now...

 

[Herodite]

@Laurelin I can't speak for all but I very much enjoy your rambles! I will of course begrudgingly subscribe to "Laurelin Lite" but I will definitely miss the Full Version!

 

[Silly Bubbles]

You won't distract them @SkyRider99 they're going in hard!

Yep, anything to support the game and help players to get more out of it.

 

[Laurelin]

@Sir Derf :

[...] Assuming multiverse-warping 32-out-of 32 4% chance outcomes, that, by classical computation has odds of 1 in 5.42E44... that isn't complicated? 10^44... well, that's smaller than the total number of atoms in the Solar System, which is about 10^52, so I guess that's not the big, is it? [...]

... that's genuinely hilarious

[...] If there was a 10th Ring that cost 150 SF, had 4% odds for a Daily, and 1% odds at 1,000 SF, you'd probably prefer that that over the 71, since hey, 1,000/150*1,000 = 6,666 possible max SF win is better than 4,225.35, right. Or an 11th ring that costs 500 SF, had 2% odds for a Daily, and 0.25% odds at 5,000 SF, cause 1,000/500*5,000 = 10,000 possible max SF win. [...]

... also very Pythonesque - while also illustrating why so many players really DO take a very remote gamble on those 300-500-value Chests!

* * * * * * * *

@Herodite : Bless you

I lived for many years with a London barrister, way back when - and one doesn't do THAT without learning all about get-out clauses ... !!

 

[Sir Derf]

Assuming multiverse-warping 32-out-of 32 4% chance outcomes, that, by classical computation has odds of 1 in 5.42E44... that isn't complicated? 10^44... well, that's smaller than the total number of atoms in the Solar System, which is about 10^52, so I guess that's not the big, is it?

Oh, noes..... I made a math mistake, which accidentally exaggerated to comedic effect the opposition's position...

32-out-of-32 was the comparison tries for the 31 Ring, which had 12% chance outcome, and thus represented odds of 1 in 3.41E30.
The correct computation for the 71 Ring should have been 14-out-of-14 4% chance outcomes, for odds of 1 in 2.68E20.

That's obviously a much smaller number, and so undeserving of the excessive humor and derision I was hurling in its direction. I mean, Avogadro's number is only 6.022E23, so 10^20 is, like a thousand times larger than the number of Hydrogen atoms in a single gram of Hydrogen.

Apologies. When I make a mistake, I own it.


On the other hand, I noticed this mistake because I wanted to add that my original intended computation really an generous understatement, as it was based on the recently reduced baseline of 1,000 SF, and not the originally discussed baseline of 6,000. The original ask was for 84-out-of-84 4% outcomes, with odds of... wait for it... 1 in 3.74E118.

10^118. How to describe 10^118.

First of all, it's larger than a googol. Not google, googol. 10^100. On the other hand it's smaller than a googolplex, 10^(10^100). I Googled "google" because I wanted to get this detail right, and according to Wikipedia, both of the above numbers were initially named by a nine-year-old nephew of a mathematician, although the original definition of googolplex was, and I quote, "one, followed by writing zeroes until you get tired". The mathematician regularized it to 10^googol, because, well, different people have different hand stamina plateaus.

"But where does 10^118 fall relative to cosmological numbers?", I hear you say... When I earlier used the phrase "multiverse-warping", that was obviously comedic hyperbole. 10^44, as I described was less than a Solar System count, so truly it was unworthy of being described as galaxy-bending, let alone universe- or multiverse-bending. But 10^118. Ho, ho, ho... that's a whole other kettle of fish. Well, hang on to your hats folks. Because, you see, with estimates of 10^11 stars in our Galaxy, and 10^11 Galaxies in the universe, the estimates of the number of atoms in the Universe is estimated at around 10^78. 10^118 would be the number of atoms in 10^30 universes. This, truly is a multiverse-warping number.

 

[Laurelin]

@Sir Derf : Er ... as you know, words, not numerals, are my thing, since Laurelin's Number (hmm... it sounds better to give it my other nickname, so let's call it Nell's Number) would be three, or five, or maybe fifteen, rather than the E-powered example favoured by far more maths-capable people such as yourself and also, it would seem, the esteemed Signor Avocado Avogadro [sorry, couldn't resist!] - but even so, I'm having trouble working out whether you may believe that I was resorting to what would have been, even by my own excruciating linguistic standards, a genuinely outrageous degree of sophistry, if not rather unkind, too... when I was just stating the simple fact that I found your post amusing - and also that I honestly DO appreciate the mathematical comparisons you've drawn, whether or not we're comparing the atoms within a whole Universe or a mere (?) mole*...!

I'm wondering especially because you began your post with "Oh, noes..." - which I've noticed, in your posts, often introduces a degree of sarcasm and/or incoming wit - and also for other linguistic reasons, too, with which I will, for once, refrain from boring the Forum at large.

Anyway. It's still funny to a maths dunce like me, even though I had (in all honesty) NO IDEA there was any error in what you wrote - oh, and also:

* I remember you once said to me, a long time ago, that you post elaborate maths at least partly because you hope that less mathematically able and/or inclined readers may thereby be inspired to seek to learn more about the subject... so, for what it's worth, it worked this time, and I can now use the term 'mole' in a new and formerly [to me] unknown sense. And that makes a word nerd like me very happy indeed!

