I've recently got into playing Yahtzee with my brother. During a game we had on my first roll for my last round I got (5 4 4 2 1). I only had my large straight left, so naturally I was hopeful with what I got. I quickly thought about it, and my instinct was to roll the 4 and the 1, at a good chance for a 3. I figured better than just one chance at a 3, and if I got it, that would leave me having a good chance at a 6 or a 1 for my last roll.
My question is this, how do you calculate the over all chance of either strategies in order to choose which is better?
I used to be great with calculus, even in electrical calculations, however probabilities are really giving me a headache.
I think I got the first strategy of rolling just one die with the calculation of 1 - 1/6 = 5/6 (not happening) for each single die roll, for a sum of 25/36 (not happening) or 11/36 (happening) or 30.56% chance. yeah?
The problem I have is with the second strategy since the first roll is with two dice, but then second roll is either one or two di(c)e depending on the outcome. How do you factor that in mathematically?