Yahtzee--

How to play Yahtzee: The game consists entirely of rolling dice. You start by rolling all five dice at once. You then pick which ones to keep and which ones to roll again. After your second roll, you choose again. You may roll a total of three times per turn. At the end of your last roll, you enter a score in one of the 13 places on the scorecard. You must enter something each turn.

How do you pick which ones to keep? You decide what to try for based on the point value of each possibility. The best thing to get is five-of-a-kind. That result is known as "Yahtzee" and is worth 50 points. Other possible outcomes include:

3 of a kind: sum all of the dice
4 of a kind: sum all of the dice
Full House: 25 points
Small straight: 30 points
Large straight: 40 points

These are the really good things to get and it's not easy. Sometimes you just end up with perhaps a pair of threes and nothing else interesting. To score that, you would go to the "THREES" spot on the upper half of the scorecard and enter 6 points (3 points for each of your threes). Pay attention to the upper half of the scorecard, because you get a 35 point bonus if your upper half totals at least 63. Sometimes it's worth it to sacrifice one of the other categories in order to get your bonus.

You are trying to maximize your total score, of course. The tricky part is that you have to enter a score each turn. If you get junk, you still have to put a score somewhere. One option is to use the "Chance" spot. You can put anything in there-just add up the total value of the dice. Another option for dealing with a crummy roll is to use the spots on the upper half of the scoring sheet. Once those spots are full, however, you still are required to enter a score each time. That might even mean putting a "zero" in one of the remaining spots. For example, you might decide that it's unlikely you'll ever get a large straight, so you go ahead and put your zero in that spot. Then three turns later, you actually get the large straight. Agony! You can't get credit for it, because there is already a zero in that spot. The best you could do is to put 30 points in the small straight spot.

You can see that you will have to make careful choices each time you get a score. Suppose you had 3 fives and 2 sixes. That's a full house, right? Worth 25 points! But if you put it in the 3 of a kind slot, you get to sum all of the dice and that would be worth 27 points instead of 25 points. Still, you were pretty lucky to get a full house and you might not get it again. If you never get it again, you will be forced to put a zero in your full house spot. So maybe you should forget about the two extra points and go ahead and put that score in the full house spot.

Something special will happen if you get two Yahtzees during a game. Should that unlikely event occur, see the instructions at the bottom of the scorecard.

Should you get Yahtzee more than once in a game, you earn a 100 point bonus, provided that you already have a fifty in your Yahtzee spot from earlier in the game. You also have to put a score somewhere, so first look in the upper half of your scorecard and see if that category is already full. If it is, you can use the extra Yahtzee as a "joker" in the lower half of the scorecard. For example, you can pretend that it's a large straight and give yourself 40 points in the large straight spot. It can be used in any spot, but you are supposed to put it in the upper half . Do you think anybody in the class will get a double Yahtzee some time today?

For homework due Thursday, write a few paragraphs explaining how one chooses what to keep and what to throw back. Is there a single best strategy, or is it a matter of personal preference? Include some discussion of probability computation.