× The Brains Behind the Game: How Optimal Yahtzee Works

The Optimal Score Analysis isn't just a set of tips; it's powered by a complete mathematical solution to the game of Yahtzee. The solution was calculated by researcher Tom Verhoeff as part of his Optimal Yahtzee Strategy project. By following this perfect strategy, a player can expect to achieve an average score of 254.59 points per game.

Solving a game of chance is done with a technique called dynamic programming. Think of it like solving a giant puzzle by working backward from the end. Instead of trying to figure out the best move from the very first roll, the program calculates the best move for every possible situation on the last turn of the game. It then uses those results to solve for the second-to-last turn, and so on, all the way back to the beginning.

To do this, the program first had to define every possible game state. A game state is a unique snapshot of the game, which can be described by three key pieces of information:

The set of open scoring categories remaining.

The player's score in the Upper Section.

Whether a Yahtzee has already been scored (which affects the value of future Yahtzees).

Analyzing all combinations of these factors results in over 33.5 million unique game states that had to be solved.

The result of this massive computation is the Game State Table (GST). This table is the "brain" of the optimal strategy. For every one of those 33.5 million game states, the GST stores a single, crucial number: the Expected Value (EV). This is the average additional score a player can expect to earn from that point until the end of the game, assuming they play perfectly every turn.

Our game's analysis engine is a digital version of this very Game State Table.

The in-game analysis feature is your direct window into this powerful strategic data. When you ask for an analysis, our game's engine takes your current game state, looks up the relevant data in the GST, and presents it to you in a helpful way.

Turn Probabilities: For immediate, tactical odds of your current turn (like the chance of rolling a Full House on your next roll), the engine uses a comprehensive probability model that contains the precise odds for every possible dice roll outcome.

Dice Analysis: The Keeper Analysis helps you decide which dice to keep when you still have rolls left in your turn. To find the best move, the game's engine consults the Game State Table for every possible combination of keepers, presenting you with the option that leads to the highest average final score.

The Optimal Score Analysis turns a complex mathematical problem into a simple, actionable guide, allowing you to learn and apply the perfect Yahtzee strategy on every single turn.

The In-Game Analysis and the Optimal Yahtzee Strategy that drives it form a powerful guide, but it's important to understand what it's designed to do.

The Goal is the Best Average Score: The strategy aims to maximize your average score over thousands of games. It is not designed to help you break your personal high score in a single game or to beat a specific opponent, as those goals would require different, often higher-risk, strategies.

Expected vs. Actual Score: Because Yahtzee involves random dice rolls, the analysis provides a projected or expected score, not a guarantee. In any single game, your luck can lead to a much different result. For instance, in one million computer-simulated games using this perfect strategy, final scores ranged from as low as 73 to as high as 845!

Optimal Play is Assumed: The projected scores are based on the assumption that you will continue to make the mathematically optimal choice for the entire rest of the game. If you choose a different move, the projected outcome will change.