Play Centennial Online

What Is Centennial?

Centennial is a race played with three dice and a strip of twelve numbered squares. You start off the board needing a 1. Each turn you throw all three dice once and use them to count upward: 1, then 2, then 3, all the way to 12, and then back down 11, 10, 9 to 1 again. Every needed number can be made from a single die, the sum of two dice or the sum of all three, and a good throw carries you several squares in one go. Any number you cannot use is up for grabs: if the dice you leave behind make the number an opponent is waiting for, they take it. The first player to complete the twenty-three-step round trip wins.

The game is also known as Martinetti and Ohio, and it has the same bones as the two-dice children’s game Round the Clock, but three dice change everything: a throw has seven combinations rather than three, chains of up to seven consecutive numbers appear from nowhere, and the stealing rule keeps you in the action on your opponent’s turn. This guide covers the rules, works through real throws, counts every combination over all 216 possible throws, and explains exactly how the version on this page plays.

A Short History of Centennial

Centennial is a counting race of the kind found in most twentieth-century dice compendiums, and like Chicago it has no documented inventor. The claim you will meet most often online is that the game was played by Roman soldiers to pass the time. That story traces back to games writer Dan Glimne, who is quoted on the game’s BoardGameGeek entry as saying it is reputed to date to Roman times. No ancient rule text describing a 1-to-12-and-back race has survived, so treat the Roman origin as folklore rather than fact.

The three names are more revealing than the legend. Martinetti is an Italian surname and is the name on modern commercial sets, including magnetic and travel versions aimed at families. Ohio is the label used in several American family-game descriptions. Centennial is the name preferred by rule sites such as dice-play, and it is tempting to connect it with the United States centennial of 1876, but no dated source has been found and that connection is speculation. What can be said with confidence is that by the late twentieth century the game was in print under all three names, with rules differing only in details such as whether a successful throw earns another throw.

Centennial Rules

Equipment

• Three six-sided dice
• A board with twelve squares numbered 1 to 12 in a row; a strip of paper works perfectly well
• One marker per player: a coin, a counter, or an initial in pencil
• Two or more players; the version on this page is you against the computer

Object of the Game

Move your marker onto square 1, up the strip to 12, and back down to 1, one number at a time in strict sequence, before anyone else does: 23 steps, twelve up and eleven down.

How a Turn Works

1. Throw all three dice once. Your turn ends after a single throw. (Some house rules award an extra throw after a successful move; the game on this page does not.)
2. Make your needed number. Count the value of any single die, the sum of any two dice, or the sum of all three. Needing a 3, a throw of 2-1-6 gives you 3 from 2 + 1; needing a 9, the same throw gives 9 from 2 + 1 + 6.
3. Keep going within the same throw. Once you have made your number, look for the next one. A throw of 4-4-1 when you need 8 gives 8 from 4 + 4 and then 9 from 4 + 4 + 1.
4. Each combination may be used once. Under the common rule, the seven combinations of a throw are the three single dice, the three pairs and the triple. A die can therefore appear in more than one combination: with 1-2-4 you can count 1, 2, 3 (1 + 2), 4, 5 (1 + 4), 6 (2 + 4) and 7 (1 + 2 + 4). Under the strict rule, each die may be counted only once, so the same 1-2-4 gives just 1 and 2.
5. Turn at the top. After 12 the sequence continues 11, 10, 9 and so on down to 1. A throw can carry you over the peak: needing 11, a 6-6-5 gives 11 from 6 + 5, 12 from 6 + 6 and 11 again from the other 6 + 5.
6. Leftovers can be stolen. When you have taken everything you can, any unused combination that makes an opponent’s needed number is theirs, and they advance one step at once. The same applies to you on their throws.
7. First home wins. The first player to count the final 1 wins, whether by their own throw or by a steal.

Which Throws Make Each Number

Every way to make each number from three dice, and how many of the 216 possible throws contain at least one of them.

