# The dice roller

### Off-Topic Discussions

Am I the only one who is fascinated with the dice Rollo and just loves rolling die?

1d20 ⇒ 6

1d20 ⇒ 16

1d20 ⇒ 18
1d20 ⇒ 13
1d20 ⇒ 8
1d20 ⇒ 3
1d20d6d1d20 ⇒ (19, 5, 12, 1, 11, 19, 18, 4, 9, 15, 7, 4, 20, 4, 20, 19, 8, 13, 8, 3, 8, 11, 15, 8, 8, 8, 13, 1, 2, 1, 1, 3, 2, 18, 18, 6, 7, 19, 19, 16, 8, 8, 9, 13, 13, 10) = 464
1d20 ⇒ 6
1d20 ⇒ 13
1d20 ⇒ 11
1d20 ⇒ 17

test roll: 1d6 + 1d6 + 2 ⇒ (3) + (3) + 2 = 8

test roll: 2d6 + 2 ⇒ (3, 5) + 2 = 10
test roll: 2d6 + 2 ⇒ (4, 2) + 2 = 8
test roll: 2d6 + 2 ⇒ (3, 3) + 2 = 8
test roll: 2d6 + 2 ⇒ (5, 6) + 2 = 13
test roll: 2d6 + 2 ⇒ (2, 6) + 2 = 10
test roll: 2d6 + 2 ⇒ (2, 5) + 2 = 9
test roll: 2d6 + 2 ⇒ (2, 5) + 2 = 9
test roll: 2d6 + 2 ⇒ (3, 2) + 2 = 7
test roll: 2d6 + 2 ⇒ (2, 4) + 2 = 8
test roll: 2d6 + 2 ⇒ (2, 3) + 2 = 7
test roll: 2d6 + 2 ⇒ (5, 3) + 2 = 10
test roll: 2d6 + 2 ⇒ (4, 1) + 2 = 7

test roll: 2d6 + 2 ⇒ (5, 2) + 2 = 9
test roll: 2d6 + 2 ⇒ (3, 2) + 2 = 7
test roll: 2d6 + 2 ⇒ (1, 3) + 2 = 6
test roll: 2d6 + 2 ⇒ (3, 6) + 2 = 11
test roll: 2d6 + 2 ⇒ (4, 4) + 2 = 10
test roll: 2d6 + 2 ⇒ (3, 3) + 2 = 8
test roll: 2d6 + 2 ⇒ (4, 1) + 2 = 7
test roll: 2d6 + 2 ⇒ (6, 6) + 2 = 14
test roll: 2d6 + 2 ⇒ (6, 6) + 2 = 14
test roll: 2d6 + 2 ⇒ (1, 4) + 2 = 7

.
.
.
.
.
.
test roll: 2d6 + 2 ⇒ (3, 6) + 2 = 11
test roll: 2d6 + 2 ⇒ (6, 6) + 2 = 14
test roll: 2d6 + 2 ⇒ (1, 6) + 2 = 9
test roll: 2d6 + 2 ⇒ (2, 5) + 2 = 9
test roll: 2d6 + 2 ⇒ (2, 5) + 2 = 9
test roll: 2d6 + 2 ⇒ (2, 4) + 2 = 8
test roll: 2d6 + 2 ⇒ (1, 6) + 2 = 9
test roll: 2d6 + 2 ⇒ (1, 3) + 2 = 6
test roll: 2d6 + 2 ⇒ (2, 1) + 2 = 5
test roll: 2d6 + 2 ⇒ (2, 6) + 2 = 10

It always fails me.... Just when I need a crit. But worthless skill checks it gets high numbers on all day. (Not very serious)<sigh>

