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bip39toolbox.com  ·  page 1 of 2

Index Dice — how to roll a word

BIP-39 has 2,048 words. Four dice give you a four-digit number, and that number is the word — no adding, no multiplying, no table. Because the first index is 0000, the highest valid one is 2047, not 2048. Type the number straight into the word boxes, or into the Index Dice box on the page.

You need — four dice, one of them marked

1× D6, re-labelled two faces 0, two faces 1, two faces 2 — two per value, never three and three. The value is what you write down, never the original face.

3× D10 in three different colours, read 10 as 0. Decide which colour is hundreds, which is tens and which is units before the first throw and keep it for the whole phrase — identical dice leave you choosing the order after they land, and a die read in the wrong place is a different word.

Use this one — the fast way

Throw the first two dice on their own

Same result as throwing all four — but only 2.5% of words have to be started over instead of 31.7%, and you throw 15% fewer dice.

  1. Throw only Roll 1 (the marked D6) and Roll 2 (the hundreds D10). Leave the other two dice alone.
  2. Read those two as a two-digit number. 21 or higher → pick up those two dice only and throw them again. Repeat until they read 20 or lower. In practice: the D6 shows 2 and the D10 shows anything but 0.
    This is safe only because Rolls 3 and 4 have not been thrown yet. You are throwing a fresh pair, not steering a result you have already seen. Once all four dice are down this stops being allowed — see the box below.
  3. Now throw Roll 3 (tens) and Roll 4 (units).
  4. Read all four left to right. That is your index. If it comes out 2048 or higher — only possible when the first two read exactly 20 — bin it and start this word again from step 1. That is about 2.5% of words.
5.0dice thrown per word, against 5.9 the plain way
2.5%of words start over — 1 in 40, against 31.7% the plain way
Identicalevery index 0–2047 stays exactly as likely as every other — checked, not assumed
An invalid roll is not a failed roll

Discarding everything from 2048 up is what makes every valid index equally likely. It is not the method going wrong — it is the method.

The one thing that would ruin the phrase

Once all four dice are on the table, never change just one of them to make the number fit.

Rerolling only the units die when you get 2100 looks harmless and is not: it makes some words 1.25× likelier than others, and 2.3× if you reroll the tens die too when the units die cannot save it. It is quiet: nothing on the paper shows it happened. There are exactly two legal rerolls — the first two dice before the other two are thrown (step 2), and all four together (step 4).

The plain way, if you would rather not split the throw. Throw all four at once, read them left to right, and if the number is 2048 or higher throw all four again. Nothing else changes. It is equally correct — just slower: about 31.7% of throws go in the bin, roughly one in three.
ExampleRoll 1 · D6Roll 2 · D10 Roll 3 · D10Roll 4 · D10Read left to right
Caught early
first two read 23		 23 ?? 23…✗ throw those two again
Good
first two read 14		 14 72 1472✓ valid index
Bin it
first two read 20, still too high		 20 61 2061✗ over 2047 — all four again
bip39toolbox.com  ·  page 2 of 2

Index Dice — the roll sheet

Throw Rolls 1 and 2 first — 21 or higher, throw those two again. Then throw Rolls 3 and 4 and read all four left to right. That four-digit number is the word's index.

D6  0,1,2 D10 D10 D10
ROLL 1ROLL 2 ROLL 3ROLL 4
THROW THESE TWO FIRST 21+ → THROW BOTH AGAIN THEN THESE TWO 
THOUSANDSHUNDREDS TENSUNITS
0   1   20 – 9 0 – 90 – 9
value, not the faceread 10 as 0 read 10 as 0read 10 as 0
Valid indexes are 0000–2047 — the two legal rerolls

Rolls 1–2 read 21+ → throw those two again. All four read 2048+ → throw all four again.

Never trim a high number to fit, and never change a single die once all four are down — that biases the phrase, silently. With the two-dice start, only about 2.5% of words have to start over.

PLACE DIE HEREPLACE DIE HERE PLACE DIE HEREPLACE DIE HERE
Roll 1 — thousands · first Roll 2 — hundreds · first · colour ______ Roll 3 — tens · colour ______ Roll 4 — units · colour ______
Roll #Roll 1
D6		Roll 2
D10		Roll 3
D10		Roll 4
D10		Index → word
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

—not rolled. The last word of any phrase is never rolled — it carries the checksum and the calculator works it out from the others.

Index Dice was called Decimal dice up to v2.0.0; an older sheet pointing at a "Decimal dice box" means this one. Keep this sheet offline and destroy it after use.