Probability and safer play
4D Permutations Explained: Why Repeated Digits Change the Count
Calculate the distinct arrangements of a four-digit number and understand the common 24, 12, 6, 4, and 1 permutation groups.
A four-digit number can have as many as 24 different arrangements or as few as one. The exact number of permutations depends entirely on how many repeating digits your number contains.
Understanding permutation math clarifies how Box and iBOX prices and payouts are determined. Permutation counting is pure combinatorics—it does not alter the fundamental randomness of the lottery draw.
The five permutation groups in 4D
Every 4-digit number between 0000 and 9999 falls into one of five distinct permutation groups based on its digit repetition pattern.
The formula for permutations of 4 items with repeating elements divides 4! (24) by the factorial of each repeating digit count: P = 4! / (k₁! · k₂! · ... · km!).
- 24 Permutations (4 distinct digits, e.g. 1234): 4! = 24 unique arrangements.
- 12 Permutations (1 pair + 2 unique digits, e.g. 1123): 24 / 2! = 12 unique arrangements.
- 6 Permutations (2 pairs, e.g. 1122): 24 / (2! × 2!) = 6 unique arrangements.
- 4 Permutations (3 identical digits, e.g. 1112): 24 / 3! = 4 unique arrangements.
- 1 Permutation (4 identical digits, e.g. 7777): 24 / 4! = 1 unique arrangement.
How permutation counts affect Box and iBOX bets
For Box bets, the permutation count directly dictates your total ticket cost. A full Box on 1234 costs 24 times the base stake, whereas a full Box on 1122 costs only 6 times the base stake. In both cases, any winning permutation pays the full prize.
For iBOX (or mBox / i-Perm / i-Bet), the permutation count determines your prize divisor. Because a RM1 iBOX on 1122 is split 6 ways instead of 24 ways, hitting 1st Prize on a 6-permutation number pays RM2,500 / 6 ≈ RM416.67, compared to RM2,500 / 24 ≈ RM104.16 for a 24-permutation number, and RM2,500 / 4 = RM625.00 for a 4-permutation number.
Permutation count does not change draw probability per number
In a fair 4D draw, every exact 4-digit sequence from 0000 to 9999 has the identical 1 in 10,000 chance (0.01%) of being drawn in any specified prize slot. The sequence 7777 is just as likely to appear as 1234 or 8392.
Buying 24 permutations gives you 24 separate chances to win because you purchased 24 distinct numbers, not because the lottery favors diverse digits. Always calculate your total outlay before placing permutation wagers.
Key points
- Four distinct digits yield 24 permutations; repeated digits reduce the count to 12, 6, 4, or 1.
- Box bets multiply your total ticket cost by the permutation count.
- iBOX bets divide the standard winning prize by the permutation count.
- Every exact 4-digit number has an identical 1 in 10,000 chance per prize slot.
- Permutation math explains ticket structures, not predictive forecasting.
Sources and further reading
Facts were checked against these operator and reference pages.
Operators display permutation categories on tickets and game guides. Verify official category definitions and prize charts before purchasing.
- Da Ma Cai - How to Play 1+3D Official operator
Related guides
Operator rules, schedules, payouts, and claim procedures can change. Confirm any ticket or possible win with the issuing operator.
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