*
*
*
*
*
*
test roll: 2d6 + 2 ⇒ (1, 1) + 2 = 4
test roll: 2d6 + 2 ⇒ (6, 2) + 2 = 10
test roll: 2d6 + 2 ⇒ (4, 4) + 2 = 10
test roll: 2d6 + 2 ⇒ (3, 2) + 2 = 7
test roll: 2d6 + 2 ⇒ (3, 4) + 2 = 9
test roll: 2d6 + 2 ⇒ (6, 4) + 2 = 12
test roll: 2d6 + 2 ⇒ (5, 4) + 2 = 11
test roll: 2d6 + 2 ⇒ (1, 5) + 2 = 8
test roll: 2d6 + 2 ⇒ (2, 3) + 2 = 7
test roll: 2d6 + 2 ⇒ (2, 1) + 2 = 5
test roll: 2d6 + 2 ⇒ (1, 6) + 2 = 9
test roll: 2d6 + 2 ⇒ (4, 6) + 2 = 12
test roll: 2d6 + 2 ⇒ (6, 1) + 2 = 9
test roll: 2d6 + 2 ⇒ (3, 6) + 2 = 11
test roll: 2d6 + 2 ⇒ (5, 5) + 2 = 12
test roll: 2d6 + 2 ⇒ (5, 1) + 2 = 8
test roll: 2d6 + 2 ⇒ (3, 3) + 2 = 8
test roll: 2d6 + 2 ⇒ (4, 4) + 2 = 10
test roll: 2d6 + 2 ⇒ (6, 5) + 2 = 13
test roll: 2d6 + 2 ⇒ (1, 3) + 2 = 6
test roll: 2d6 + 2 ⇒ (4, 1) + 2 = 7
test roll: 2d6 + 2 ⇒ (4, 5) + 2 = 11
test roll: 2d6 + 2 ⇒ (2, 2) + 2 = 6
test roll: 2d6 + 2 ⇒ (6, 5) + 2 = 13
test roll: 2d6 + 2 ⇒ (4, 1) + 2 = 7
test roll: 2d6 + 2 ⇒ (5, 6) + 2 = 13
test roll: 2d6 + 2 ⇒ (6, 2) + 2 = 10
test roll: 2d6 + 2 ⇒ (3, 1) + 2 = 6
test roll: 2d6 + 2 ⇒ (1, 4) + 2 = 7
test roll: 2d6 + 2 ⇒ (1, 1) + 2 = 4
test roll: 2d6 + 2 ⇒ (6, 2) + 2 = 10
test roll: 2d6 + 2 ⇒ (6, 4) + 2 = 12
test roll: 2d6 + 2 ⇒ (2, 2) + 2 = 6
test roll: 2d6 + 2 ⇒ (2, 1) + 2 = 5
test roll: 2d6 + 2 ⇒ (2, 2) + 2 = 6
test roll: 2d6 + 2 ⇒ (1, 3) + 2 = 6
test roll: 2d6 + 2 ⇒ (3, 4) + 2 = 9
test roll: 2d6 + 2 ⇒ (4, 1) + 2 = 7
test roll: 2d6 + 2 ⇒ (1, 6) + 2 = 9
test roll: 2d6 + 2 ⇒ (2, 5) + 2 = 9
test roll: 2d6 + 2 ⇒ (4, 3) + 2 = 9
test roll: 2d6 + 2 ⇒ (4, 2) + 2 = 8
test roll: 2d6 + 2 ⇒ (1, 3) + 2 = 6
test roll: 2d6 + 2 ⇒ (2, 5) + 2 = 9
test roll: 2d6 + 2 ⇒ (4, 3) + 2 = 9
test roll: 2d6 + 2 ⇒ (3, 3) + 2 = 8
test roll: 2d6 + 2 ⇒ (2, 1) + 2 = 5
test roll: 2d6 + 2 ⇒ (5, 6) + 2 = 13
test roll: 2d6 + 2 ⇒ (3, 6) + 2 = 11
test roll: 2d6 + 2 ⇒ (4, 5) + 2 = 11
test roll: 2d6 + 2 ⇒ (6, 3) + 2 = 11
test roll: 2d6 + 2 ⇒ (2, 4) + 2 = 8
test roll: 2d6 + 2 ⇒ (6, 2) + 2 = 10
test roll: 2d6 + 2 ⇒ (1, 2) + 2 = 5
test roll: 2d6 + 2 ⇒ (2, 2) + 2 = 6
test roll: 2d6 + 2 ⇒ (6, 4) + 2 = 12
test roll: 2d6 + 2 ⇒ (1, 3) + 2 = 6
test roll: 2d6 + 2 ⇒ (3, 5) + 2 = 10
test roll: 2d6 + 2 ⇒ (1, 4) + 2 = 7
test roll: 2d6 + 2 ⇒ (2, 1) + 2 = 5
test roll: 2d6 + 2 ⇒ (4, 2) + 2 = 8
test roll: 2d6 + 2 ⇒ (4, 3) + 2 = 9
test roll: 2d6 + 2 ⇒ (3, 5) + 2 = 10
test roll: 2d6 + 2 ⇒ (6, 4) + 2 = 12
test roll: 2d6 + 2 ⇒ (2, 6) + 2 = 10
test roll: 2d6 + 2 ⇒ (3, 2) + 2 = 7
test roll: 2d6 + 2 ⇒ (5, 1) + 2 = 8
test roll: 2d6 + 2 ⇒ (3, 5) + 2 = 10
test roll: 2d6 + 2 ⇒ (4, 6) + 2 = 12
test roll: 2d6 + 2 ⇒ (3, 1) + 2 = 6

