Yahtzee: What You Need to Know to Get the Highest Score

People keep asking, what’s the perfect score in Yahtzee.

Well, this isn’t easy to answer. Firstly, Yahtzee has so many variations that coming up with just one “perfect score” will not answer the question. Second, there are many probabilities that non-mathematicians, like most of us, will find it difficult to understand how to arrive at the outcome.

Yahtzee is a classic board game with a new look involves rolling five dice to produce specific number combinations. You roll the dice throughout each round to get a favorable mix of numbers; different combinations result in various points. Yahtzee is primarily a game of chance, but the strategy may make a significant impact.

The basis for this is that each combination can only be scored once, and the total number of combinations that may be achieved is equal to the total number of turns in the game. As a result, you must be strategic about when to score in each combo and cautious about the pairings you look for at each round. 

Assumptions

So instead of telling you the direct answer, let’s see the possible top score you can get when you play each variation of Yahtzee. Afterall, this game is supposed to improve your math and thinking skills. 

We will presume that the player is intelligent, makes the best re-roll, and holds decisions at every crucial point.

It is simple to determine the likelihood of rolling a Yahtzee in a successful roll. There are five dice. Thus, there is a 1/6 probability that the second dice will produce the same number as the first. If it happens, there is a 1/6 likelihood that the third, fourth and fifth will also be the same.

Thus, in a single role, the probability is 1/6 x 1/6 x 1/6 x 1/6 = 1/1296.

Moving on, starting with three rolls, counting becomes more challenging. We may adjust how many dice we roll each turn, and there are numerous variations. From this stage, you can use tools like the Markov Chain to help you predict the probability for each roll.

Simple Math Explanation

The highest score possible in any Yahtzee is 1535 points. This point calls for the player to toss a Yahtzee (5 of a kind), with more than 1/2 being all sixes on each toss. The highest possible score in Electronic Yahtzee would be 999. The score display can only show three numbers, but the microchip knows the exact score. Additionally, the Yahtzees will continue to tally up internally even though the game markers (hash marks underneath the word “Yahtzee”) show 4 Yahtzees more than the original.

The microprocessor would know that the actual score is 1535 even if the screen would indicate 535 and 4 hash marks if someone maxed out their score. Our information places the highest score at between 875 and 900. Only if they begin with a Yahtzee on their first turn would the players with scores in that bracket continue a game. They click “New Game” and start over if they do not score a Yahtzee on their initial round.

Crazy, But Possible Explanation

The likelihood of throwing a Yahtzee in one three-roll turn is 4.6209%.  Suppose a roll takes five seconds to complete. Therefore, after the first roll, you have five seconds to study the dice before collecting them. Five more seconds are added for each successive roll.

Consequently, you toss the first shaker. 21 rounds with three rolls each, all fail.  The 22nd, though, Yahtzee. 324.612 seconds are equivalent to 21.640805 turns multiplied by 3 rolls every turn and 5 seconds per roll. It takes a little about 5.5 minutes to get a Yahtzee. All is well so far.

It’s time to attempt the second consecutive Yahtzee. Unsuccessful. So, you begin a brand-new game. You repeat the 1 in 21.640805 probability until you hit another Yahtzee, but this time on the 21st turn. It’s time to attempt a second straight round. Failed.

This method must be repeated over 21 times to roll two Yahtzee’s consecutively. 1/(0.046209)2 = 1 in 468.32444. For the first 468 rounds, you either catch a flip or get excited after receiving a Yahtzee just to come up empty-handed. It will tease you by giving you one Yahtzee and then, on the next roll, a 1-1-1-1-2 or one of many other versions of that.

You continue; I think you can already imagine how agonizing this will become after getting 12 consecutive Yahtzees (millions of years later, we’ll come to it). Now, you get four 2s and a card on its side; if you’re lucky, you’ll get a tip, a 3!

The calculation is relatively straightforward: 1/ (0.046209)13 =… Your first 13 turns have a 0.000000000000000043797% probability of doing this. A probability of 1 in precisely 481 numbers following the decimal point (out of 228,325,589,819,893,405).

How long would it require you to do that, then? The product of 228,325,589,819,893,40 spins x 3 rolls per turn x 5 seconds each roll is:

3,424, 883,847,298, 401, 075 seconds, or 108,602,354,366 years, 141 days, 11 hours, 51 minutes. Interesting fact: If you keep all the decimals and fractions, this computation comes out to exactly 15 seconds (which it should since you are rolling every 5 seconds).

You would have to play Yahtzee for 2,117,513,853 generations before someone rolled the perfect game. So don’t mind the perfect score; you’ll not going to get it anyway. Just keep the fun in being at home with friends!