Sic Bo Table

Sic Bo Table Bets & Payouts As the name implies, sic bo or hi-lo offer both high and low bets. Like craps, players are able to bet on as many combinations as they wish. The two most popular bets are low, meaning the sum of the dice drops between 4-10, and high, meaning the sum of the dice drops between 11-17. Sic Bo involves the rolling of three dice. The dealer shakes them after players make wagers. There are dozens of wagers on the table that involve combination of dice and point totals. The best wagers at Sic Bo are 4-10 and 11-17 if it pays even money. The Sic Bo table contains a combination of squares offering an intermix of numbers and words. To play Sic Bo is very straightforward and easy to understand compared to slot games, for example. You can access the games through a computer or smartphone.

A new SIC BO with a golden dragon motif played with three dice. Wins are determined by combinations of three dice. On each dice, the “1” pip showing a dragon symbol indicates the availability of progressive. When the dice lands on the dragon symbol, there is a chance to win a jackpot with a dice roll of 2 or more dragons.

The dice game that is super fun and easy to play!

Originating from China, Sic Bo is a dice game that is quickly growing in popularity. In Chinese, Sic Bo is called Tai Sai or Dai Siu, which literally means “Big Small” in English. If you have never been to Macau to see Sic Bo in action, then you have been missing out on a real cultural experience. Betting is fast and furious in Macau casinos, and the players in Asia really get into it! If anything, learn about Sic Bo to enjoy the experience of a truly popular Asian betting game.

Table Layout

The table layout is very different to Baccarat, Roulette, or any other casino game, and naturally for new comers this can be quite confusing and intimidating. There are many different betting patterns, and the table can be quite large. Often the table is covered in transparent glass or plastic, with the patterns seen through the glass. The patterns behave very much like Roulette or Craps, whereby the player is required to place their chips on the anticipated band of the outcome of the dice. After the dice are rolled and the winning band is determined, lights underneath the glass table turn on to show which bands are winning bands.

In a corner of the table, at the hand of the dealer are three dice contained in a covered glass dome. The dice are shaken and then displayed in the glass dome. The dealer enters the results of the dice into a computer programme which then lights up the winning bands on the table.

There is only one layout for all players, with standard casino chips used. The online Sic Bo table layout is exactly the same as the layout found at land casinos.

Payouts

Please note that pay outs can vary between casinos and online casinos. Knowing this, the casino edge may increase greatly in their favor. In this guide, I have used the most common payouts and casino edges.

How to play Sic Bo

There are several variations of bets that you can place to predict the result of the three dice after they have been shaken.

You can choose from big/small totals, odd/even totals, specific doubles or triples, specific totals of the spots on the dice and various number combinations.

Big Small Bets

When viewing the table layout front on, you will see that on the far left and right are betting boxes for Big and Small respectively. Placing a bet in either of these boxes is betting that the total value of the three dice is either high or low. A bet that it is high means a result that is 11 – 17. A bet that it is low means a result that is 4 – 10. On any result that the dice has rolled a triple all bets either Big or Small are lost. Totals of 3 and 18 are therefore excluded from the range, and rolls of triple 2, 3, 4 and 5 are also deemed as a loss.

These bets usually pay even money, but because the triples result in a loss the casino has an edge of just under 2.8%.

Odd Even Bets

Most table layouts will offer the betting boxes for Odd or Even. Placing a bet in either of the Odd or Even boxes is betting that the total value of the three dice will either be odd or even respectively. Again, should a triple be rolled then all bets, either odd or even are lost.

These bets usually pay even money, as with Big Small bets. And similarly, if triples arise a loss results, hence the casino edge is also just under 2.8%.

Double Bets

Split into three blocks of three, you can bet on any two dice matching their score and forming a Double. The betting outcome is therefore either a pair of 1, 2, 3, 4, 5 or 6 after the dice has been shaken. The outcome of the third dice if the other two dice are a pair has no bearing on the outcome.

A winning bet in these bands normally results in a pay out of 10-1. These bets give the house a huge edge of 18.5%.

Triple Bets

Triple bets can be placed in two categories. You can either specifically bet that the outcome are triple 1, 2, 3, 4, 5, or 6. Or you can place a bet on a category which covers any triple.

A winning bet in these bands normally result in a pay out of 180-1 for specific triples or 30-1 for any triple. These pay outs may sound great, but in essence the edge to the casino is 16.2% and 13.2%, again not great odds for the player.

Dice Total Bets

Sic Bo Table Games

In the middle of the layout are boxes which hold numbers that the value of the three dice might total. You will notice that there is no option for 3 or 18, which is covered by the Triple Bets.