test roll: 2d6 + 2 ⇒ (3, 1) + 2 = 6

If you replace the angled brackets with rectangular brackets, then
<dice>1d99999999999999</dice>
becomes
1d1 ⇒ 1
However,
<dice>1d100000</dice>
becomes
1d1001 ⇒ 988
What's the maximum die value?
1d1001 ⇒ 195
1d1001 works properly....
1d1001 ⇒ 922
but 1d1002 becomes 1d1001!
1d999 ⇒ 198
1d1001 ⇒ 726

So, it looks like 1001 is the maximum die size. Die sizes only a little larger than 1001 are reduced to 1001, but substantially larger rolls are reduced to 1d1.

How big does it need to be to become 1d1?
1d1001 ⇒ 670
1d1 ⇒ 1
So, the "breaking point" where 1dX stops turning into 1d1001 and starts turning into 1d1 is 2^31=2147483648. I.e., 1d2147483647 is changed to 1d1001, but 1d2147483648 or higher is changed into 1d1. Presumably is a bug caused by the way Java handles integers.

Now let's see what the maximum number of dice you can roll is.
<dice>1002d4</dice>
becomes
100d4 ⇒ (4, 4, 3, 1, 1, 1, 3, 3, 4, 4, 4, 1, 4, 1, 4, 4, 3, 2, 2, 2, 3, 3, 2, 3, 2, 2, 1, 3, 1, 4, 4, 4, 3, 1, 3, 1, 3, 2, 3, 4, 1, 1, 4, 4, 2, 1, 1, 3, 2, 3, 2, 2, 3, 3, 3, 2, 1, 1, 1, 3, 1, 2, 3, 4, 1, 1, 1, 4, 4, 2, 1, 3, 2, 2, 3, 1, 2, 3, 2, 2, 2, 1, 3, 3, 1, 3, 2, 4, 1, 3, 3, 2, 1, 4, 4, 2, 2, 4, 1, 3) = 243
and
<dice>1002d2147483647</dice>

becomes
100d1001 ⇒ (175, 673, 580, 368, 943, 961, 95, 859, 845, 296, 638, 143, 364, 688, 150, 319, 626, 136, 844, 16, 446, 531, 906, 916, 767, 576, 918, 571, 541, 843, 839, 333, 936, 403, 593, 30, 819, 911, 964, 781, 378, 724, 280, 982, 833, 231, 592, 719, 10, 806, 889, 372, 76, 400, 212, 10, 477, 172, 549, 730, 352, 158, 435, 378, 465, 370, 711, 306, 667, 159, 803, 721, 913, 38, 215, 3, 75, 571, 64, 280, 651, 278, 419, 11, 71, 430, 127, 932, 719, 113, 763, 535, 769, 314, 300, 74, 897, 296, 446, 911) = 49525
The maximum number of dice appears to be 100.

100d1 ⇒ (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 100
If the size of the dice is 2^31 or above, it does not cause a further bug in the number of dice (but all the dice are changed to d1s, as noted in my previous post).

0d10 ⇒ (-) = 0
Rolling a very large number of dice causes a bug which results in rolling zero dice.

100d10 ⇒ (9, 7, 9, 9, 1, 4, 9, 7, 8, 2, 8, 3, 8, 2, 2, 2, 5, 1, 7, 2, 7, 5, 2, 10, 1, 2, 9, 10, 1, 2, 10, 9, 7, 1, 4, 10, 9, 6, 10, 3, 3, 9, 6, 3, 9, 9, 9, 10, 6, 2, 5, 2, 1, 9, 9, 2, 1, 5, 7, 2, 6, 7, 9, 8, 9, 2, 1, 8, 4, 8, 5, 2, 9, 7, 5, 7, 7, 1, 9, 5, 4, 9, 4, 8, 2, 2, 3, 1, 1, 7, 6, 10, 2, 7, 5, 6, 7, 9, 8, 1) = 553
0d10 ⇒ (-) = 0
Once again, the cutoff for this bug is 2^31=2147483648. Rolling 2147483648 dice will cause you to roll zero, whilst rolling between 100 and 2147483647 dice will cause you to roll 100.

