Dice

Dice

How to Win at Dice

Whether you are playing at home or in a casino, dice games are fun games of chance and probability. Traditionally, a dice game refers to a gambling game such as craps typically played at casinos, but home games such as Yahtzee provide the same kind of fun and excitement as casino games, no matter your age. To increase your chances of winning, you can use probability to play to odds to your advantage.

Here are some methods for understanding the probability of dice games and how to apply those odds to certain games.

Method 1: Understanding Dice Probability

Learn the total number of combinations. The range of probability will vary depending on the number of dice you have and how many sides each dice has. The number of combinations is determined by how many different number combinations dice can make. For each dice, there is a one in six, or 1/6, chance that you will get any given number, with six possible numbers in total. The number of chances increases with each die you have. For each additional dice, the total number of possibilities increases times 6. There are a total of 36 (6 x 6) combinations for two dice, 216 (36 x 6) combinations for three dice, and so on.

Determine the likelihood of a number. To determine how frequently a number will be rolled, you must figure out how many times that number can be made by the number of dice you have. For example, if you have three dice, the probability of getting an 8 is 21/216. The combinations that are possible are 1-2-5, 1-3-4, 1-1-6, 2-3-3, and 2-2-4. For each combination that uses three unique dice, there are 6 total combinations of dice. For each combination that uses two unique dice, there are 3 total combinations of dice. For the number 8, there are two number combinations that have three unique dice (6 + 6) and three number combinations that have two unique dice (3 + 3 + 3), for a total of 21 possibilities

Learn the probability of two dice games. Most dice games, as well as many board games in general, use two dice. Learning to compute the probability of two dice games can come in handy when you’re deciding your strategy. The probability in two dice games is easy to compute. Simply multiple the number of combinations by 2 to figure out the maximum number of ways you can reach that number.

  • For example, a total of 7 may be obtained by rolling a 1 and 6, a 2 and 5, or a 3 and 4. Since there are two dice, double number of combinations (3 x 2), which is a total of 6/36 combinations.
  • You can also use the odds in any board game. For example, you are playing Monopoly and are about to roll for the first time while you are in jail. The likelihood that you will roll a 12 is 1/36, or 2.7%. These aren’t high odds, so you might want to pay the $50 to get out of jail so you don’t spend three turns not playing the game, especially since you will have to pay the money in the end anyway if you don’t roll a 12.
  • These statistics are based on six-sided dice. If your game uses dice with more sides, the probability of each number combination would change.

Method 2: Playing the Odds in Craps

Compute the odds in Craps. Craps is a game of chance, but you can use statistics to figure out how to place your bets. You win in craps on the first roll if you roll a 7 or an 11. The combinations that will result in a 7 are 1-6, 2-5, and 3-4. Because there are two dice, you need to multiply the number of combinations by 2 (3 x 2), giving you a total of 6 out of 36 chances, or 17%, that you will roll a 7 on the first roll. An 11 is only made by rolling a 6-5, so the total number of chances you’ll get an 11 is 2 out of 36, or 5.5%. To find out the overall probability of winning on your first roll, add 1/6 and 1/18, which makes your overall probability of rolling a winning number on the first roll 8/36, or 22%. 

  • Look out for rolls of 2, 3, and 12. These are considered the natural losing numbers in craps and no matter what you bet, you lose if these numbers are rolled. Don’t worry too much, though, because the likelihood of each of these numbers being rolled is 1/36, or 2.7%

Bet the pass line. The pass line is where you bet for the roll of 7 or 11 on the first roll. You can start by bidding the pass line, which will win you money 22% of the time on your first roll if you roll a 7 or 11. This can be a nice way to gently build yourself up to betting higher.

Bet on 6s or 8s. If you don’t want to bet the pass line, you can bet on the point numbers. Point numbers are the numbers that aren’t natural winners and losers, which are the 4, 5, 6, 8, 9, and 10. When your first roll doesn’t automatically win or lose, you end up with a point number, which you have to roll one additional time to win. 6s and 8s are the most probable point numbers, and these numbers will be more likely to win you money than any of the other point numbers. There is a 10/36, 27%, chance that your point number will be either a 6 or an 8. Your chances decrease once a point number is rolled, with the odds of 5/36, or 13.8%, that you will get the matching point number.

  • Even if these odds seem low, they are the highest for any point numbers. The chances of you winning with a 5 or 9 is 4/36, or 11%, and with a 4 or 10 is 3/36, or 8.3%. These are much lower than the 13.8% chance that you’ll win off the 6 or the 8.

Work the odds. Even if you’re on a losing streak, following the odds will likely pay out in the long-run, regardless of short-term losses. Odds will always even themselves out, but that process may be much longer than you anticipate. If you have plenty of money to burn, playing against the odds can be a fun risk to take.

Method 3: Using the Odds in Yahtzee

Understand the odds. Yahtzee is a great dice game, but relying on five dice to fall your way can be a daunting task. There is only a 6/7776 chance that you’ll roll that coveted Yahtzee combination, which are not great odds at all. There is a 7056/7776, or 91%, chance that you’ll get a pair on your roll, so you might want to try to strive for something higher early on since you are much more likely to get at least a pair or two on your final roll.

