Quote:
Originally Posted by Banzai-
Assuming whosnext's post #3 is correct (I didn't double check the math but the logic all looks good), you have about a 1/25256 chance of rolling a Yahtzee in the first two throws (~1/25319 of exactly 2).
Higher numbers than that get really hard. The simplest idea would be to just apply binomial distribution for the later rolls, but that would be undercounting because of cases where for example on the first roll you roll 3 3s, and then when you reroll the 7 other dice you hit 5 5s, I assume you keep the 5s there? If you are "locked in" to the number you keep the first time the math is probably pretty doable.
Oh wow, I did not consider that scenario, or the effect that it would have on the math.
The way we have been playing lately though takes that scenario out of the equation. Basically, since the scores have gotten better, and harder to beat, we roll all the dice over and over until we hit a roll with five matches. We then separate the five (or more) dice and continue with the second roll with the remaining dice.
So, we never get locked in. I am not sure what a binomial distribution is, but I appreciate the help. Thanks for verifying the chance of me losing the current record.
Quote:
Originally Posted by whosnext
I could not think of an easier and more reliable way to derive the 10-dice transition probabilities than a brute force approach so I coded up a simple routine. Here is what I get for the numerators for the transition probabilities of moving from P matches to Q matches (denominators listed at bottom).
I didn't want to quote the whole post with the Markov transition matrix, but that helps immensely whosnext.
It makes it very easy to see the odds of moving from one outcome to the next. That will be very handy next time we play the game.
I am surprised how seemingly easy it is to get the Yahtzee in three rolls (I now fear more for my record being tied.) Lol.
I thought it would be more difficult to attain.
...
I will undoubtedly have further questions, but right now I am going to take a little time to go over the links and answers provided. Right now I feel a little like I did in high school, looking in the back of the book for the answers, lol.
I appreciate the help, and will say that the questions I asked were answered completely. Thanks for the tutorial.