Need to get my dice warmed up.
attack, Power Attack: 1d20 + 6 - 1 ⇒ (8) + 6 - 1 = 13
attack, Power Attack: 1d20 + 6 - 1 ⇒ (4) + 6 - 1 = 9
attack, Power Attack: 1d20 + 6 - 1 ⇒ (17) + 6 - 1 = 22
attack, Power Attack: 1d20 + 6 - 1 ⇒ (16) + 6 - 1 = 21
attack, Power Attack: 1d20 + 6 - 1 ⇒ (1) + 6 - 1 = 6
attack, Power Attack: 1d20 + 6 - 1 ⇒ (8) + 6 - 1 = 13
attack, Power Attack: 1d20 + 6 - 1 ⇒ (7) + 6 - 1 = 12
attack, Power Attack: 1d20 + 6 - 1 ⇒ (3) + 6 - 1 = 8
attack, Power Attack: 1d20 + 6 - 1 ⇒ (2) + 6 - 1 = 7
attack, Power Attack: 1d20 + 6 - 1 ⇒ (10) + 6 - 1 = 15
attack, Power Attack: 1d20 + 6 - 1 ⇒ (18) + 6 - 1 = 23
attack, Power Attack: 1d20 + 6 - 1 ⇒ (9) + 6 - 1 = 14
attack, Power Attack: 1d20 + 6 - 1 ⇒ (9) + 6 - 1 = 14
attack, Power Attack: 1d20 + 6 - 1 ⇒ (20) + 6 - 1 = 25
attack, Power Attack: 1d20 + 6 - 1 ⇒ (7) + 6 - 1 = 12
attack, Power Attack: 1d20 + 6 - 1 ⇒ (17) + 6 - 1 = 22
attack, Power Attack: 1d20 + 6 - 1 ⇒ (19) + 6 - 1 = 24
attack, Power Attack: 1d20 + 6 - 1 ⇒ (17) + 6 - 1 = 22
attack, Power Attack: 1d20 + 6 - 1 ⇒ (14) + 6 - 1 = 19
attack, Power Attack: 1d20 + 6 - 1 ⇒ (10) + 6 - 1 = 15

To the Moon Alice: 2d20 + 12 ⇒ (2, 1) + 12 = 1512d4 + 6 ⇒ (2, 2, 4, 1, 1, 1, 4, 3, 2, 4, 4, 4) + 6 = 38

Woof!! Those were terrible attack rolls. A 1 and 2?! Seriously, critical miss much?

1d20: 1d20 ⇒ 16

here we go...: 3d30 ⇒ (23, 28, 9) = 60

Arcana: 1d20 + 6 ⇒ (13) + 6 = 19

Stats 1: 4d6 ⇒ (2, 6, 1, 2) = 11 - 1 = 10
Stats 2: 4d6 ⇒ (2, 6, 2, 5) = 15 - 2 = 13
Stats 3: 4d6 ⇒ (6, 2, 3, 4) = 15 - 2 = 13
Stats 4: 4d6 ⇒ (1, 6, 2, 4) = 13 - 1 = 12
Stats 5: 4d6 ⇒ (6, 3, 1, 6) = 16 - 1 = 15
Stats 6: 4d6 ⇒ (2, 3, 4, 4) = 13 - 2 = 11

HP: 7d12 ⇒ (10, 4, 2, 6, 5, 1, 4) = 32

money: 1d10 ⇒ 2

1d20 ⇒ 1
1d20 ⇒ 18
1d20 ⇒ 19
1d20 ⇒ 10
1d20 ⇒ 16
1d20 ⇒ 2
1d20 ⇒ 13
1d20 ⇒ 8
1d20 ⇒ 14
1d20 ⇒ 10
1d20 ⇒ 8
1d20 ⇒ 3
1d20 ⇒ 6
1d20 ⇒ 3
1d20 ⇒ 6
1d20 ⇒ 3
1d20 ⇒ 6
1d20 ⇒ 1
1d20 ⇒ 11
1d20 ⇒ 16