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A 4K in the hand is worth 1.88
by firebus
07/17/2009 - 13:40
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.
Comments
Your stats ignore the
Your stats ignore the obvious - Yahtzee has no penalty for rolling the third roll. So, you either HAVE a 4K, or a Yahtzee. And no reason not to find out.
Since yahtzee is based on human-centric rules, it makes sense... But an additional "in X rolls" multiplier could be done today with computer-rendered versions of the game, and might add to the fun of going for a "par" bonus, like the left-side bonus.
overthink
i know, i know. i realized in the middle of writing the post that i was overthinking/forgetting the fact that no matter what you have 4 sixes and your worst outcome is still a good one.
but i went ahead and posted anyway, even though it's a very simple case.