Originally Posted by Maladaptive

There is a 55% chance to draw at least one Gold or Rainbow in a 10+1 draw (.93^11), and therefore a 45% chance to only get Silver and Bronzes.

Understandably, a 10+1 draw can easily be disappointing (45%). A single Gold is average. A Rainbow or 2 or more Golds is winning.

That might be the change but RNG Gods do not believe in chance, you hear of more people getting no gold then those who get at least one.

Double rainbow? Check.
Gold? Check.

Yeah I'd say you're a winner.

Originally Posted by Maladaptive

There is a 55% chance to draw at least one Gold or Rainbow in a 10+1 draw (.93^11), and therefore a 45% chance to only get Silver and Bronzes.

Understandably, a 10+1 draw can easily be disappointing (45%). A single Gold is average. A Rainbow or 2 or more Golds is winning.

What kind of math is that? 10 + 1 is not a pool, cumulative, or aggregate. All 10 + 1 is the fact that you choose to roll ten times at once, and receive an extra roll for free.

The odds of seeing any one particular girl remains the same. 6★ still has a 0.5% chance, regardless if you rolled once, or ten times in a row.

I myself have experienced at least 3 10+1 rolls where the highest I had was a 4★, and one of those rolls where nothing but 3★.

Edit: To clarify, the quote was assuming a pool which has a fixed number (high end) and also assumes that you will not (a) pull duplicates, triplicates, etc. and (b) that somehow each additional roll beyond the first increases the chances of obtaining something that you had not already obtained. Both do not square away with my experience, and that of many thousands of other players, and no where did Nutaku said that your normal 10 + 1 pull guaranteed anything (Unless there's a special circumstance, like receiving a ticket, but that DOES NOT COUNT when calculating the odds, because the ticket is outside the function of the gacha)

Edit 2: What I think many people don't realize is that gacha follows the same principles as a gambler at a craps table, or any other game of chance.

https://en.wikipedia.org/wiki/Gambler%27s_fallacy

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature). In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false. This fallacy can arise in many practical situations, but is most strongly associated with gambling, where such mistakes are common among players.

Originally Posted by Discoceris

What kind of math is that? 10 + 1 is not a pool, cumulative, or aggregate. All 10 + 1 is the fact that you choose to roll ten times at once, and receive an extra roll for free.

The odds of seeing any one particular girl remains the same. 6★ still has a 0.5% chance, regardless if you rolled once, or ten times in a row.

I myself have experienced at least 3 10+1 rolls where the highest I had was a 4★, and one of those rolls where nothing but 3★.

Edit: To clarify, the quote was assuming a pool which has a fixed number (high end) and also assumes that you will not (a) pull duplicates, triplicates, etc. and (b) that somehow each additional roll beyond the first increases the chances of obtaining something that you had not already obtained. Both do not square away with my experience, and that of many thousands of other players, and no where did Nutaku said that your normal 10 + 1 pull guaranteed anything (Unless there's a special circumstance, like receiving a ticket, but that DOES NOT COUNT when calculating the odds, because the ticket is outside the function of the gacha)

Edit 2: What I think many people don't realize is that gacha follows the same principles as a gambler at a craps table, or any other game of chance.

https://en.wikipedia.org/wiki/Gambler%27s_fallacy

Ah, but avarages do exist, even in RNG. It just doesn't simply work additively, and often you need to make odd calculations to get the results you want. When you plot out all the possible resultsand the chance for them to happen, you get the well known Bell Curve (because it's shaped like a bell). Still, it remains RNG, and people (gamblers specifically) like to take their chances at getting something from the far right side of the curve, even though they have the same chance at ending up on the far left side, and that the peak of the bell curve is just the most common result, but that no guarantee is ever given that you'll actually manage even that result.

Oh hey. Math. I'm really freaking bored, so why not.

...

Pulling up the odds for a single roll in the "Winner's Gacha", they are as follows:

* 0.5% : Six star
* 6% : Five star
* 30% : Four star
* 63.5% : Three star

Therefore, the odds to get "at least an X star" in a single roll are:

* 0.5% : At least a six star (duh)
* 6.5% : At least a five star
* 36.5% : At least a four star
* 100% : At least a three star (more duh)

...

