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Dice Strategy and Probability

Dice Probabilities Dice games are probably the most widely played and well-known genre ever created. The concept of Dice games have been around for literally thousands of years, with ancient peoples sometimes using shells and bones as Dice to add the element of controlled chance into their otherwise lackluster games. Also known to many as "Bones", Dice have been thrown by millions of people and have given birth to other games which are derived from their concept, most notably Dominoes.

With so many Dice-based games available, we decided to create a collection of the various theory and strategy ideas associated with Dice for gamers to access whenever they needed them. Our dice probability charts are well organized and detail the probabilities that affect up to five dice when thrown simultaneously. We'll also detail the ease in which new Dice games can be created using the Chess and Poker Dot Com dice strategy guide. Let's have a look to see how dice interaction can be understood and utilized.

Alea jacta est: Dice Probability

Dice Interaction The appeal of Dice games is rooted in the fact that when two or more Dice are thrown simultaneously, a beautiful interaction occurs. Before the initial throw the Dice are in fact separate entities. However, once multiple Dice are thrown, the totals they create (arrived at by adding all the values together) unbalance the games in which they are being used into various channels of chance and strategy. Based on the number of Dice thrown, certain totals become increasingly more likely than others. As more and more Dice are thrown together at once, the expected outcomes begin to fluctuate and alter the strategy that a player may use accordingly.

Probability is the number of times something occurs divided by the number of times it could occur.

We'll take a look at the various combinations you will arrive at when rolling two, three, four and even five dice together, as well as some of the games that these outcomes affect. When researching the Dice statistics for this page, I could not find any one grouping of charts that showed all the numbers I was looking for. Logically, I then decided to create them myself. The following charts should be read from left to right, and they detail all of the possible Dice Counts, Sums and statistical percentages (probability) that they should occur. The following charts are based on the sums of all the Dice that are thrown. I call this the "Dice Count". For example, if you roll two Fives, your Dice Count would be 10 (5+5=10) and rolling a Three, Four and a Six would give you a 13 Count (3+4+6=13).

ChessandPoker.com Dice Probability Charts

The left side of each line (in bold) shows the various Dice Counts. In most cases, there are two Counts shown for each line. This means that the Sums and Percentages detailed to the right of them apply to both of the counts listed. For example, "2 or 12" means that both Two Counts and Twelve Counts share the exact same probability of occurring. If only one Count is shown, then the percentages apply to only that certain Count.

Each chart also details the exact number of combinations for each count that can occur out of ALL THE POSSIBLE COMBINATIONS for that number of Dice. For example, in the Two Dice chart below "3 combinations each" is listed for the 4 / 10 Counts entry. This means that when you're rolling two Dice, a Four and also a Ten both have 3 different combinations each out of the 36 total number of combinations possible between two Dice (there's more about this below). There are three different ways to make a Four (1-3, 2-2, 3-1) and also three ways to make a Ten (4-6, 5-5, 6-4). And finally, the number of possible combinations for each entry is displayed as a percentage at the end of each line. Using the above 4 / 10 section for Two Dice, we see that each count has three different combinations or an 8.33% chance of occurring. This method is used for all of the charts in this guide.

Two Dice Probability (36 combinations)

Three Dice Probability (216 combinations)

Four Dice Probability (1296 combinations)

Five Dice Probability (7776 combinations)

Understanding the Probability Charts

As you can see, the Counts at the top of the charts are much less likely to occur than those at the bottom. The further down you go on a chart, the more likely the listed counts are to occur. For example, the bottom-most entry in the "Two Dice Probability" chart is the 7 Count. This means that the 7 Count is the most likely to occur, with a 16.67% chance of occurrence. So how do you utilize the raw data found in our charts? Here's an explanation with the oft-used two-dice game Craps. One of the first bets you can make in the game of Craps is the Pass Line Bet. This bet will win instantly for you when the shooter (the person throwing the dice) throws a 7 or 11 on their first throw. You will lose this bet if the shooter instead throws either a 2, 3 or 12 on the first throw. Let's use the Two Dice Probability Chart to determine the chances of each of those outcomes.

The winning throws for the Pass Line bet are 7 or 11. Using the chart, we see that a 7 count has a 16.67% chance of occurring and the 11 count has about a 5.56% chance. That totals up to approximate winning chances of 22.23%. The losing throws are 2 (2.78), 3 (5.56) or 12 (2.78) counts. So the losing chances equal 11.12%. We can see that concerning the Pass Line bet the shooter is almost twice as likely to roll a winning total than they are to roll a losing one. If this were the only bet and factor in the game it would be pretty simple, wouldn't it? Actually, there is much more to the game than just this as any Craps player will surely tell you. Using the chart again we can see that while the player is more likely to throw a winning 7 or 11 compared to a losing 2, 3 or 12, a whopping 66.66% (about 2/3 of the time) one of the other counts (4, 5, 6, 8, 9 or 10) should occur.

Now we are beginning to see how the charts can be used to better understand the Dice games you are involved with. But what about the Dice games that don't already exist? Knowing the mechanics of what makes a dice game work should put you well on your way to creating games of your own. Want an easy 3 Dice game? Make a game where the players get huge rewards when they throw a 10 or 11 count. Since this is the most likely occurrence for three dice, more often than not they should come out pretty good. Need it a bit harder? Try a 4 dice game where you have to roll a 4, 5, 6, 22, 23 or 24 count to win a point. Even though that's 6 winning counts, the combined percentage chance of a winning count occurring is only 2.32%!

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