Determine the odds of a Yahtzee. To determine the chance of a Yahtzee, you simply multiply the number of sides that a die has as many times as there are dice (6 x 6 x 6 x 6 x 6). This is your base number (7776). And since there are 6 numbers that can be used to make a Yahtzee, then your probability is 6/7776, or 0.1%. The other combinations have much greater odds, so settling for one of the other combinations is more likely to get you a higher score and win the game than always holding out for a Yahtzee.

Keep a full house. A good way to pick up some extra points in Yahtzee is to always take a full house when it first comes up. The full house is much more likely (300/7776, 3.9%) than four of a kind (150/7776, 1.9%) and it yields more points (25) than the highest four of a kind can yield (24). Although you might want to try for a Yahtzee as well, the likelihood is so low that taking the easy points early on will likely work in your favor. Plus, a full house can be elusive late in the game when you really need it.

Go for the large straight. On your first roll in the game, there is only a 3.1% chance that you will throw a large straight. If you happen to roll three of four numbers in a row, play the odds and keep rolling. Say you roll a 2-2-3-4-5 combination. There is a 2/6, or 33%, chance that you will get either the 1 or 6 needed to complete the straight if you re-roll the 2. The likelihood that you will get enough 2s to make a four of a kind or Yahtzee are not nearly as promising, so go with the straight.

Get the bonuses. If you roll a three of four 4s, 5s, or 6s, use them in your upper section as your total score for those numbers instead of counting them as three and four of a kinds. This will add more points to your overall upper section score and help you to get your bonus of 35 points. If you count them as three and four of a kind, you are just guaranteed the total on the dice. If you get your bonus on the upper section, you get the score for those dice plus an additional 35 points.

  • If you are left near the end of the game with only one or two of the higher numbers in the upper section to count as your totals for those numbers, you may lose your bonus, which will decrease your overall score by 35 points.

Before you play any dice game it is good to know the probability of any given total to be thrown. First lets look at the possibilities of the total of two dice.

The table below shows the six possibilities for die 1 along the left column and the six possibilities for die 2 along the top column. The body of the table shows the sum of die 1 and die 2.

Two Dice Totals

DIE 1 DIE 2
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

The colors of the body of the table illustrate the number of ways to throw each total. The probability of throwing any given total is the number of ways to throw that total divided by the total number of combinations (36). In the following table the specific number of ways to throw each total and the probability of throwing that total is shown.

TOTAL NUMBER OF
COMBINATIONS
PROBABILITY
2 1 2.78%
3 2 5.56%
4 3 8.33%
5 4 11.11%
6 5 13.89%
7 6 16.67%
8 5 13.89%
9 4 11.11%
10 3 8.33%
11 2 5.56%
12 1 2.78%
Total 36 100%

The following shows the probability of throwing each total in a chart format. As the chart shows the closer the total is to 7 the greater is the probability of it being thrown.

Dice strategies to boost your win chance

While all provably fair dice games generate numbers at random, you can always boost your win chance by strategizing according to the following pointers.

Martingale Strategy – This tactic is a very popular dice strategy that allows you to bet the same amount if you win, and keep betting double if you lose. If you have never heard about this dice winning strategy, it goes something like this: the player chooses his odds that will double his money if he wins. Every time he loses, he doubles his bet so that he will recoup from his losses. If he loses again, he doubles again. If everything goes according to plan, the player should be able to make money indefinitely, simply by doubling his bet to win back any losses.

D’Alembert Strategy – This dice strategy is almost the same with the Martingale Strategy except here, you do not double your bet when you lose but rather just increase the amount of your bet by 1x on your next roll. And when you win, you don’t reduce your bet by half but rather by one also. Remember: You should only wager the amount you can afford to lose, and never go over that amount. Always use a money management system to prevent yourself from losing substantial amounts of bitcoins.

Paroli Strategy – Here, you begin by betting an amount of your choice. If that bet wins, double your bet in your next rolls until you incur a loss. But if you continue to be in a winning streak and have already won big, consider tempering your bet. In other words, each time you lose and each time you notice a series of wins, reduce the amount of your bet. This dice strategy is relatively safer than the D’Alembert and Martingale strategies, because this scheme aims at taking advantage of the lucky straight wins.

Hybrid Strategy – If you think your dice rolling session will be a long spree, consider doing a mix-and-match of the first three tactics mentioned. Try out one strategy for a couple of rolls and see if it works. If it does not, consider switching to another tactic. And if it gives you the upper hand, stay right beside that dice strategy until you feel it’s about time you make your betting streaks follow a different pattern.

Indeed, there is no surefire dice strategy to beat the odds. However, it wouldn’t be a mistake if you try your hand with the above mentioned strategies. After all, it is given that it is impossible to control luck but you have all the power and means to adjust how much you’ll bet and how much you’ll possibly win basing on a strategic plan.