Worked Examples

• Opening throw 1-2-4, needing 1. Count 1 from the 1, 2 from the 2, 3 from 1 + 2, 4 from the 4, 5 from 1 + 4, 6 from 2 + 4 and 7 from 1 + 2 + 4. Seven steps, every combination used, nothing left to steal. Under the strict rule the same throw gives 1 and 2 and stops, because the 1 and 2 are spent and the 4 cannot make a 3.
• Opening throw 1-1-1, needing 1, opponent needing 2. You count 1 from one die, 2 from a pair, 3 from all three. But a throw has three pairs, and the unused 1 + 1 makes the 2 your opponent needs, so they take it. Under the combination rule identical dice still form distinct pairs; under the strict rule all three dice are spent and nothing is stolen.
• 6-6-5 needing 11 on the way up. 11 from 6 + 5, 12 from 6 + 6, and 11 on the way down from the other 6 + 5. You have turned the corner in one throw. Only 6-6-5 (3 throws in 216) does this; 6-6-6 gives 12 from a pair but no 11.
• 2-2-5 needing 4, opponent needing 9. You take 4 from 2 + 2 and 5 from the single 5. The triple 2 + 2 + 5 = 9 remains, so your opponent moves from 9 to 10 on your turn. No reading of the throw avoids this, and your two steps are worth more than the one you give away.
• 3-3-5 needing 12, opponent needing 11. Nothing makes 12, so you stand still, and the triple 3 + 3 + 5 = 11 is stolen. This is the classic Centennial misery: stuck at the top while feeding the player behind you.

The Odds Over 216 Throws

Three dice produce 6 × 6 × 6 = 216 equally likely ordered throws, and the table above counts how many of them contain a usable single, pair or triple for each number. Four things stand out.

The curve is lopsided. Every number from 1 to 6 can be made by a single die, and a given face appears in 91 of the 216 throws (42.1%). Sums pile on top: the 6 can be a single 6, three pairs or three triples, making it the easiest number at 75.0%. At 7 the single die vanishes and the chance drops to 48.6%. From there it slides to the 12, which needs 6 + 6 or one of six three-dice patterns and arrives only 19.0% of the time.

The peak is the whole game. Because the sequence goes up to 12 and back, you must pass through 11, 12 and 11 in a row, three consecutive steps with success chances of 26.4%, 19.0% and 26.4%. Getting from “need 11” on the way up to “need 10” on the way down costs about 11 throws on average, more than the climb from 1 to needing 9, which takes about 8. A solo player under the combination rule needs about 34 throws for the whole 23-step trip: roughly 12 to reach the 11 on the way up, 11 to get over the top, and 15 for the run from 10 down to the final 1. Under the strict rule the trip takes about 49 throws.

Long chains are rare. From the starting line, 125 of 216 throws (57.9%) contain no 1 and gain nothing. Of the remaining 91, 48 gain one step, 9 gain two, 13 gain three, 3 gain four, 6 gain five, 6 gain six (1-2-3 in any order) and 6 gain seven (1-2-4). Under the strict rule the same 91 throws split into 60 one-step, 25 two-step and 6 three-step throws, so the strict game takes half as long again.

Steals depend on who needs what. A steal comes from whatever you could not use, so it is most likely when your opponent needs an easy number and you need a hard one. Stuck on 12 while your opponent needs a 6, 162 of your 216 throws (75.0%) hand them a step. If both of you need a 12, only 6-6-6 (1 in 216) lets one player take it with a pair and the other steal it with a different pair; if both need a 1, a steal requires two or more 1s, 16 throws in 216 (7.4%).

Centennial Strategy

On this page there is nothing to decide once the dice land, so the advice below is about reading a throw quickly at a real table, understanding the race, and choosing house rules.

1. Read all seven combinations every time

A throw has three singles, three pairs and one triple. Beginners see the singles, then the total, and miss the pairs. When you need 8 and throw 3-5-2, the 8 is 3 + 5 and the 10 after it is 3 + 5 + 2. List the pairs first: most numbers from 7 to 11 come from them.

2. Chase the chain, then count what is left

At a real table you choose which combination makes your number, and it matters when two readings gain the same steps but leave different leftovers. Needing 6 with a 6-3-3 while your opponent needs 3, take the 6 from 3 + 3: a lone 3 left over is a steal, a lone 6 is not.

