Rolling Fives

For much of the first week of June, the wife and I were on our first camping trip of the season. It was a nice trip, regardless of all rain, but at least for a couple days the rain was either in evening/night, or night/morning. During rain events we are in the screen tent or the camper. We read, and play some games to pass the time. One game we often play is Yahtzee. Yahtzee involves rolling dice and choosing what you wish your role to count toward. My wife is a Yahtzee master.

The second Yahtzee game we played, my wife seemed to roll the same combination of numbers on the dice, which included two fives. She took her fives and a few other categories. She then started to complain when she once again shook two fives, and as she is shaking three other dice, having once set aside two fives, she shakes three fives giving her Yahtzee. It sure shut her complaining up quick.  I said "What were you going to say about always shaking fives?" I think the world's smallest violins played as she shook her Yahtzee of fives after having complained about getting only fives, and until that last shake, about to complain again.

 In Yahtzee you get three rolls of the dice, or die, to get a desired requisite combination. Showing that statistics is about as scientific as medicine, a search on the internet turned up varied probabilities of shaking Yahtzee on first, second and third try. It seems that most of the sources I quickly examined had the probability at .08% on one try, 1.23% on the second, and 3.43% on the third try. Since, they are all independent of one another, they are added up which yields a 4.64% probability of shaking Yahtzee in one turn. I have to think the odds are worse, because I cannot recall the last time I got a Yahtzee.

Even as she complained about shaking fives, she tends to master Yahtzee. Although, as this game showed, getting a Yahtzee does not guarantee a win. For, in the end, I won the game by an unlike Tom masterful performance on the top where I garnered more points than necessary to win the top and earn bonus points. It may have been the first time in years I won the top. Even though on the bottom I had two big 0's, to Yahtzee Girl's one 0, the bonus points were sufficient for me to earn a rare victory. My ability to win at Yahtzee is lower than the probability of throwing a Yahtzee. One should get a Yahtzee in every 21 or 22 turns, but if that was the case, one should earn a Yahtzee every two games. The Yahtzee card has thirteen categories, six on the top, and seven on the bottom (including Yahtzee). Meaning a person gets thirteen turns a game. If you take a zero on Yahtzee and then get a Yahtzee, you are out of luck you are stuck with a zero if on  later roll you rolled five of the same number. I suppose there is a rare instance where this happens. 

I always thought Yahtzee was a game of chance, but after this game, I realized there is some skill in deciding where on the score card to place your throw of the dice. During the game in which Yahtzee Girl got that Yahtzee with fives, I had a high throw of four of a kind, which I took on the top, rather than in the lower half of the score sheet under four-of-a-kind. On the top, you need three of each kind of die number, from one to six to "make" the top. Yet, an extra four helps, as it can, for example, make up for the loss of two two's (total four) if I only got one two to place on the twos. That critical decision, recommended by Yahtzee Girl, helped me make the top and thereby earn the 35 bonus points, for a rare probability of besting Yahtzee Girl in a game. 

Yahtzee is still primarily, I believe, a game of luck and chance, but those critical decisions as to where to place your score can make a difference. A survey of US residents by Statista in 2020 (I have to register to get additional information such as number of respondents) showed that 49% of those surveyed believe Yahtzee is a game of luck compared to 22% as a game of skill. The difference is divided among people that did not know, or thought it no applicable. 

Yahtzee Girl may have rolled five fives, but doing so failed to allow her to win yet another game of Yahtzee. Since, she beats me so often, I have to go with the 49% who think it is a game of luck. Who knows what will occur the next time we play, perhaps I will roll a series of fives for Yahtzee.