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.