4 and 17

These totals are the least unlikely and therefore the pay out is a whopping 60-1. The casino edge however is still quite high at 15.3%.

5 and 16

These totals are the second least likely and pay out 30-1. The casino edge is 13.9%.

6 and 15

The pay out is 17 -1 with the casino edge 12%.

7 and 14

The pay out is 12 -1 with the casino edge 9.7%.

8 and 13

The pay out is 8 -1 with the casino edge 9.7%.

9 and 12

The second most likely of outcomes pay out 6 – 1 with a casino edge of 7.4%.

10 and 11

The most likely of outcomes pay out 6 -1 with the casino edge of 12.5%.

Bets on Precise Number on 2 dice

On the table layout you will see boxes that appear to look like dominoes. These bets ask you to predict the outcome of two out of the three dice. All combinations except doubles can a bet be placed on. The pay out is 6-1 with a casino edge of 2.78%.

Bets on a number appearing on any three dice

At the bottom of the layout of the table, you can place a bet on a number appearing on any three of the dice. I.e. 1, 2, 3, 4, 5 or 6. If the number you have selected appears more than once, then the pay out is even higher.

• If your number appears once, the pay out is 1 – 1.
• If your number appears twice, the pay out is 2 -1.
• And if your number appears three times, the pay out is 3 -1.

Top 3 Sic Bo Casinos

Sic Bo Strategy

Sic Bo is a game of luck, and therefore simply put the best strategy is to play the table layout with bets on boxes with the best odds for the player. Similar to Craps and Roulette AVOID the betting bands that have poor casino edges.

Therefore the best bet to play at Sic Bo is Big/Small or Odd/Even. These boxes offer the best odds. Even though the pay out is only 1 -1 the house edge is a mere 2.8%. So this will stretch your bank roll.

Having said that, that doesn’t mean you can’t place a bet on any other betting boxes. You can, but be aware of the pay out ratios as described in the previous sections.

Managing your betting amounts can be performed in two ways: either keep to the minimum wager at all times, or if the betting limit allows a small enough wager use the Martingale strategy. The Martingale strategy will allow you to earn a consistent profit if there is sufficient bank roll.

Summary

Sic Bo, Big Small or Dai Siu is a great game to learn and play. It’s very simple which makes the game fun and entertaining. If you are looking to stretch your bank roll, then keep to placing bets on Big/Small or Odd/Even and keep bets small. Remember, this game is a game of luck not of skill. Don’t over analyse the previous outcomes, as each new game has the same odds of outcome as the previous game.

The Mathematics of Sic Bo

By

Michael Shackleford

January 21, 2005

Sic Bo, meaning 'dice pair' is an ancient Chinese gambling game. Today it is one of the lesser known casino games and is often confined to designated rooms for Asian games. The game uses three dice and a table with a variety of betting options on the roll of those dice. The odds and table layout may also vary from place to place. If you must play Sic Bo I would suggest sticking to only the 'low' and 'high' bets.

Following is a list of the bets available. The payoffs listed are for Atlantic City and the Mirage in Las Vegas. Other casino’s odds will vary.

• Small: Wins on total of 4-10, except for a three of a kind. Pays 1 to 1.
• Big: Wins on total of 11-17, except for a three of a kind. Pays 1 to 1.
• 4: Wins on total of 4. Pays 60 to 1.
• 5: Wins on total of 5. Pays 30 to 1.
• 6: Wins on total of 6. Pays 17 to 1.
• 7: Wins on total of 7. Pays 12 to 1.
• 8: Wins on total of 8. Pays 8 to 1.
• 9: Wins on total of 9. Pays 6 to 1.
• 10: Wins on total of 10. Pays 6 to 1.
• 11: Wins on total of 11. Pays 6 to 1.
• 12: Wins on total of 12. Pays 6 to 1.
• 13: Wins on total of 13. Pays 8 to 1.
• 14: Wins on total of 14. Pays 12 to 1.
• 15: Wins on total of 15. Pays 17 to 1.
• 16: Wins on total of 16. Pays 30 to 1.
• 17: Wins on total of 17. Pays 60 to 1.

