My Chance 3 — Lottery and betting odds mathematics | mychance3.com
Straight pick-3 odds are 1 in 1,000; boxed odds with three different digits are about 1 in 167 — and the payout gap between them decides which is the worse deal.
A straight bet names one exact order of three digits. With ten digits per position there are 10 × 10 × 10 = 1,000 ordered combinations, so a single straight ticket covers one outcome and wins with probability 1/1,000 — 0.1%.
A boxed bet names three digits and wins on any order. When the digits are all different they can be arranged 3! = 6 ways, so the ticket covers 6 of the 1,000 combinations: odds of 6/1,000, about 1 in 167. The win is six times as likely as a straight hit on the same digits.
On narrow screens, swipe or scroll the plate sideways.
Repeated digits change the coverage. A pair such as 4-4-7 has only three distinct orders, so its any-order version covers 3 combinations — odds of about 1 in 333. A triple has a single order and is effectively a straight bet, which is why operators exclude it from boxed play.
Payouts mirror the coverage. US lotteries typically pay a straight hit at 500-to-1 to 600-to-1, while boxed prizes are scaled down in proportion to the combinations covered. Because break-even on a straight is 999-to-1, the 500-to-1 version carries a 50% expected loss per unit staked before tax.
The practical comparison is therefore not which bet wins more but which bet loses less. Both sit deep below break-even; the boxed ticket trades prize size for hit frequency, and the operator's margin survives the trade in both directions. For the same arithmetic applied to jackpot games, see how to calculate lottery odds, and for a casino comparison see the roulette house edge table.
Further reading