There are many end game considerations to make actually. With one unfilled score box there is one hand left to be played and usually you are shooting for a particular outcome. For example, you may need a Large Straight or four 2’s. Strategically, the play of the hand becomes fairly apparent. Assume your score card is complete except for the Large Straight. That is, you have one hand left to play, and if you can make a Large Straight you will get 40 points. However, if you don’t make the hand, you’ll have to take the zero points for this last box, since the rest of your scorecard is already full. Of course, you won’t always make the Large Straight. So, on average how many points is this unfilled category really worth?

Through expert analysis, it is shown that the Large Straight will be made 27% of the time, assuming there is perfect play in trying to achieve it. It may surprise you to learn that an unfilled Small Straight, although only worth 30 points, actually has a higher expected value. In instances where it is the Small Straight or nothing, you will succeed about 62% of the time. This means that an empty Small Straight box is worth more than an empty Large Straight box. Specifically, it is worth about 8 extra points to your total score if you are looking at averages of all the points in all of your games. So, if you are presented with a situation in which only the two boxes of Small and Large Straights are unfilled, and you must choose one of the to fill with 0, do you know what you should do?

You need to consider the game in which you are playing. Let’s assume you have just finished playing the 12th hand and the final outcome was 3-3-4-4-5. This is neither a Small Straight nor a Large Straight, but one of those two boxes must be filled with zero. If you fill Small Straight with 0, then the expected value for the last hand is 10.6 points, since the Large Straight is left unfilled. However, if you fill the Large Straight with zero, then the expected value for the last hand is 18.5 points since you only have the Small Straight to fill in. To maximize your expected score, the correct answer is to fill the Large Straight with zero and hope to fill the Small Straight on the final hand.

Putting a zero in a box with a potential of 40 points as opposed to one with 30 points may seem difficult to do, but you are far more likely to get the Small Straight as opposed to the Large Straight. That is why it is more valuable to preserve the Small Straight than the Large Straight late in the game.

When you are late in the game, there really is an order in which you should be placing your zeros if you find yourself in that situation. The key order to remember is Yahtzee, then 4 of a kind, Full House, and then the Large Straight. This is the proper thing to do not just on the last hand, but throughout the entire end game.