• Two of a kind: Player may bet on any of the 15 possible two dice combinations (for example a 1 and 2). Bet wins if both numbers appear. Probability of winning is 13.89%. Pays 5 to 1.
• Double: Player may bet on any specific number (for example a 1). Player wins if at least 2 of the 3 dice land on that number. Probability of winning is 7.41%. Pays 10 to 1.
• Triple: Player may bet on any specific number (for example a 1). Player wins if all 3 dice land on that number. Probability of winning is 0.46%. Pays 180 to 1.
• Any Triple: Wins on any three of a kind. Pays 30 to 1.
• Individual Number: Player may bet on any specific number from 1 to 6. If chosen number appears 1 time bet pays 1 to 1, if it appears 2 times bet pays 2 to 1, and if it appears 3 times it pays 3 to 1.

The critical step in calculating the odds in Sic Bo is to find the probability of any given total in the throw of three dice. Following is a formula for s spots over n dice, taken from The Theory of Gambling and Statistical Logic by Richard A. Epstein, formula 5-14.

For example, let's look at the number of ways to get 11 spots over 3 dice.

int[(s-n)/6] = int[(11-3)/6] = int[1.33] = 1

The total would be 6^-3 * [-1⁰*combin(3,0)*combin(11-6*0-1,3-1) + -1¹*combin(3,1)*combin(11-6*1-1,3-1) ] =
1/218 * [1*1*combin(10,2) + -1*3*combin(4,2)] =
1/218 * [1*1*45 + -1*3*6] =
1/218 * [45-18] = 27/216 = 12.50%

Alternatively, if you can program a computer that would probably be the fastest way to get the results.

Here is a simple function in C++.

Following is the output of the function.

If you don’t know how to program you’re going to have to do this the hard way. What I recommend is list every combination of 3 dice. To avoid the list being 6³=216 items long do not repeat the same combinations in different orders. In the interests of not listing the same number twice always order each combination from lowest to highest, not forgetting combinations with a pair or three of a kind.

So we start with 1,1,1.

Next would be 1,1,2.

Then 1,1,3; 1,1,4; 1,1,5; and 1,1,6.

Obviously you can’t roll a 7 with one dice so next we increment the second die.

1,2,?

The third die must be greater or equal to the second die so the next combination in full would be 1,2,2.

Next comes 1,2,3; 1,2,4; 1,2,5; and 1,2,6.

Then comes 1,3,3.

I hope you see the pattern. The whole list would look like the following.

Next we have to determine the number of permutations of each combination. A combination is a set without regard to order and a permutation is a set with regard to order.

With a three of a kind there is only one way permutation. For example if the three dice are 1,1,1 there is only one way to roll that a 1 each time.

If the combination is 1,1,2 there are three ways to roll that: 1,1,2; 1,2,1; and 2,1,1.

If all three dice are 1,2,3 there are six possible permutations: 1,2,3; 1,3,2; 2,1,3; 2,3,1; 3,1,2; 3,2,1

The general formula is that if you have a total of d dice and the totals of each number are x₁, x₂, x₃…x_n then the number of permutations are d!/(x₁!*x₂!*x₃*…*x_n). So the number of ways to get a three of a kind would be 3!/3! = 6/6 = 1. The number of ways to get a pair would be 3!/(2!*1!) = 6/(2*1) = 3. The number of ways to get three different numbers would be 3!/(1!*1!*1!) = 6/(1*1*1) = 6.

Next we go through the tedious process of adding the number of permutations for each total. For example a total of 6 has the following combinations with the corresponding number of permutations.

The final table will look like this, not unlike the result of the computer function earlier.

So now lets add a column to our list for the number of combinations of each set. Let’s also add a total for the three dice.

Now we can divide each total number permutations by the total number 3-dice permutations (216) to get the probability of each total.

Finally, we are ready to evaluate the expected value of each bet. The expected value is the ratio of the amount the player can expect to win to the amount he bets on any given bet. So a fair bet would an expected value of zero. A positive expected value would mean the player has the advantage. A negative expected value would mean the dealer has the advantage.

Let’s start with the 4 bet. This wins with a total of 4 and pays 60 to 1. For those who don’t know, '60 to 1' means if the player wins he wins 60 times his bet and KEEPS his original wager. Had the odds paid '60 for 1' the player would NOT keep his original bet. Most table games pay on a 'to 1' basis.

The probability of a total of 4 is 3/216 = 0.013889. Thus the probability of losing is 1-(3/216) = 1-0.013889 = 0.986111.

The expected value of any bet with only two possibilities, winning or losing, is:

(Probability of winning)*(Amount of win) + (Probability of losing)*(Amount of loss).

For the 4 bet the expected value is

0.013889 * 60 - 0.986111*-1 = -0.15278.

So, this tells us that for every dollar the player bets on a total of 4 he can expect to lose 15.278 cents on average. Or, the house edge is 15.278%.

