What really are the odds? Aka Gambler's fallacy

You may be given a situation where you have to roll a die, a 1/6 chance of getting it, and 6 rolls. You may think, well since I got 6 rolls, I will roll that number in 6 rolls or less theoretically. But really, those odds(aka the average 1 in 6 rolls) is actaully lying to you. You need to look closer to find out the real odds. Lets start out with a coinflip, you have 2 flips to get heads, you have a 1/2 chance of getting it. On average, every 2 flips equals 1 heads. But in real life, thats not true. In fact, if you look at the odds of NOT getting heads, 1/2 and 1/2, you get 1/4, which is 25 percent. Lets go to a 6 sided die, and you need to roll a 1 or a 6, you would think you have a "100 percent chance of getting it in 6 rolls or less" but really, when you calculate the odds, you have to cube 2/3(4 sided are not 1 or a 6) because of a 3 rolls. In the end, you have a 8/27 chance of not getting either 1 or a 6 in 3 rolls. Which is almost 30 percent. And I notice something, as it gets less likely to get something in a single try, the odds get much less likely to do that by the average amount of rolls needed to get the number. But over time, it increases less and less, and this graph shows it
As you can see, it starts at 25 percent, spikes up from 3-7 but then gets the rate gets slower and slower. There is barely any increase from 1/50 50 rolls, to 1/100 in 100 rolls. A pattern here is that it is apporching 50 percent, when you get 1/infinity with infinity rolls, thats going to be 50 percent. Overall, you only got from 75 to just 60 or 55 percent chance of that actually happening. And think about it, when you buy all the tickets needed in the lottery to get to 1:1 raito, is it really 100 percent? Of course, if you got every combo, you do, but if you left it to random chance,(aka quick pick) chances are you don't have that much odds of getting it. In conclusion, if your given the odds of like 1/50, and you got 50 chances to get it, make sure to think, don't listen to the voice in your mind saying " Oh im going to get it, since on average, it gets what I want every ___ rolls." Be careful on what the odds really are. Edit: Thanks to tinytiger for saying that this is Gambler's fallacy! Make sure to resteem and up vote for more deep content.