3-digit Lotery Games
May be because of their rather deceptive look of simplicity, 3-Digit games are by far the most popular lottery games in the
United States. They are played by selecting a 3-digit number from 000 to 999. For example, 160. In addition to the selected
number, you have to indicate the desired play type and the amount to wager.
Play Types of 3-digit games
Below are listed all the possible play types of a 3-digit game. Except a straight play and a box play, which are always
available in all games, the others may not be offered by all. Although the names of the play types also vary, we shall use here
the most widely used names.
How much the player wins for matching a certain play depends on the house edge of the game. The house edge is the percentage that
the state or the government retains. The value is uasually 50%. The payout for every unit of money (e.g., $1) can be approximated
by multiplying the house edge by the odds of the play type listed below. For example, the odds of a straight play are 1:1000, and
if the lottery agency retains 50%, then the payout for a staright game will be 50% * 1000 = 500 for every unit of money wagered.
Note that some may pay out in pari-mutuel basis, that is, dividing the allocated prize money equally among the winners.
- Straight (Exact Order) : You'll win if the number drawn is exactly the same as your selection. The odds are 1:1000
- Box (Any Order) : The number drawn can match your selected number in any arrangement as long as all the three digits are there.
The odds are 1:167 if all the three digits are different (6-way box), 1:333 if two of the digits are identical (3-way box).
Note that triples (all three digits identical) cannot be boxed since any rearrangement results in the same number.
- Straight/Box (Exact/Any) : Here you are betting half of the amount wagered on a straight and the other half on a box.
So, you are actually betting on two plays of the same number, therefore the odds have two parts that correspond to the two plays.
Note that triples cannot be played as straight/box.
- Combo (Combination) : This play type is simply a straight play of all the possible arrangements (permutations) of the number.
For example, if you play combo of the number 282, you are actually playing 282, 228, and 822 as straights, since these are all the
possible arrangements of the number. A $1 combo doesn't cost $1, instead, you have to pay $1 for every possible arrangement of the
number. Thus a 6-way combo (i.e., non-repeating digits) costs $6, a 3-way combo (i.e., one digt repeating) costs $3.
The odds are obviously just like a staright play. Note that triples cannot be played as combo.
- Front Pair (Match Front) : Here, you are betting only on the first two digits in exact order. The odds are 1:100.
- Back Pair (Match Back) : Betting only on the last two digits in exact order. The odds are 1:100.
- Split Pair : Betting only on the first and last digits in exact order. The odds are 1:100.
- Sum (Lucky Sum) : This is betting on the sum of the digits instead of the numbers and their arrangements.
The odd, thus the payout, depends on the sum itself. A sum of 0 and a sum of 27 have odds exacly the same as a staright play (1:1000)
since there is only one number whose digits sum up to 0 (000), and there is only one number whose digits sum up to 27 (999).
The highest odds (lowest payouts) are for a sum of 13 and 14 since there are the maximum (75) numbers whose sum of the digits are 13,
and other 75 with sum of 14. You can find the sum of all 3-digit numbers in the section 3-digit games analysis.