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Amateur mathematician crunches the numbers in gigantic Yahtzee data sample

You don’t have to be an accountant or mathematician to find numbers extremely sexy, the way the two looks like a woman’s head in profile and a seven looks like the profile of an excited man from waist down in the number 27, some numbers can be so sexy they should only be sold in adult stores. The only way the number 27 could possibly get more sexy is if it was drawn as suggested and placed next to a 27 filled in the 4 of a Kind Total of all Dice field on a Yahtzee score pad (both drawings have been provided below for your crude, depraved sexual pleasure), which would mean you might have rolled four 6s and a 3. Every Yahtzee fan knows the secret value of rolling a six, it’s six points and therefore the highest number you can roll on a six sided dice which means it’s also cause for mild celebration when one is rolled.


If you don’t know what a Yahtzee is – it’s a game consisting of 5 dice, a cup, strategy and luck – or the rules then you can read them here. If you’re reading this post because you were drawn to it because it’s about Yahtzee then you probably don’t want to waste anymore time getting to the point.

The point is, we here at The Packed Vacuum have been so busy compiling the largest Yahtzee scorecard record this cosmos has ever seen we haven’t had time to post anything since the last post whenever that was, I don’t know, I can only see dice.

My fiancee, DD, and I, PT, have just completed a mammoth Yahtzee tournament against each other. The tournament consisted of six rounds of Yahtzee. Each round consisted of six scorecards each. And as everyone knows, each scorecard has six games on it. Yep, we danced with the numerical devil so let’s make like the devil with the charred torso of a sinner and get crunching!


It took us roughly one hour to complete one scorecard of Yahtzee each, this hour includes the compulsory mid-scorecard cigarette, beer, tea, food, change the music, toilet break between games three and four. One hour per scorecard multiplied by six scorecards per round then multiplied by six rounds equals 36 hours. We spent 36 hours each, together, to complete the 36 Yahtzee scorecards in the tournament, which is like, what, a day and a half of pure Yahtzee bliss. Obviously we didn’t play it that way but you know what I mean.

Yahtzee cup


As mentioned, each scorecard has six games on it. So, in that 36 hours we completed 216 games of Yahtzee, each. Each game has 13 fields that need to be completed and to complete those fields we rolled the dice a maximum of three times or a minimum of one time, because, you know, you can’t do anything in Yahtzee without the dice. Or cup. It’s illegal to roll the dice in our house with your hands. So, if we rolled the dice the minimum amount, which is once, every time, 13 times per game for all 216 games we would have rolled the dice 2,808 times, each, in those 36 hours. If we rolled the dice twice per field, 13 times per game for all 216 games we would have rolled the dice 5,616 times, each, OR, if we rolled the dice the maximum amount, which is three times, every time for the 13 fields per game for the 216 games we could have rolled the dice a total of 8,424 times, each, in those 36 hours. The average roll per field, roughly, is 2.7 times, so we roughly rolled the dice 7,581.6 times, each, over the 36 hours. I probably haven’t used my wrist so vigorously in such a short amount of time since I discovered free porn on the lingerie pages in department store catalogues when I was thirteen years old.


Since the tournament meant my fiancee and I were battling it out on the kitchen table with dice what it really comes down to is the scores. After 216 games of Yahtzee each, DD had amassed a grand total of 49,566 points from rolling dice. I had amassed a grand total of 51,372 points. The difference between the two scores was a poultry 1,806 points which averages out to only 8.3611 points per game which could easily have been made up in the 3 of a Kind or 4 of a Kind fields, or more Full Houses scored along the way. DD averaged 229.47 per game while I averaged 237.83 per game. Those scores, according to the internet, are pretty average.

Yahtzee scorecards


The strategic rules of Yahtzee aren’t written in the game’s instructions but come with years of practice and observation.

The first rule: don’t go chasing the small straight, large straight or full house. By chasing I mean don’t set out to roll those, they pretty much always seem to magically appear. Full Houses can be rolled straight up multiple times per game but since it’s always preferable to put all 3 of a kinds in the top section to secure the bonus 35 points the poor old full house slot is left empty. This strategy means statistically, DD’s 71% and my 76% full house strike rate doesn’t reflect the true amount of full houses rolled.

