All in all

All in all

 

To sum up with, the extra Yahtzee bonus feature means in average 8.5 points in addition to the version when playing without the extra Yahtzee bonus. It extends though the possibility to obtain considerably bigger scores.

The upper section bonus in average means 16.24 points in addition to the version when playing without any bonuses.

The most probable score is 266, and this not depends on whether you play the variant with or without the extra Yahtzee bonus

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Fig07

Fig08

High scores

My program played 10m games in the Yahtzee version with all bonuses and it scored only once 934 points (the highest score obtained during these games). It also scored in 714 cases more than 700 points, in 40 cases more than 800 points, and in 4 cases more than 900 points.

What is the probability for someone playing manually to achieve a high score? If you are a strong and fast player and you follow the best strategy, futhermore, if you manage to play one game in every 30 seconds, you would play 10m games in about 9.5 years (playing continuously).

From purely statistical point of view you will probably obtain a score higher than 700 once in every 4.8 days, a score higher than 800 once in every 3 months, and a score higher than 900 once in every 2.4 years! If you don’t follow the right strategy this could be even worse!

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