The Math Behind Dice Probabilities

When it comes to dice games, the odds all depend on the game you’re playing, the die you’re using and how many dice you’ve thrown. Probabilities are a key part of any game, regardless of whether you’re gambling, getting in some practise or just playing for leisure. The probability of rolling the right dice combination, hitting the slot jackpot or even getting the right hand in poker all differ dependant on the style of game and more, but ultimately come down to a spot of math.

We’re taking a look at just what that math is, below.

Independent Events vs. Dependent Events

Before we dig deep into the numbers, it’s important to understand the difference between independent and dependent events, and which one a dice roll falls under. In basic terms, an independent event, or two independent events, would be an event that doesn’t have a direct effect on another. Dependant events, on the other hand, refer to any event that has an effect on another or is affected by another.

If you were to roll two dice, the outcome of both would be the result of an independent event. What happens with one die will not have an effect on the odds or probability of the other, at least in terms of what the dice will land on. In some cases, the effect on one dice can affect the probability of securing a particular hand or score, but we’ll dig deeper into this later.

Drawing cards, on the other hand, would be a dependent event. Once you remove one card, the odds of picking out any other card immediately changes accordingly. There will be fewer cards to compete with, therefore improving the odds of picking the card you want.

Standard Dice Probabilities

When it comes to determining the probable outcomes of a dice roll, we first have to assume that the dice themselves are straight and haven’t been tampered with or weighted in any way. From here, we can them assume that every throw will be entirely random and that all outcomes will be a matter of chance, rather than casino or player intervention.

With a single, standard 6-sided die, there will always be six possible outcomes that you could reach. Then, providing that the die in use isn’t weighted or crooked in any way, the probabilities of getting any number will be 1 in 6. Add an additional dice, and the odds need to be multiplied by 6 – in other words, there will be 36 possible outcomes when you roll two dice. Add another dice, and you’ll need to times 36 by 6, and so on.

To then calculate your odds – or probability – of getting a certain outcome, you need to do a little more math:

Total Number Of Outcomes - Number Of Combinations = The Odds.

Say you needed a total of 8 across two dice. There are five possible combinations to make this number: 4-4, 5-3, 3-5, 6-2 and 2-6. Minus 5 from 36, and you have 31. The odds would, therefore, be 31 to 6.

If you’re using polyhedral dice, the general math remains relatively the same, however, you’ll need to change some of the numbers. A d4 dice (a four-sided dice) will only have 4 possible outcomes, and so the odds would become 1 in 4 for any possible chance. Similarly, any number on a d20 dice would have 20 to 1 odds.

Casino Odds

If you take to the casino for a game or two involving dice, the odds will be a little different – at least when it comes to the payout. These changes are brought about by the house edge. Any seasoned casino-goer will already know what the house edge is, but for those of you just delving into the gambling world, the house edge is how a casino or gaming provider makes their money. A casino with a house edge of even 1% or lower can still earn quite the profit, and it’ll only appear to affect your odds a small amount.

If you calculate your standard odds, and the odds at the casino appear lower, chances are that this is due to that edge. For example, if a casino used two dice within a game, with odds of 34 to 1, you can tell from the offset that this has been affected by the house edge. It puts the player at a slight disadvantage. While this doesn’t often have a huge effect on the gameplay, it’s worth investigating in order to improve your winning chances all the same.

The math behind a dice roll is relatively simple, providing you aren’t playing with a crooked or weighted dice. By following the odds and calculating how many rolls it should take to get the result you want, you can theoretically form a strategy to encourage a win, or at least know when to stop. Good luck!

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