Yahtzee Strategy and Odds
Most players lose Yahtzee games they could have won, and they rarely lose them on the dice. They lose them on the decision of where to write the score. The dice are the same for everyone over a long enough run; the choices are not.
Here is what the odds actually are, and what to do with them.
The odds, measured
The table below comes from simulating two million turns per combination. In each one the target is chosen on the first roll, the useful dice are kept, and the rest are rerolled twice.
| Combination | First roll | Within three rolls |
|---|---|---|
| Three of a kind | 21.3 % | 74.3 % |
| Small straight | 15.5 % | 56.9 % |
| Full house | 3.9 % | 35.9 % |
| Four of a kind | 2.0 % | 29.1 % |
| Large straight | 3.1 % | 19.2 % |
| Yahtzee | 0.08 % | 4.6 % |
Two numbers are worth sitting with.
A Yahtzee comes once every twenty-two turns or so when you chase it. Over a thirteen-turn game you will see roughly one every other game. Playing as though it is coming is the fastest way to wreck a score sheet.
A small straight, on the other hand, lands more than half the time. It is the most reliable 30 points on the sheet, and it is badly underused by beginners who keep a pair instead.
These figures assume you commit to one target. Real turns are messier: you often hold something that could still become two different things, which is exactly where the game gets interesting.
The 63-point bonus decides most games
Thirty-five points is a lot. It is more than a large straight, and nearly as much as a Yahtzee. Games between evenly matched players are usually decided by who got the bonus, not by who rolled better.
The target is three of a kind in every upper box. Track it as a running balance rather than box by box: every die above three is credit, every die below is debt.
Four sixes puts you six points up. Two fives puts you five points down. As long as your balance stays positive, the bonus is on track, and you can afford to write two ones in the Aces box without panicking.
This changes what you keep. Early in a game, three fives are usually worth more than a possible full house, because they carry the bonus. Late in a game, once the bonus is out of reach, those same three fives are worth only their fifteen points and you should be looking elsewhere.
The corollary: give up on the bonus as soon as the arithmetic says it is gone. Players who chase it to the last turn end up with a sheet full of small upper scores and nothing in the lower section.
Which dice to keep
Two pairs, and you need a full house. Keep both pairs and roll one die. You have a one in three chance of pairing it up.
Three of a kind, early in the game. If it is fives or sixes, bank it in the upper section. Under that, roll the other two: you are chasing the four of a kind and the Yahtzee at once.
Four to a straight. Always keep them. One die, one open end for a small straight, and 30 points more than half the time.
A large straight is open at both ends. 2-3-4-5 can become either straight. 1-2-3-4 can only become one. Same four dice, twice the chance, and it should change what you keep.
Nothing at all. Roll all five again. Keeping a single six because it is a six is the most common wasted roll in the game.
Where to write a bad turn
Every game has two or three turns that produce nothing. Deciding where the damage goes is a skill in itself.
Aces is the cheapest zero on the sheet. It costs at most five points, and if the bonus is already lost, it costs nothing at all.
Yahtzee is the most expensive, and not only for the 50 points. Zero in that box also kills every 100-point bonus for the rest of the game. Write it there only when the game is nearly over and nothing else is free.
Chance should be kept as long as you can bear it. It absorbs any turn without penalty, which makes it the safety net for the ugly rolls that always come. Spending it on turn two to bank 22 points is a trade you will regret around turn ten.
Playing against other people
Against opponents, the arithmetic shifts. Playing to maximise your average is right when you are alone with a score sheet. At a table it is not.
If you are behind late in the game, take the low-percentage shot. Chasing a Yahtzee at 4.6 % is a bad play in isolation and the correct one when the safe line loses anyway.
If you are ahead, do the opposite. Fill the reliable boxes, protect the bonus, and let the player behind take the risks. Their 4.6 % will usually fail, and that is your win.
In duplicate games everyone gets identical rolls, so none of this is about luck at all. Your score against the table is purely a measure of your decisions, which is why the format tends to attract the players who take the game seriously. Duplicate tables, along with Yahtzee 6 and the scheduled tournaments, run on Ludicash, the platform behind the game on this site.
The mistakes that cost the most
Chasing the Yahtzee. It arrives once every two games, and the turns spent hunting it are turns not spent on the bonus.
Spending Chance early. It is the only box that never fails you. Keep it for the turn that does.
Ignoring the upper section balance. The bonus is worth 35 points and most players never work out whether they are still on track for it.
Keeping a lone high die. A single six is not progress. Roll all five.
Writing zero in Yahtzee too early. It forfeits the 50 and every 100-point bonus that might have followed.
Once the odds are familiar, the rest is repetition. The rules page has the full score sheet if you need to check a box, and the table is always open.