I watched a video on youtube which stated the probability of rolling a yahtzee in a single roll (same value on 5 six sided dice) before 1296 rolls is 63%. The probability of rolling a yahtzee on any single roll is 1/1296. I know my math is not up to the level of you guys on here, I'm a programmer, but I couldn't get my mind around how 63% makes sense.. so I threw together a program to test it out and it is indeed the case. 63% of the time a yahtzee was rolled in a single roll before the 1296 roll. My program also reported that the average number of rolls to get a yahtzee is 1301 or 1302 after a few tests of 1,000,000 rolls.
Could someone please explain where that 63% comes from? And also, an average of 1301 or 1302 to get a yahtzee seems a bit strange to me as well given the 1/1296 probability. Although I put it together quickly, I'm fairly sure my program is working properly. Do those numbers make sense in terms of the math? And if so, why is the average not 1296?