The next table shows the expected value and how it was calculated for all bets of a total of 4 to 17.

Two of a kind

There are combin(6,2)=6!/(4!*2!)=15 ways to choose two numbers out of six. Each of these combinations is listed on the table and the player bet on as many as he wishes. If both numbers appear on the roll of the three dice then the player wins and is paid 15 to 1.

Let’s assume the player picks a 1 and 2 as his two numbers. What is the probability that both a 1 and 2 occur in the roll of 3 dice? One way to do this would be to note all the possible winning permutations:

Thus there are a total of 30 winning permutations.

There are 6³=216 total permutations, so the probability of winning is 30/216 = 1/36 = 0.1388889

The two of a kind bet pays 5 to 1. So the expected value is 0.1388889*5 + (1-0.1388889)*-1 = -0.16667. In other words the house edge is 16.67%.

Double

There are six double bets available, one for each number from 1 to 6. The player may be on any one or combination of bets. Any given bet wins if at least two of the three dice land on that number.

Let’s assume the player bets on the 1.

One way to solve it would be to note all the winning permutations:

Thus there are a total of 16 winning permutations.

There are 6³=216 total permutations, so the probability of winning is 16/216 = 0.0740741.

The double bet pays 10 to 1. So the expected value is 0.0740741*10 + (1-0.0740741)*-1 = -0.18518. In other words the house edge is 18.52% (ouch!).

Triple

Sic Bo Payout Table

Player may bet on any specific number (for example a 1). Player wins if all 3 dice land on that number.

There is obviously only one way to win this bet, so the probability of winning is 1/216 = 0.0046296. The bet pays 180 to 1 so the expected value is 0.0046296*180 + (1-0.0046296)*-1 = -0.16204. So the house edge is 16.204%.

Any Triple

Sic-bo Table Games Top View

The Any Triple bet pays if any three of a kind is thrown. There are obviously six winning combinations (1,1,1; 2,2,2; 3,3,3; etc.). So the probability of winning is 6/216 = 0.027778. The bet pays 30 to 1 so the expected value is 0.027778*30 + (1-0.027778)*-1 = -0.13889. So the house edge is 13.89%.

Low

The low bet wins if the total of the three dice is 3 to 10, without being a three of a kind. The probability of any total 10 or less is exactly 50%. The average number on any one die is (1+2+3+4+5+6)/6 = 21/6 = 3.5. So the average of three dice is 3*3.5 = 10.5. It stands to reason that the probability of getting under or over 10.5 is 50%.

However the bet loses on a three of a kind. There are 3 three of a kinds that would turn a winner into a loser: 1,1,1; 2,2,2; and 3,3,3. So the probability of having a total of 10 or less as a three of a kind is 3/216 = 0.0188889. So the overall probability of winning is 0.5 – 0.188889 = 0.4861111. The bet pays 1 to 1 so the expected value is 0.4861111*1 + (1-0.4861111)*-1 = -0.02778. Thus the house edge is 2.78%.

High

The high is just the opposite of the low bet, so it stands to reason the house edge would also be 2.78%.

Individual Number

Player may bet on any specific number from 1 to 6. If chosen number appears 1 time bet pays 1 to 1, if it appears 2 times bet pays 2 to 1, and if it appears 3 times it pays 3 to 1. Probability of 1 match is 34.72%, 2 matches is 6.94%, 3 matches is 0.46%.

Let’s assume the player picks the number one.

There is only one way to get three ones: 1,1,1. So the probability of three ones is 1/6³ = 1/216.

Sic Bo Tables

Following are the ways to get two 1’s and the number of permutations of each.

So the probability of two ones is 15/6³ = 15/216.

Following are the ways to get one 1 and the number of permutations of each.

So the probability of two ones is 75/6³ = 75/216.

Another way to arrive at the probability of one 1 would be find the probability that the first die is a one and the second and third are not:

Pr(one)*Pr(not one)*Pr(not one) = (1/6)*(5/6)*(5/6) = 25/216.

However the one could appear in the first, second, or third position, so multiply by 3: 3*(25/216) = 75/216.

The probability of rolling zero ones is Pr(not one)*Pr(not one)*Pr(not one) = (5/6)*(5/6)*(5/6) = (5/6)³ = 125/216.

The following return table shows the possible outcomes, and the number of combinations, probability, and return of each. The return is the product of the probability and the win or loss to the player.

So the total expected return is -0.0787, or the house edge is 7.87%.

Sic Bo section at the Wizard of Odds.
How to calcualte the 3-dice permutation in Visual Basic.