Crown and Anchor Rules, Symbols and Payout Variations
Crown and Anchor is a traditional three-dice matching game. Each die commonly carries six symbols—crown, anchor, heart, spade, diamond and club—instead of numbered faces. A participant selects a symbol, all three dice are rolled, and the result is determined by how many dice show the selected symbol.
The game is traditional and sometimes gambling-based, but it should not be treated as a universally standardized modern casino product. Payouts and operating rules vary. This guide analyzes one explicit selected-symbol schedule: net payouts of 1:1 for one match, 2:1 for two matches and 3:1 for three matches.
- Responsible editorial role
- Desk research and calculation review
- Research method
- Source-linked desk research and direct probability calculation; no hands-on testing claimed
- Review status
- Ruleset-specific calculation checked; historical claims limited to the cited collection records
- Last modified
On this page
Essential Crown and Anchor and payout terms
- Selected symbol
- The crown, anchor, heart, spade, diamond or club chosen before the roll in the version analyzed here.
- Match
- One die showing the selected symbol. A three-dice roll can contain zero, one, two or three matches.
- Net payout
- The winnings excluding the returned initial stake. A 2:1 net payout on an initial one-unit wager produces two units of net winnings.
- Total return
- The initial stake returned together with the net winnings. For a one-unit wager paying 2:1 net, the total return is three units: two units won plus the original unit.
- Paytable
- The documented schedule of payouts for each winning outcome. A house-edge calculation cannot be transferred to a different paytable without recalculation.
- Ordered outcome
- A result that distinguishes what appears on each die. Three six-faced dice have 6 × 6 × 6 = 216 ordered outcomes.
- Expected value
- The probability-weighted average net result across all possible outcomes. It is a long-run mathematical average, not a prediction for the next roll.
- House edge
- The average expected player loss as a percentage of the specified initial wager. It is not the probability that one round will lose.
Hit rate and house edge describe different things. Hit rate measures how often a wager wins; house edge also accounts for how much each result pays. Continue with the rules and paytable used for this calculation.
Equipment, symbols and rules used in this guide
Museum Wales documents Crown and Anchor equipment consisting of three dice with six traditional symbols:
- Crown
- Anchor
- Heart
- Spade
- Diamond
- Club
Featured analyzed version
Before the roll, the participant selects one symbol. All three dice are rolled, and the number of dice showing that symbol determines the result.
| Selected-symbol matches | Net result | Total return on one initial unit |
|---|---|---|
| No matches | Lose 1 unit | 0 units |
| One match | Win 1 unit at 1:1 net | 2 units |
| Two matches | Win 2 units at 2:1 net | 3 units |
| Three matches | Win 3 units at 3:1 net | 4 units |
Under this paytable, zero matches lose the selected-symbol wager. The quoted returns include the original unit only in the “total return” column.
Other traditions may differ. Changing a payout or adding an exception changes expected value. Do not treat this featured version as an official ruleset for every venue or informal game.
How to play a selected-symbol round
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Select one symbol
Choose crown, anchor, heart, spade, diamond or club before the dice are rolled.
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Record the wager if money is involved
The featured calculation assumes one initial selected-symbol wager. Procedures for accepting or marking wagers are venue-specific and are not part of the probability model.
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Roll all three dice
The three dice are rolled and evaluated together.
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Count the matches
Count how many of the three dice show the selected symbol: zero, one, two or three.
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Apply the stated paytable
In the featured version, zero matches lose; one pays 1:1 net; two pay 2:1 net; and three pay 3:1 net.
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End the round
The selected-symbol wager resolves from that roll. A later roll is a new round.
These are the essential mechanics for the featured version. Equipment handling, betting windows and special exceptions can differ. Verify the local paytable before applying these instructions elsewhere.
Worked example: the selected symbol appears twice
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Initial state
The selected symbol is anchor. An illustrative one-unit wager is used only to make the payout wording clear.
