- Maths reviewed by Josh Miller
- Tested by Diana Westfield
Crown and anchor is three dice, six symbols and a cloth board, and for a game that looks this simple it hides its edge well. You put £1 on the anchor. The banker shakes the cup. One anchor shows and you get £1 back on top of your stake; two anchors, £2; three, £3. It feels like the payouts climb in your favour. The free CasinoCalcs calculator shows what the board really keeps over a night of play, and the odds of each result.
Crown and anchor odds, roll by roll
Three dice with six faces make 216 equally likely results. Pick any one symbol and count: on 125 of those 216 rolls it doesn’t appear at all. It shows on exactly one die 75 times, on two dice 15 times, and on all three just once.
| Your symbol shows | Ways out of 216 | Chance | Pays on £1 |
|---|---|---|---|
| Not at all | 125 | 57.9% | −£1 |
| On one die | 75 | 34.7% | +£1 |
| On two dice | 15 | 6.9% | +£2 |
| On all three | 1 | 0.46% | +£3 |
Add those up over 216 rolls at £1 and you win £75 + £30 + £3 = £108 while losing £125. That’s £17 down on £216 staked, a house edge of 7.87%. It’s why crown and anchor was a favourite with sailors’ and soldiers’ bankers and still turns up at fetes and race nights: the banker hardly ever has a bad night.
Why it looks fairer than it is
The trap is the “three dice, so a 1 in 2 chance” feeling. Three dice each have a 1 in 6 chance of showing your symbol, and 3 × 1/6 is a half, so it seems as though you should hit about half the time. You don’t, because the dice overlap: some of those hits land on the same roll as doubles and triples. The real figure for “at least once” is 91 in 216, or 42%.
Spreading your money doesn’t help either. Back the crown, the anchor and the heart for £1 each and you’ll see something pay on most rolls, which feels like winning. On average you still lose 7.87% of the £3, roughly 24p a roll. Over 60 rolls, that’s around £14, and the calculator will show you the same figure with your own stakes.
Crown and anchor rules and close relatives
The board has six squares: crown, anchor, heart, diamond, club and spade. Players place stakes on as many squares as they like, the banker rolls three matching dice, and each die that lands on a symbol pays the money on that square at evens. Stakes on symbols that don’t show go to the banker. Some charity boards pay a little more on a triple to make a big moment of it; even 10 to 1 on three of a kind only trims the edge to 4.6%.
Chuck-a-luck, played with numbers in a wire cage, and the Chinese game hoo hey how, with a fish, prawn and crab among its pictures, are the same game, with the same 216 outcomes. Casino sic bo uses three dice too, but with dozens of bets; its single-number bet is crown and anchor with better payouts on doubles and triples. For other three-dice maths, the dice probability calculator handles any target.
Fun at a fete, expensive as a habit. BeGambleAware.org has free support if you’d like to talk.
