On the second roll of a play, I had 4 sixes and a five.

4K and Yahtzee were both open.

Obviously, the play would be worth 29 points in 4K, and Yahtzee is only a 1 in 6 chance, with a 2 in 3 chance of getting less than 29 on the next roll.

My heuristic is to *always* roll for Yahtzee on 4K if Yahtzee is open (and sometimes if Yahtzee is closed and Large Straight is open).

Expected outcome in this case is the average of all the possible outcomes: avg(50, 29, 28, 27, 26, 25) = 30.88. Go heuristics.

Typically what happens is that on your first roll you get 3 ones, and maybe a potentially useful singleton.

And you've already used the ones box.

So the question is, should you go for Yahtzee here? Or should you try to build off the singleton or just re-roll all five dice?

I suspect that if the probability is reasonably close to 1 in 6, it's probably your best chance at a Yahtzee in the game, and thus worth risking the Yahtzee box on.

There are 3 ways to get to Yahtzee from here, and we can sum their individual probabilities to get the overall chances.