 

[Sir Derf]

I think I have another candidate for best strategy... Let's see if this works out...

So, talking about suns, and galaxies, and universe, and cosmic thigs like that, reminded me about cosmic rays.

What are the odds that a cosmic ray might hit the memory in the INNO server that holds the numerical representation of your SF, increasing your SF, and thus obviously providing massive quantities of Dailies?

Well, apparently studies by IBM in the 1990s suggest that computers typically experience about one cosmic-ray-induced error per 256 megabytes of RAM per month. This boils down to a probability of 1.4E-15 per byte per second. Is Elvenar 32-bit, or 64-bit? Hmmmmm. Let's guess 32... next, the binary representation of 6,000 SF would be 00000000 00000000 00010111 01110000. So, let's say the first two bytes are our target, as a change in even the lowest bit would produce a sudden windfall of 65,536 free SF. So, we're looking at an event with a probability of 2.8E-15 per second, or 1 in 3.57E14. How long does an Elvenar Event last? Well, LLF last 20+ days, lets bump that up a few to 23+ and call it a nice, round 2 million seconds. That means, you would have a probability of 5.6E-9 per event, or 1 in 1.78E8. 10^8. One Hundred Million. This is sooooooooooooo much more likely than 10^118. I mean, beneficial memory cosmic ray alterations will happen 10^100 times for every 84-out-84 4% bonus SF win. This is practically a sure thing.

Of course, even if INNO expands to 10 events a year (*shudder*), this will probably take half-way to 1.78E8, or 89 Megaannum before this happens for you.

Thankfully, the sun doesn't expand and engulf the Earth until 7.6 billion years, so we have plenty of time before that happens.



Three caveats to all of the above.

First, what are we sacrificing? Well, remember how we focused on the first two bytes, where an error turns a 0 to a 1 and increases your SF stash? Well, look at those lower bytes, There's 7 1s in there, where if an error occurs and flips a 1 to a 0, it will decrease your SF count, slightly. That's almost a full byte, so with odds of almost half of all the above, a cosmic ray might decrease your SF.

Second, It's highly likely that INNO implemented the SF number as a signed integer. That means that the very first bit, one of the 16 that we considered in the initial computations wouldn't increase your SF count, and it wouldn't decrease your SF count... It would give you negative SF. It would take your 6,000 SF and change it to -6,000 SF. Now, this could mean you lost all your SF, get no Dailies, and are a big loser. Orrrrr....... If you tried to play the game in this state, you might end winning negative Dailies, and have buildings removed from your inventory or city. Now, that's what I call risky.

Third, this has all been worse than an exercise in Semi-Pointless Math (tm). This has actually all been a waste of your time. The mythical Fully-Pointless Math (tm pending). Because standard computer hardware for decades has incorporated error-correcting aspects in the use of memory, preventing exactly this type of thing. Even should a cosmic-ray flip a bit, the system would work around this and continue to use the correct value, thus preserving your 6,000 SF bounty.



Caveat Caveat

Now, if multiple cosmic rays were to strike in the same memory in the proper bits that are involved in the error correction of a single bit, close enough together in time, that might end up making a modification that would slip past the protections and actually alter the numerical representation permanently. Making a rough estimate (whaaaaaat, not doing the full math? Sue me.) that's possibly 3 times 16 times the earlier odds squared, or maybe 1 in 1.5E18.


Or, you could just pick 31 Rings.

 

[Jake65]

Or, you could just pick 31 Rings.

I'm going to stick with my tried and tested method of staring the seahorse/chicken/event-animal in the eye and looking for it's 'poker' tell

 

[Sir Derf]

Ugh....

I didn't keep track of details as I went, so. I have incomplete info, but..

I went in with my fully accumulated 5,300 SF, and followed strategy for Dailies. However, I preferred a particular Daily, namely the Manta Ray from Day 1, an efficient Mana producer. I Rerolled sooooo many times. RNG denied me. At least it didn't insult me by bringing it up on my final Reroll, when I only had 40 SF left.

In the end, I have 15 new buildings of varying types, including 5 Manta Boats (which is not the same, you can't fool me) (and of which I at one point got 3 in a row), and hit the Daily an uncounted number of times when they were various Goods or Instants.

Oh, I probably should go back and collect my Grand Prizes... shows how single-minded I was on those Dailies...

Okay, I'm back... 236 Points, so 12 Grands, including 6 Artifacts for an evolving I don't particularly care for. 4 points shy of the Expiring building that gives Pet Food... Well, I got a few more locked Daily Quests to do, so I should be able to get that one, too. Free Pet Food, yum. I finished all this an hour ago, and at that point it was good enough for Iron League, but the hourly recalc has already dropped me back to Bronze.

Ooo, another SF has dropped in my city... Savory Bites, I'm coming for you...

 

[Jake65]

I can't figure the timing of the savoury bites.
It lasts for 10 days (240 hours) and coughs up a pet food every 45 hours.
So it's going to spend it's last few hours just relaxing in my city doing nothing productive.
Like the Orcs, mutter mutter...