3. Never give up a step to avoid a steal

A steal moves your opponent one step; a step you fail to take costs you one. A reading that gains two steps and gives one away therefore beats one that gains a single step and gives nothing. The version on this page follows exactly that logic: maximum steps first, fewest steals as the tie-breaker.

4. Expect to camp at the top

The 11-12-11 stretch is where races are won and lost, and it is mostly luck. If you are stuck there, the player behind you is fed from your throws whenever they need a low number; if you are the one behind, the peak is your chance to catch up.

5. Watch your opponent’s throw as closely as your own

In table play a steal must be claimed before the dice pass on; a missed steal is gone. Know your needed number before your opponent throws and scan their dice for it. The game on this page does this for you; around a real table it is the skill that separates players.

6. Pick the rule that fits the table

The combination rule is faster and produces spectacular seven-step throws; the strict rule is slower, steadier and easier for children to verify, because each die is moved aside once counted. The Each die once toggle on this page switches between them. Either way, keep it moving: like Aces in the Pot, Centennial suffers when anyone stops to think.

Common Mistakes

• Missing a pair. Needing 9 with 4-5-3 and announcing “no 9” because the total is 12. The 4 + 5 was there all along.
• Forgetting the way back. Players reach 12 and keep looking for a 13. After 12 you need 11, and a 6-6-5 can get you there in the same throw.
• Mixing up the two rules. Using a die twice under the strict rule, or refusing to reuse one under the combination rule. Agree the rule before the first throw.
• Letting a steal go by. If you need 4 and your opponent’s throw has a 4 in it, say so before the dice are picked up.
• Stealing more than one step. A steal moves you one number only; only the thrower may chain.

Variants and House Rules

• Strict dice. Each die counted once per throw. Slower and simpler; available here via the Each die once toggle.
• Extra throw. A player who moves at least one step throws again, listed as a variation on dice-play. Not used on this page, where every turn is exactly one throw.
• No stealing. Play the race side by side without claiming leftovers if you prefer a gentler game; you lose the reason to watch every throw.
• One way only. Race up to 12 and stop. That is Round the Clock with three dice; a solo climb takes about 20 throws instead of 34.

For more three-dice speed, Going to Boston resolves a whole turn in three quick throws. For counting games with two dice, Chicago runs eleven rounds numbered 2 through 12 with one throw each, and for a chip race with the same social energy try Left Center Right.

Glossary

• Sequence / Course: The 23 steps 1, 2, … 12, 11, … 1 that each player must complete.
• Needed number: The next number in the sequence for a player; shown as “5 ↑” or “11 ↓” on this page.
• Combination: One of the seven ways to read a throw: three single dice, three pairs, one triple.
• Steal: An opponent taking one step from a combination the thrower did not use.
• Strict rule: Each die may be counted only once per throw (“each die once”).
• Combination rule: Each combination may be used once, so a die may appear in a single and in a pair from the same throw.
• Home: Having counted the final 1 on the way down; the game ends immediately.

Play Centennial Online on Dice.now

The game at the top of this page is a race between you and the computer. Each side’s 23-step course is shown as a strip, 1 up to 12 and 11 back down to 1, with completed squares filled in, the current square marked and squares just gained highlighted. The status bar shows what each side needs (“5 ↑”, “11 ↓”), whose turn it is, and your win-loss record on this device.

On your turn press Roll Three Dice. You get one throw per turn, and the game reads it for you: every consecutive needed number that can be formed from an unused combination is taken automatically, and when several readings are possible it picks the one that gains the most steps and, among those, the one that leaves nothing for the computer to steal. The counted dice light up, and the Last Throw table lists each number taken, the dice it was made from, and who received it. Any unused combination that makes the computer’s needed number is stolen immediately, marked “(steal)” in the table, and the same happens for you on the computer’s throws. A steal is always one step, and it can win the game.

The computer plays by the same automatic rules with no hidden advantage; it simply rolls after a short pause. The Each die once chip switches from the default combination rule to the strict rule; you can toggle it between throws, the change is written to the game log and applies from the next throw. The game log keeps the last 40 events, the end-of-game overlay reports what the loser still needed, and your record is saved only in your browser. Ready to race? Roll three dice.