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Roll
The three dice show anchor, anchor and heart.
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Rule applied
Two of the three dice match the selected symbol. Under the featured paytable, two matches pay 2:1 in net winnings.
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Result
The net winnings are two units. The original one-unit stake is also returned, so the total returned is three units.
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Explanation
The heart does not match and adds nothing to the payout. A different paytable could resolve the same two-anchor roll differently.
How often zero, one, two or three matches occur
Each die has six possible symbols, so three dice produce 6 × 6 × 6 = 216 ordered outcomes. For one selected symbol, each die has a 1-in-6 chance of matching and a 5-in-6 chance of not matching.
| Match count | Reproducible count | Outcomes | Probability | Approximate percentage |
|---|---|---|---|---|
| Zero matches | 5 × 5 × 5 | 125 of 216 | 125/216 | 57.87% |
| One match | 3 × 1 × 5 × 5 | 75 of 216 | 75/216 | 34.72% |
| Two matches | 3 × 1 × 1 × 5 | 15 of 216 | 15/216 | 6.94% |
| Three matches | 1 × 1 × 1 | 1 of 216 | 1/216 | 0.46% |
Why the counts work
- Zero matches: every die must show one of the five other symbols, giving 5³ = 125 outcomes.
- One match: choose which of the three dice matches, then give each remaining die one of five nonmatching symbols: 3 × 5² = 75.
- Two matches: choose which one die does not match, then choose one of its five other symbols: 3 × 5 = 15.
- Three matches: all three dice show the selected symbol, producing one ordered outcome.
One or more matches occur in 75 + 15 + 1 = 91 of 216 outcomes, approximately 42.13%. No match occurs in 125 of 216 outcomes, approximately 57.87%. That winning hit rate does not reveal the wager’s expected value by itself; the payout attached to each match count must also be included.
For a broader explanation, see how ordered outcomes, hit rate, expected value and house edge are calculated.
Expected value with 1:1, 2:1 and 3:1 net payouts
| Wager | One selected symbol |
|---|---|
| Ruleset | Three independent six-symbol dice; zero matches lose |
| Net payouts | 1:1 for one match, 2:1 for two matches, 3:1 for three matches |
| Winning outcomes | 75 one-match, 15 two-match and 1 three-match outcomes; 91 winning outcomes in total |
| Any-payout probability | 91/216, approximately 42.13% |
| Losing outcomes | 125 zero-match outcomes |
| Loss probability | 125/216, approximately 57.87% |
| Denominator | 216 ordered outcomes |
| Expected-value formula | (75 × 1 + 15 × 2 + 1 × 3 − 125 × 1) ÷ 216 |
| Expected net result | −17/216 unit per unit initially wagered |
| House edge | 17/216, approximately 7.87% |
| Source basis | Direct combinatorial calculation using the explicitly stated paytable |
| Verification date |
In plain language, the stated paytable produces a theoretical average player loss of about 0.0787 unit per unit initially wagered across repeated trials. Individual rounds can win or lose; the 7.87% figure is not the probability of losing one roll.
This is not a universal Crown and Anchor house edge. A different payout, commission, push, bonus or special rule changes the expected value and must be calculated separately.
Why Crown and Anchor payouts can vary
Using three dice and six symbols establishes the match probabilities, but it does not establish what those matches pay. A rules description is incomplete if it lists the equipment without documenting the paytable and exceptions.
If any answer differs from the featured assumptions, recalculate expected value from that documented schedule. Unsupported historical or venue-specific payouts should be labeled “varies by rules,” not filled with speculative figures or blended into an average.
Applicable figure: the approximately 7.87% house edge on this page applies only to the selected-symbol wager paying 1:1, 2:1 and 3:1 net under the stated assumptions.
Use the dice-game paytable guide to audit net payouts, total returns, commissions and exceptions.
