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Dice probability calculator

Probability is something that most people think they understand, but it turns out to be more complex than they imagined.

There are only two possible results (we’ll discount the chance it lands on the edge) which are heads or tails. The dice probability calculator that the next throw is heads is 1 in 2.

Based purely on that, if the next throw comes up as tails, then logically the next throw after that must be heads – after all, it’s a 1 in 2 chance, and that would be the second throw.

But that’s not how dice probability works. The previous throw does not affect or determine subsequent throws. If you get heads 20 times in a row, the chance of the next throw coming up tails is still 1 in 2, as there are only 2 possible outcomes, every single time.

So how does that work with dice? Assuming we are using standard 6 sided dice, rolling a single die gives a 1 in 6 chance of any number coming up, assuming the die is perfectly manufactured and not weighted on one side.

The chances of the same number coming up on a subsequent throw are 1 in 6. It never changes.

However, when you add a second die to the mix, things get interesting. The possible results on throwing two dice are in the range 2 to 12, so 11 results in all. You’d think that the dice probability of getting any particular number is 1 in 11 – but you’d be wrong.

The total is now dependent on two factors, not one. If you roll a total of 2, you can only get that one way – both dice must show a 1. If you roll 12, you can only get that one way too – both dice must show a 6.

Simple so far, right? If you roll a 3, there’s two ways of getting that. Die A shows a 1, and Die B shows a 2 – or – Die A shows a 2 and Die B shows a 1. The probability of rolling 3 is twice as likely as rolling a 2.

As you progress through this exercise in mathematics, you’ll realize the easiest number to roll is 7. You can get this by rolling 1+6, 2+5, 3+4, 4+3, 5+2, or 6+1 – there are 6 combinations that give you 7 as a total. We know this is a little complicated, but we are working on a dice probability calculator, that will make the calculations for you.

As you move away from 7, the combinations decrease. For 6 or 8, there are 5 combinations, for 5 or 9, there are 4 combinations, and so on. The total number of combinations is equivalent to the number of faces on each die multiplied together – 36.

This means the probability of rolling 7 is 6 in 36, or 1 in 6. The dice probability of rolling 5 is 4 in 36, or 1 in 9. The probability of rolling 2 is 1 in 36.

Adding a third die into the mix give you a total of 216 possible outcomes, with the least likely being a score of 3 or 18. Whoever said dice probability calculation was simple?