When it comes to the small straight (we played the rule where a sequence of four dice are required for small straight and a sequence of five for large straight) there really is no issue with rolling that unless you straight up roll a large straight first then leave the small straight for last and somehow don’t roll it. Like all rules there are exceptions, in the case of chasing a large straight, it’s best to do so after on your first roll you roll 2, 3, 4, 5 and another number that isn’t 1 or 6. That way the odds of rolling the missing number in the sequence (1 or 6) has risen to 1/3 as opposed to 1/6 if you were trying to finish off a large straight with 1, 2, 3, 4 which means you’d have to roll a 5 and 5 only to complete the sequence.

In the top section of the scorecard there’s a free 35 points to be had if you manage to score 63 points or more. To score 63 points you must complete each of the six fields in the top section with 3 of a kinds. This is where the issue with where to score 3 and 4 of a kinds. Strategically, if you can score 3 and 4 of a kinds in the top section (preferably 4s, 5s and 6s) early in the game then you’re better placed later in the game to complete the bottom section and if you’re ahead of the minimum scoring rate to achieve the 63 minimum any unused fields in the top section can become “free rolls” which means worst case scenario is you have to score a 0 in the 1 or 2 field but you’ll still achieve the 63 score which will earn you the 35 bonus points.

But herein lies the problem, it’s tempting to place a 1 in the ones section at the beginning of the game if the game begins poorly then move on to absorb the two point deficit later in the game with a 4 of a kind of anything else, but the pressure to do so can mount if 4 of a kinds are hard to come by.

Yahtzee box


Nothing else matters when it comes to rolling a Yahtzee straight up on the first roll, however. Scoring a Yahtzee is the best thing ever, it’s like hurling the winning three-pointer from the other end of the basketball court right on the buzzer, it’s like scoring the last home run in the baseball thingo, like scoring a six off the last ball when you’re team is 5 runs down in a test match that will decide not only the trophy but world rankings, it’s like being blown so well that you’re mind leaves your body and you meet god and he gives you a big thumbs up, that’s what it’s like, but, like, even better. For the new comers, rolling a Yahtzee is rolling 5 of a kind, whether it be straight up which is super rare or building a Yahtzee across the three rolls in the turn. All Yahtzees are as satisfying as each other but some are in fact more satisfying than others.

There’s no real strategy to rolling a Yahtzee, it’s just like giving oral sex, you know what you need to do, you feel it, you have an idea as to what you want the outcome to be so you just dive in and go for it. Conversely, unlike oral sex, the Yahtzees have been documented and quantified throughout the tournament. DD rolled 82 Yahtzees across her 216 games which equates to a 38% Yahtzee strike rate. I scored 88 Yahtzees which gave me a 42% strike rate. DD and I both rolled an extra 15 Yahtzees, or bonus Yahztess, throughout the tournament after already scoring a Yahtzee in a game, with one game each across the tournament where we rolled a Yahtzee plus two bonus Yahtzees. We both rolled an extra two Yahtzees on top of the already mentioned that weren’t scored as a Yahtzee nor a bonus Yahtzee. So the true total amount of Yahtzees rolled for DD is 99 and for myself is 105. Which really raises the strike rate for DD to 45% and for myself 48%. The thing with bonus Yahtzees is that they can only be scored after you’ve scored a Yahtzee which makes the chance of scoring a second Yahtzee extremely low, we both ended with a 7% strike rate when it came to rolling a second Yahtzee, which to be honest isn’t a true reflection of the percentage since the 7% is calculated across every game, not just the games in which Yahtzees were scored. That kinds of number crunching is for intermediate mathematicians at worst. Having added that, some, if not all of the data is probably wrong.

I probably should have mentioned at the beginning that a slight degree of knowledge and experience in Yahtzee would help in understanding this number crunch. Oh, and below you can download the super-radical excel spreadsheet to enjoy and play with yourself by clicking the Yahztee Score Cards link below, just don’t hurt your wrists like a 13 year old boy trying to replicate our tournaments. If you check out the spreadsheet let us here at The Packed Vacuum how much we failed with our maths. Also, since writing this we completed a mini tournament with one round of Yahtzee consisting of six scorecards each and the stats have been added to the spreadsheet. Up until this point, we didn’t use the extra Yahtzee as a joker rule, rather, we took the 100 bonus points as the turn which then gave us another turn in the game.

Yahtzee score cards


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