How many times to roll a dice to get 6?

A fair die never guarantees a 6, so the only honest answer is about six rolls on average, but that average hides a lot of spread. The chance on every single roll stays at one in six, no matter how many times you've already tried, and that's the whole trap of a losing streak.

Fifteen misses in a row sounds bad but it's not that unusual. The probability of missing fifteen straight times is (5/6)^15, which works out to roughly 6.5%. That's over one in twenty. You wouldn't call it a rare event if you saw it in a crowd, and it happens to plenty of people on a board game night.

What you're describing is the gambler's fallacy. The die has no memory. It doesn't know you're stuck on the last square, it doesn't owe you a six, and the odds on roll sixteen are exactly the same as they were on roll one. The dice don't even out over a single evening, they even out over thousands of rolls, and you won't see that from one game.

What you can do is flip the question. Instead of asking how many rolls you need, ask how many rolls you can expect to wait. The average wait for a 6 is six rolls. But that's an average, not a promise. Half the time you'll see one before that, half the time after, and sometimes you'll wait twenty or thirty rolls for no particular reason.

So no, the die isn't rigged, and the game isn't cursed. You just hit the unlucky end of the distribution. If you keep rolling, a 6 will show up eventually, but you can't put a number on when. That's probability for you.

There's no fixed number. A fair die stays at 1/6 every roll. On average you'd see your first 6 around roll six, but variance means you can blow way past that.

Fifteen misses is annoying, not suspicious. Previous rolls change nothing, that's the gambler's fallacy. About six on average is the only honest range you get.

Roughly 34 rolls before you're over 95% sure of having seen a 6, but each roll stays at 1/6, no accumulation.

I tested this once with a real die, 50 rolls. Average landed just above 6, but the spread was wild, once I went 21 rolls without a 6. Short runs prove nothing. Your 15 misses is well inside what a fair die does.

Rolling five 6s is (1/6)^5, about 1 in 7776. Getting a 1-2-3-4-5 in any order is 120/7776, roughly 1.54%. A full 1-2-3-4-5-6 in order is 1 in 46656. Rare, but that's a different question entirely from your single 6.

Stop chasing the number. The gambler's fallacy hits hardest after 20+ misses without a 6. I ran a simulation once and saw a streak of 41 rolls without a 6. Even insanely long droughts happen. You just enjoy the game and let the dice fall.