In Yahtzee is important to note that it can easily happen that you start a turn deciding to go for a given combination, then you roll and choose another combination to go for. Why? Simply, because with the second combination you can score more.
During one turn you can switch twice: between the first and second roll, then between the second and third roll. After the third roll you have to choose an empty box/place.
We don’t take into consideration the extra Yahtzee bonus at this point.
This possibility to change the targeted combination between rolls increases the overall probabilistic value of combined boxes. For example, if there are only the Ones and Twos boxes left/unused, their combined probabilistic value is bigger than 2.10 + 4.21 = 6.31. It is actually 7.12.
Similarly, in case of Ones and Sixes the pv of these combined places is 16.98 instead of 14.73.
To sum up with, the probabilistic value of combined places increases with the number of boxes if you follow a right strategy and change the targeted place/combination as needed.
Thus if you follow the right strategy, the probabilistic value of the combined places: Ones & Twos & Threes & Fours & Fives & Sixes is about 71.95. This is clearly more than 63, which is the minimum score for getting the 35 upper section bonus points! As a result, it really makes sense to go for the Upper Section bonus!
There is only a single question left: what is the right strategy? This is a difficult question …..
Next
