A three-dice game of chance
Sic bo is a game of chance. Every bet carries a house edge, no strategy, pattern or timing changes the odds in the player’s favor over time, and most players lose money over time. Nobody should gamble money they cannot afford to lose, and anyone struggling with gambling can contact a local support service.
Sic bo is played with three dice, usually shaken in an enclosed container or rolled by a machine, with a layout of boxes on which players place bets. Each box covers a different outcome: a single number, a pair, a total, a combination of two numbers, a range such as big or small, or a triple. After the dice are shown, winning bets are paid at the posted ratios and the rest lose. Online and live versions use the same layout and rules.
Counting the outcomes
With three six-sided dice there are 6 × 6 × 6 = 216 equally likely ordered outcomes. Distinguishing the dice, as if they were different colors, makes the counting simple, and every bet’s probability is a count out of 216. This is the same dice combinations method used for two dice in craps, extended one die further.
Paytables vary by place, so the payouts below are common examples, to be checked against the table rules.
Big and small
The small bet wins if the total of the three dice is from 4 to 10, and the big bet wins if the total is from 11 to 17. Both pay 1 to 1. In most rule sets, a triple (all three dice the same) loses both bets, even if its total falls in range.
Counting the totals from 4 to 10 gives 3 + 6 + 10 + 15 + 21 + 25 + 27 = 107 combinations out of 216. Two of those are triples (2-2-2 with a total of 6 and 3-3-3 with a total of 9) and lose, leaving 105 winning combinations. The other 111 combinations lose, including the total of 3 (1-1-1) and totals 11 and above.
Average result per unit: (105 − 111) ÷ 216 = −6 ÷ 216 ≈ −2.78%. The big bet is symmetrical, with the same edge. This is the cheapest family of bets on the layout, but a 2.78% edge is still higher than many of the lowest-cost bets elsewhere in the casino.
Single numbers
A single-number bet wins if the chosen number shows on at least one die, paying 1 to 1 for one die, 2 to 1 for two dice and 3 to 1 for three. Counting:
- No die shows the number: 5 × 5 × 5 = 125 combinations (lose).
- Exactly one die shows it: 3 × 5 × 5 = 75 combinations (pay 1).
- Exactly two dice show it: 3 × 5 = 15 combinations (pay 2).
- All three show it: 1 combination (pays 3).
Check: 125 + 75 + 15 + 1 = 216.
Average result: (75 × 1 + 15 × 2 + 1 × 3 − 125) ÷ 216 = (75 + 30 + 3 − 125) ÷ 216 = −17 ÷ 216 ≈ −7.87%.
This bet looks generous, because a chosen number appears on at least one die in 91 of 216 rolls, about 42% of the time. But the payout structure produces an edge nearly three times as large as big or small. A well-known older dice game played with three dice and a numbered layout follows the same single-number math and has the same edge.
Specific triple
A bet on one specific triple, such as three 4s, wins only for that one combination out of 216. A common payout is 150 to 1. Average result: (150 − 215) ÷ 216 = −65 ÷ 216 ≈ −30.1%.
Any triple
A bet on any triple wins on 6 of the 216 combinations (1-1-1 through 6-6-6), with a common payout of 24 to 1. Average result: (6 × 24 − 210) ÷ 216 = (144 − 210) ÷ 216 = −66 ÷ 216 ≈ −30.6%.
Totals
Bets on a specific total pay more for totals that occur less often. For example, a total of 4 occurs in 3 of 216 combinations (1-1-2 in its three orders), and a typical payout is 60 to 1. Average result: (3 × 60 − 213) ÷ 216 = −33 ÷ 216 ≈ −15.3%. Totals near the middle occur more often and pay less. Paytables differ, so other totals should be checked individually.
Summary of the examples
| Bet | Chance (out of 216) | Common payout | Approximate edge |
|---|---|---|---|
| Big or small | 105 | 1 to 1 | 2.8% |
| Single number | 91 (at least one die) | 1, 2 or 3 to 1 | 7.9% |
| Total of 4 | 3 | 60 to 1 | 15.3% |
| Specific triple | 1 | 150 to 1 | 30.1% |
| Any triple | 6 | 24 to 1 | 30.6% |
These are illustrations based on common payouts. A table with different payouts has different edges, and these should be recalculated from the rules shown.
Why the spread is so wide
The pattern is the same as with other rare-event bets. The more remote the outcome, the larger the headline payout appears, and the more of the true value is withheld. A 150 to 1 payout sounds large, yet the true odds against a specific triple are 215 to 1. The rarer the event, the bigger the gap can be hidden behind a large number.
Because the game is fast and the layout offers many bets at once, it is also easy to place several bets each round and multiply the amount wagered. Betting on many boxes does not average the edges away. The total expected loss is the sum of the loss on each bet, so covering more of the layout is just a larger wager. This is the same logic as with hedging bets: spreading money over several outcomes changes the shape of the result, not its average cost.
A note on streaks
The dice have no memory. Having seen several smalls in a row does not make a big more likely. People often read a run of results as a trend, but random streaks are normal, and betting on the idea that one is due is the gamblers fallacy.
Practical points
- Count outcomes out of 216 to check any posted payout.
- Compare payouts with the table above to see which bets are costly.
- Check the rules on triples for big and small.
- Decide how much to spend beforehand, and stop when it is reached.