Yatzy

Up to three. The first is always all five dice. After it you may roll any of them again, twice at most. You can stop and write the roll in after any of the three.

Yes, as long as you have a roll left. Keeping a die is not final. Between rolls every die can be moved either way, also the ones that sat out the last roll.

You take a zero. Every turn fills a row, so a roll that scores nothing in any open row still has to go somewhere. Which row to give up is one of the real decisions in the game.

By reaching 63 in the six upper rows. That is three dice of each number, but it does not have to come that way. Four 6s make up for a pair of 3s that never came.

Not on its own. A full house is three of one number and two of another. As a joker it does: a second Yatzy written in the Full house row scores 25.

Yes. Five numbers in a row hold four in a row, so the roll can be written in Small straight for 30 when Large straight is taken.

100 bonus points, plus the row it is written in. The bonus is paid only if the first one scored 50 in the Yatzy row.

About 4.6 percent in a turn spent going for it, or one such turn in 22. That is with all three rolls, keeping the number you have most of each time. In a single roll of five dice it is one in 1,296.

• Three of a kind or better: 21.3 percent.
• A small straight or better: 15.4 percent.
• A full house: 3.9 percent, one roll in 26.
• A large straight: 3.1 percent, one roll in 32.
• Four of a kind or better: 2.0 percent.

These are exact, counted over all 7,776 ways five dice can fall.

Around 250 is what flawless play averages. The exact figure for these rules is 254.59. The weakest level on this page averages about 199 and the strongest about 254, so a total over 250 is a good game whoever plays it.

1,575. It takes five of a kind in all thirteen turns: 375 in the rows and the upper bonus, and twelve bonuses of 100.

No. A roll stands. Undo here puts back the dice you have moved since the last roll, one press at a time. It also takes back a row you have just written in, but only until the computer has rolled.

Hardly. Each side fills its own card, and nothing one side does changes the other side's dice. The side that goes second does know, in its last turn, exactly what it has to beat. On this board you roll first, unless you give the first turn to the computer under Settings.

Mostly luck in one game, and skill over many. Even with flawless play the total swings by about 60 points from one game to the next. The levels on this page show what the decisions add up to: about 55 points a game between the weakest and the strongest, and each level beats the one below it in roughly six games of ten.

No. Every roll comes from the same source, whoever's turn it is, and the computer is never shown a roll before it is on the lid. How the dice are made is further down this page.

The 35 points for the upper section are the easiest points in the game to lose without noticing. The mark to measure against is three dice of each number: 3 in Ones, 6 in Twos, 9 in Threes, 12 in Fours, 15 in Fives and 18 in Sixes.

Keep count of whether you are ahead of that or behind it. Four of a number puts you ahead and two puts you behind, and the high numbers move the sum most.

Early in a game, with most rows open, the dice worth keeping are usually the ones that match. A pair or better feeds several rows at once: the upper row for that number, 3 of a kind, 4 of a kind, the full house and the Yatzy.

Four numbers in a row that are open at both ends, like 2, 3, 4 and 5, become a large straight with a 1 or a 6. That is one chance in three on a roll, and 56 in 100 with two rolls.

Four that can be finished by one number only, like 1, 2, 3 and 4, or 2, 3, 5 and 6 with the 4 missing, have one chance in six on a roll and 31 in 100 with two. The small straight is already made in the first case, so the roll costs nothing. In the second it is all or nothing.

With two pairs on the lid, the fifth die makes a full house one roll in three. With two rolls left it comes 56 times in 100.

Sooner or later a roll fits nowhere. Early on, the cheapest row to give up is Ones: the most it can ever hold is 5, and the bonus count misses it least. Late in a game it is often the Yatzy row, which pays in only one turn in 22 even when all three rolls are spent on it.

A Yatzy is worth more than its 50. With the 50 written in, every later five of a kind pays 100 on top of the row it goes in. A zero in the Yatzy row ends that for the rest of the game.

Chance takes any roll at its full sum. It is worth most as the place for a turn that went wrong with high dice on the lid: a straight that did not come, three of a kind that stayed a pair. Filled early with a middling roll, it is gone when you need it.

All of this is about getting the most points on average. Near the end the other card matters too. Behind with two turns left, a safe 20 does not help: play for the row that can still catch up. Ahead, take the points that are certain.

The Hint button shows what the computer would do at full strength with the dice on the lid: which of them to keep, or which row to write the roll in. It plays for the highest total it can expect and does not look at the other card, so at the end of a close game your own judgment may be the better one.

Each side fills its own card, so for one player the game can be worked out exactly: for every state a scorecard can be in, what the final total will be on average with perfect play from there. For these rules that average is about 254.59 points, counted from an empty card.

The engine makes the same kind of calculation. With a roll on the lid it goes through every way of keeping dice and every row the roll could be written in, and works out what each is worth by the end of the game. The top level counts four of its own turns in full, the one in progress included, and estimates the rows that are left after them. Once no more than seven rows are left open, it plays the rest of the game exactly.

Measured on 600 scorecards, the top level gives up 0.38 points a game against perfect play.

The computer plays its own card. It does not look at yours, so it does not gamble when it is behind or play safe when it is ahead.

All of it happens on your own device, in your browser.

Keeps the dice of the number it has most of and rolls the rest, takes a full house or a straight when one turns up, and writes the roll in wherever it scores most right now. It averages about 199 points a game.

Works out the odds on the dice exactly, but only for the points of the turn in progress. It spends good rows on middling rolls and never thinks about the bonus. About 218 points a game.

Knows that a row can be worth more later, but counts that at less than half of what it is really worth, and leaves the upper bonus out of the calculation. About 229.

Counts almost in full what the open rows are worth later, but still leaves the bonus out, and reaches it in only one game in six. About 241.

Plays for the highest total it can expect, the bonus included. About 254 points a game.

Each level has played the one below it: 4,000 games for each step, and 1,000 for the top one.

• Easy against Beginner: 67.2 percent.
• Medium against Easy: 58.9 percent.
• Hard against Medium: 58.7 percent.
• Expert against Hard: 57.6 percent.

The steps are small because the dice decide so much. A dozen points a game is a large edge in a game whose total swings by about 60, and the best play still fails to beat the level below it in more than four games of ten.

The Hint button asks the engine at Expert's strength. It is the choice with the highest total to expect at the end of the game: which dice to keep, or which row to fill.

When a game starts, the page draws one random number. Every roll in that game is worked out from that number and the number of the roll: the first roll of the game, the second, and so on, whoever makes it. The code that makes the roll does not know which side it is for.

The computer is handed the scorecards and the dice that are on the lid, and nothing else. It never sees a roll that has not been thrown yet, its own included. A roll is never taken back either, so there is no way to fish for a better one.

On 9 October 2026 the generator was run for 2 million rolls of five dice, 10 million dice in all. Each of the six faces came up between 16.65 and 16.68 percent of the time, where a perfect die gives 16.67. The average die showed 3.500 on odd-numbered rolls and 3.500 on even-numbered ones. Five of a kind in a single roll came up 1,515 times, where fair dice give 1,543 on average.

The rolls you remember are the ones that cost you something. A straight that needs one exact number misses with two rolls 69 times in 100, and it feels like bad luck every time. The three 6s that came on the first roll of the turn before felt like good play.

Rare things also happen in a long game. Each side rolls up to 39 times, and the computer will now and then get a Yatzy at the moment you least want it to. It gets them at the same rate you do.