Now, for multiple rolls. Let's find out the odds of getting N number of "five stars or greater" in a 10+1 roll. Really, it boils down to the same math involved in "getting heads N times total in 11 flips", just with a probability of heads that's not 50%.

* Probability of success (a five star or above): Ps = 6.5%
* Probability of failure (a four star or below): Pf = 100-6.5 = 93.5%

The probability of 11 failures - that is, 11 pulls and everything is four stars or below - is quite simple to find. After all, there's only one possible result.

* Probability of 11 failures = Pf^11 = 0.935^11 = 0.4774 = 47.74%

The probability of 1 success and 10 failures is only slightly trickier. We 1) find all possible ways we could hit 1 success/10 failure, 2) calculate the probability of each, and 3) sum them up. There are 11 ways (one for each of the positions), and each of those ways has identical odds (since they're independent), so it's not that tough.

* Probability of 1 success and 10 failures = 11*(Ps*(Pf^10)) = 11*(0.065*(0.935^10)) = 0.3651 = 36.51%

Going further up the chain gets more taxing to do by hand, as the number of permutations grows (well, going further towards the middle does; the far end is just as simple to calculate as the near one). But the same basic math still applies. And, thankfully, computers are damned good at doing simple math exceedingly fast.

Probability of getting exactly N shinies (five star or greater) in a 10+1 pull
--------------------------------------------------------------------
* 0 : 47.74498042254755603 %
* 1 : 36.51086738194813819 %
* 2 : 12.69094320762902939 %
* 3 : 2.64677425185846049 %
* 4 : 0.36800069811935815 %
* 5 : 0.03581611072605517 %
* 6 : 0.00248989005047442 %
* 7 : 0.00012363854337726 %
* 8 : 0.00000429759642755 %
* 9 : 0.00000009958779600 %
* 10 : 0.00000000138464315 %
* 11 : 0.00000000000875078 %

(And for anyone concerned, the sum of those numbers - not the shown numbers, the actual ones used in the underlying script's array = totals to "1.0000000000000004". So there's a tiny bit of precision error in there, past 15 decimal places or so. But that's still good enough for a few significant figures, even for the smallest probability above. Besides, even if the 11 success case was 100x larger, it's still really damned microscopic.)

...

You could derive other interesting numbers - for example, the total probability of getting 4 or greater shinies in a single 10+1 is actually slightly rarer (0.41%) than getting a single six star in a single pull (0.5%) - but meh.

That was fking awesome. I love math too.

Well I just had my 12.69% win with 2 golds from 1 10+1 pull. Madonna (new for me and now my 5th 5* skill activation girl!) and Nasturtium (A dupe but the 1st I have gotten of her so at least an extra equip slot).

Congrats on both those golds and beating the 12.69% odds, Zandel. Madonna's waifu tier up there with Anthurium and dupes are always a welcome addition.

Just to test I put 5 1.2xskill girls on one team... it's a 2x total but if you swap one with Cymbidium it becomes 3.6x round 1 and 1.8x after... so enough to kill anything in a few rounds tops.

Originally Posted by Zandel

Just to test I put 5 1.2xskill girls on one team... it's a 2x total but if you swap one with Cymbidium it becomes 3.6x round 1 and 1.8x after... so enough to kill anything in a few rounds tops.

Interesting.
Well at least reading through the last few posts I finally got an Idea how that buff stacks.
I always though it to be weird that "Oh 5. 1,2 6x the activate rat, so if my girl has 30% activation rate, times 6 I have a guaranteed 100% of her activating it), or at least thats what I used to think. Granted I considered it to be kinda wonky and over the top.
So the scaling is much reduced, 0,2 per girl to be precise.
Still a 30% skill rate, time 1,8/ / 2,0 is over the 50/50 range which makes it pretty solid. It requires a full skill act. team though. But certainly is solid.