Scoring at least 18 with a shot at scoring 24 in SIXES is one of the keys to getting a high score.ī. The fact that “f: Keep 6” scores the lowest seems to show the importance of targeting the SIXES when your first roll has at least two 6s. Although it probably depends upon what is needed on top to get a total of 63 or higher. I suspect the ranking of these options would be flipped if this roll occurred late in the game, because Full House is so hard to get points for when you target it, rather than get it accidently. Keep all and score 25 in Full House: 253.91 +/- 57 These results are from the Verhoeff paper on Optimal Yahtzee Strategies.ī. The problem comes when you are rolling for Yahtzee or 4oak and you get say, two 6s on the first roll, but the second roll is three 4's, then you switch to fours. whenever you have one 6 you will roll four dice and the outcome probabilities for one, two, three, four, five 6's are always the same when you start a roll with 2 sixes you will roll 4 dice and there will be another set of transiotion probabilities for two, three, four and five dice, etc. Parts of the problem involving the three rolls in a given round can be addressed by Markhov chains e.g., pursuing 6's, i.e. I suspect once you get going (programming wise) it's a matter of cranking a very big handle. Then like BJ look at where you're at and where you might land up and work out the EVs (or expected score). So I guess at N options to go you look at the and which dice to keep. Also I noticed that One thru Sixes are always going to be X thru 6X, since it's just a matter of how many of "what you want" you get multiplied by the value. ![]() I can see the recursive approach, similar to how to do BJ. (I never said these would be simple problems.)Īny general comments on the Yahtzee Strategy problem are welcome as well! keep the three 3s and reroll hoping to roll more 3s ![]() keep the two 6s and reroll hoping to roll more 6s Including the 35 point bonus as appropriate, what is the EV in points for the last three rounds if you decide to : ![]() You need 27 points between the "THREES" and "SIXES" to make the 35 point bonus for the top categories. You need to fill "THREES", "SIXES" and "FULL HOUSE". Do you hold one dice and roll four dice? Or do you reroll all five dice? What is the strategy for the third roll? What is the expected probability of making a LONG STRAIGHT with this initial roll? Your initial roll, unluckily enough, is a Yahtzee: 11111. Problem #2 There is only one round left, and you need to fill the LONG STRAIGHT line with either 65432 or 54321. What is the probability of being successful? Problem #1: There is only one round left, and you need to fill the FULL HOUSE line. Here are some problems to get us started: To get us started, here is some information I've calculated on what occurs on the initial roll of 5 dice. And, if nothing else, we can pose some interesting problems for the math geeks on this forum to analyze. So, I am starting this thread because this is the best damn forum to take some bites out of the Yahtzee strategy problem. There are lots of websites with general strategy principles/rules but some of the strategy decisions when you have only a few rolls left still seem to be relatively unanalyzed. There are so many possible situations in Yahtzee, that I don't think anyone has ever calculated optimum strategy for the entire game. The tension in Yahtzee game strategy arises from the need to make decisions about which objective to pursue after seeing the outcome of the 1st and 2nd rolls in any given round. You are trying to maximize the number of points you achieve at the end of all 13 rolls. In each round you make an initial roll, hold 0 to 5 dice and roll the remainder, then hold 0-5 dice and and proceed with the final roll. You have 13 rounds of rolling dice to make 13 objectives which are awarded with different number of points. ![]() I think everyone knows how to play Yahtzee (please google the rules if you don't).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |