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Lottery Odds Calculator

C(n, k) combinations. Free online Lottery Odds Calculator. Calculate lottery odds online — fast, accurate, mobile-friendly, no signup needed.

Odds (1 in)
13,983,816

Derivation

  1. ├── 01Givenn = 49, k = 6
  2. ├── 02Formulat};return n(t) / (n(a) × n(t-a))
  3. ├── 03Substitutet};return 49(t) / (49(a) × 49(t-a))
  4. └── 04Compute Odds (1 in)13,983,816
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§01What is

Understanding the Lottery Odds Calculator

The Lottery Odds Calculator computes Odds (1 in) from 2 inputs: pool size, numbers picked. C(n, k) combinations.

Games and puzzles mix math with pattern-spotting. Whether it’s a lottery combination, a dice probability, or a game-theory decision, the numbers behind the fun are worth running properly. The Lottery Odds Calculator sits in that toolkit — it C(n, k) combinations. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t};return n(t) / (n(a) × n(t-a))

Where

n
Pool size
k
Numbers picked
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Pool size = 49, Numbers picked = 6.

  1. 01Start by noting the input — Pool size: 49.
  2. 02Start by noting the input — Numbers picked: 6.
  3. 03Substitute these values into the formula: t};return n(t) / (n(a) × n(t-a))
  4. 04Compute Odds (1 in): the calculator returns 13983800.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Lottery Odds Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Pool size halved

n = 24.5 (from 49)

Keep every other input at its default and halve the pool size. See how odds (1 in) responds.

  1. 01New Pool size: 24.5
  2. 02Baseline Odds (1 in): 13983800
  3. 03New Odds (1 in): 134596
  4. 04Odds (1 in) decreases by 99% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Pool size doubled

n = 98 (from 49)

Keep every other input at its default and double the pool size. See how odds (1 in) responds.

  1. 01New Pool size: 98
  2. 02Baseline Odds (1 in): 13983800
  3. 03New Odds (1 in): 1.05262e+9
  4. 04Odds (1 in) increases by 7427.4% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Numbers picked halved

k = 3 (from 6)

Keep every other input at its default and halve the numbers picked. See how odds (1 in) responds.

  1. 01New Numbers picked: 3
  2. 02Baseline Odds (1 in): 13983800
  3. 03New Odds (1 in): 18424
  4. 04Odds (1 in) decreases by 99.9% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Numbers picked doubled

k = 12 (from 6)

Keep every other input at its default and double the numbers picked. See how odds (1 in) responds.

  1. 01New Numbers picked: 12
  2. 02Baseline Odds (1 in): 13983800
  3. 03New Odds (1 in): 9.22637e+10
  4. 04Odds (1 in) increases by 659689.4% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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