Roll 10 D21 dice

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10D21 Dice Roller

10D21 Dice Roller
Rolls 10 D21 dice
Lets you roll multiple dice like 2 D21s, or 3 D21s. Add, remove or set numbers of dice to roll
Combine with other types of dice (like D19 and D23) to throw and make a custom dice roll

Statistics of this Dice Roller

Roll10D21
Total Kinds of Dice1
Total Dice10
Minimum Sum10
Maximum Sum210
Lowest Dice Face1
Highest Dice Face21
Highest Dice Face of the Smallest Die21
10D21
Total Possible Combinations 30,045,015

Number of combinations are calculated using the formula [ (21+10-1) choose (10) ]

You can try generating all the combinations using the following combination generator
All possible combinations of 10D21
10D21
Total Possible Permutations 16,679,880,978,201

Number of permutations are calculated using the formula [ 21^10 ]

You can try generating all the permutations using the following permutations generator
All possible permutations of 10D21

Probabilities of this Dice Roller

10D21

Probability of getting a 1

In technical terms this is equivalent of getting atleast one 1. This is close to 0.39, about 38.61% percent.

This is calculated by multiplying all the probabilities of not getting a 1 for each dice and then subtracting the answer from 1.

1 - (20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21)

Probability of not getting a 1

Probability of not getting any 1 is close to 0.61, about 61.39% percent.

This is calculated by multiplying all the probabilities of not getting a 1 for each dice.

20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21

Probability of getting all 1's

Probability of getting all 1's is close to 0.00000000000006, about 0.000000000006% percent.

This is calculated by multiplying together all the probabilities of getting a 1 for each dice.

1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21

Probability of getting 10 1s

Probability of getting 10 1's is close to 0.00000000000006, about 0.000000000006% percent.

This is calculated by multiplying together all the probabilities of getting a 1 for each dice that has a 1.

1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21

Probability of getting a 21

In technical terms this is equivalent of getting atleast one 21. This is close to 0.39, about 38.61% percent.

This is calculated by multiplying all the probabilities of not getting a 21 for each dice and then subtracting the answer from 1.

1 - (20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21)

Probability of not getting a 21

Probability of not getting any 21 is close to 0.61, about 61.39% percent.

This is calculated by multiplying all the probabilities of not getting a 21 for each dice.

20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21 x 20/21

Probability of getting all 21's

Probability of getting all 21's is close to 0.00000000000006, about 0.000000000006% percent.

This is calculated by multiplying together all the probabilities of getting a 21 for each dice.

1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21

Probability of getting 10 21s

Probability of getting 10 21's is close to 0.00000000000006, about 0.000000000006% percent.

This is calculated by multiplying together all the probabilities of getting a 21 for each dice that has a 21.

1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21

Probability of getting all highest faces

Probability of getting all the maximum faces (10 21's) is close to 0.00000000000006, about 0.000000000006% percent.

This is calculated by multiplying together all the probabilities of getting the maximum face for each dice.

1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21

Probability of getting one of a kind

Probability of getting one of a kind is close to 0.0000000000013, about 0.00000000013% percent.

There are 21 ways to get one of a kind (all 1's, all 2's, all 3's, all 4's, all 5's, all 6's, all 7's, all 8's, all 9's, all 10's, all 11's, all 12's, all 13's, all 14's, all 15's, all 16's, all 17's, all 18's, all 19's or all 20's and so on). The probability of getting all of any kind is then caclulated by adding the probability of getting all 1's, all 2's, all 3's, all 4's, all 5's, all 6's, all 7's, all 8's, all 9's, all 10's, all 11's, all 12's, all 13's, all 14's, all 15's, all 16's, all 17's, all 18's, all 19's or all 20's and so on. Since, probabilities of getting all 1's through all 21's are the same, we can multiply them all together. So, multiplying the probability of getting all 1's by 21 will give us the probability of getting all of any kind.

    
    21 x (1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21 x 1/21)

Javascript code to create this dice roller


    // code to create a 10D21 dice roller

    
                   
        // define the range of numbers to pick from
        var lowest = 1;             // lowest possible side of the dice
        var highest = 21;           // highest possible side of the dice
        var numbers_of_dice = 10;    // how many dice to roll     
        
        var this_roll = []; // array to store the results of this roll

        for (var j = 1; j <= numbers_of_dice; j++) {

            // loop for the number of dice

            // for each dice, generate a number between lowest and highest
            var dice_face = Math.floor(Math.random() * (highest-lowest+1) + lowest);
            this_roll.push(dice_face); //store this in the array
        }
            
        
        // print all the generated rolls
            
        for (j = 0; j < this_roll.length; j++) {

            // loop through the dice array 

            //print each dice roll value followed by a space
            document.write(this_roll[j]);
            document.write(" ");

        }
            
        
    

    /* 

    Sample output 

    

    */