When Crown and Anchor matches Chuck-a-Luck mathematically
A selected Crown and Anchor symbol and a selected Chuck-a-Luck number have the same match distribution when both wagers use three independent dice, each die has six equally likely options, and the selected option appears once per die.
| Characteristic | Crown and Anchor | Chuck-a-Luck |
|---|---|---|
| Selected option | One of six symbols | One of six numbered faces |
| Dice | Three six-symbol dice | Three six-sided numbered dice |
| Zero through three match counts | 125, 75, 15 and 1 | 125, 75, 15 and 1 under equivalent assumptions |
| Same expected value? | Only when the payouts and all relevant rules are also equivalent | |
Condition: equivalent outcome counts do not guarantee an equivalent house edge. If one game pays more for three matches, charges a fee or applies a special exception, its expected value changes.
The mathematical resemblance also does not prove identical legality, current availability or historical origin. Read the complete Chuck-a-Luck rules and payout analysis for that game’s assumptions and alternative paytables.
Documented Crown and Anchor objects and historical context
Museum collection records provide evidence that physical Crown and Anchor equipment survives, but individual objects do not establish one complete origin story or universal historical ruleset.
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Three-dice set documented by Museum Wales
The Museum Wales Crown and Anchor collection record (external site) documents a set using three dice and the traditional crown, anchor, heart, spade, diamond and club symbols.
This supports the equipment and symbol description used on this page. It does not, by itself, prove that every version used the featured 1:1, 2:1 and 3:1 paytable.
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World War I-era object documented by Museums Victoria
The Museums Victoria Crown and Anchor collection record (external site) identifies a game object associated with World War I and dated 1915.
The object is evidence of historical material culture. It does not establish that the game originated in a particular place, was primarily military entertainment or followed one continuous rules tradition.
Previous rolls do not make a symbol due
When the dice are fair and conditions remain unchanged, each new roll is independent. A long absence of anchors does not make an anchor more likely on the next roll. A recent run of crowns does not make another crown more or less likely.
The belief that an opposite or balancing result has become due is the gambler’s fallacy. Records of earlier independent outcomes do not change the next roll’s 1-in-6 chance for a particular symbol on an individual die.
A winning round also does not remove the featured paytable’s negative expected value. House edge describes a long-run expected cost, not a guaranteed outcome in one round or session. Chasing losses by continuing or increasing wagers can increase financial harm.
Ruleset, calculation method and sources checked
- Featured wager
- One symbol selected before a three-dice roll
- Equipment assumption
- Three fair, independent dice, each with one crown, anchor, heart, spade, diamond and club
- Payout interpretation
- Net winnings of 1:1, 2:1 and 3:1 for one, two and three matches; zero matches lose
- Outcome denominator
- 6³ = 216 ordered outcomes
- Match-count method
- Direct binomial counting: 125 zero-match, 75 one-match, 15 two-match and 1 three-match outcome
- Expected-value formula
- (75 × 1 + 15 × 2 + 1 × 3 − 125 × 1) ÷ 216 = −17/216
- Calculated house edge
- 17/216, approximately 7.87%, for the featured selected-symbol wager only
- Primary sources
- Museum Wales and Museums Victoria collection records for equipment and historical-object context
- Secondary calculation check
- The four match counts reconcile to 216 outcomes, and the expected-value numerator independently simplifies to −17.
- Historical confidence limit
- The collection records document equipment and objects; they do not establish a universal paytable, continuous ruleset or single origin narrative.
- Last checked
- Review status
- Direct calculation reproduced from the displayed assumptions. Historical statements remain limited to the cited museum evidence.
Sources
- Museum Wales, “Dice Game, Crown and Anchor.” Source type: museum collection record. Checked . View the Museum Wales record (external site).
- Museums Victoria, “Game: Crown and Anchor, World War I, 1915.” Source type: museum collection record. Checked . View the Museums Victoria record (external site).
- Direct combinatorial calculation. Source type: reproducible mathematics based on three independent six-faced dice and the featured paytable. Verified .
Correction history
No material corrections recorded.
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