Lotto 6/49 Fixed Numbers: How to Calculate Odds of Winning (Even When One Fixed Number Misses)

Using fixed numbers is a practical way to focus budget and improve efficiency. In this guide, we lock 2 fixed numbers in Canada’s Lotto 6/49 so the remaining pool becomes 47, and we show how to calculate lottery odds — rank by rank — under this setting. You will see the probability of winning the lottery in each case and verify everything with the LottoApex Odds Calculator.

This guide explains how to calculate lottery odds in Lotto 6/49 when you use 2 fixed numbers. We keep the official bonus rule (the Classic Draw structure with a bonus ball), we walk through the rank-by-rank math with C(n,r), and we give you a one-click way to verify your probability of winning the lottery in the free LottoApex Odds Calculator.

Contents

1. What are fixed numbers?
2. Rank odds with fixed numbers (formulas)
3. Step-by-step calculations for each rank
4. When fixed numbers are/aren’t in the winning draw
5. Check lottery probability instantly in the LottoApex Odds Calculator

Lotto 6/49 Odds Series

• Canada Lotto 6/49: How to Calculate Rank-by-Rank Probability (Series 1)
• Canada Lotto 6/49: Excluded Numbers Odds Formula (Series 2)
• Canada Lotto 6/49: Fixed Numbers & Winning Probability (Series 3)
• Canada Lotto 6/49: Winning Odds Calculator | LottoApex (Series 4)

1. What are “fixed numbers”?

“Fixed numbers” are numbers you must include in every ticket you generate. In Lotto 6/49, if you lock 2 numbers and choose the remaining 4 freely, your effective candidate pool becomes 47. The total number of unique tickets is then C(2,2) × C(47,4) = 178,365, compared to C(49,6) = 13,983,816 without fixed numbers.

By narrowing the pool, you reduce wasted lines and can evaluate the lottery ticket probability of hitting each rank with far clearer math.

Note: This article covers the Classic Draw with the bonus rule. It does not discuss the separate Gold Ball game.

2. Rank odds with fixed numbers (formulas)

Start with the best-case scenario: both fixed numbers are part of the winning draw. In that case, your working pool is 49 − 2 = 47, so the denominator for odds is C(47, 4) = 178,365 (because each of your tickets already contains the 2 fixed numbers).

Fundamental identities

Before calculating ranks, memorise these four identities:

• X C X = 1 → choose all, there’s only one way (e.g., 2C2, 3C3)
• X C 0 = 1 → even choosing none counts as one way (e.g., 6C0, 29C0)
• X C 1 = X → choosing one equals the total count (e.g., 30C1 = 30)
• X C (X−1) = X → leaving one out gives X ways (e.g., 5C4 = 5)

3. Step-by-step calculations for each rank

We continue under the assumption that both fixed numbers are in the winning set. The denominator is C(47, 4) = 178,365, because each of your tickets already contains the 2 fixed numbers. Below are the worked examples:

✅ 1st prize — 2C2 × 4C4 × 43C0

• 2 fixed in the winning set → 2C2 = 1
• the remaining 4 winning numbers → 4C4 = 1
• none from the other 43 → 43C0 = 1

Favourable cases = 1
odds of winning the lottery for 1st prize = 1 / 178,365.

✅ 2nd prize — 2C2 × 4C3 × 1C1 × 42C0

• 2 fixed in the winning set → 2C2 = 1
• 3 of the remaining 4 winning numbers → 4C3 = 4
• include the bonus → 1C1 = 1
• none from the other 42 → 42C0 = 1

Favourable cases = 4
odds of winning the lottery for 2nd prize ≈ 1 / 44,591.

✅ 3rd prize — 2C2 × 4C3 × 1C0 × 42C1

• 2 fixed in the winning set → 2C2 = 1
• 3 of the remaining 4 winning numbers → 4C3 = 4
• bonus excluded → 1C0 = 1
• pick 1 from the other 42 → 42C1 = 42

Favourable cases = 4 × 42 = 168
probability of winning the lottery for 3rd prize ≈ 1 / 1,061.7.

✅ 4th prize — 2C2 × 4C2 × 43C2

• 2 fixed included → 2C2 = 1
• 2 of the remaining 4 winning numbers → 4C2 = 6
• 2 from the other 43 → 43C2 = 903

Favourable cases = 6 × 903 = 5,418
probability of winning a lottery for 4th prize ≈ 1 / 32.92.

✅ 5th prize — 2C2 × 4C1 × 43C3

• 2 fixed included → 2C2 = 1
• 1 of the remaining 4 winning numbers → 4C1 = 4
• 3 from the other 43 → 43C3 = 12,341

Favourable cases = 4 × 12,341 = 49,364
lottery probability for 5th prize ≈ 1 / 3.61 (~27.68%).

4. When fixed numbers are/aren’t in the winning draw

With 2 fixed numbers in Lotto 6/49, the probability of winning the lottery depends heavily on whether your fixeds actually appear in the winning set. Below is a 5th-prize example for three cases (both, one, none). The same structure applies to other ranks — only the formulas change.

✅ Worked example (5th prize with exactly one fixed)

• include 1 of your 2 fixeds → 2C1 = 2
• take 2 from the 4 winning (non-bonus) numbers → 4C2 = 6
• take 3 from the other 43 → 43C3 = 12,341

Favourable cases = 2C1 × 4C2 × 43C3 = 148,092
Total winning-set scenarios (when exactly 1 fixed is in the draw) = 2C1 × 47C5 = 3,067,878
Probability to win the lottery (5th prize in this scenario) = 148,092 / 3,067,878 ≈ 1 / 20.72 (≈ 4.82%)

5. Check lottery probability instantly in the LottoApex Odds Calculator

Feelings can be misleading; numbers aren’t. In the LottoApex Odds Calculator, you can see exactly how your chances of winning the lottery change as you add 0 → 1 → 2 fixed numbers. You can also separate scenarios where the fixeds appear in the winning draw from those where they don’t.

Main features:

• Compare by number of fixeds — watch the odds of winning the lottery shift as you add fixed numbers
• Separate “fixed in draw” vs “not in draw” cases — see the real lottery probability you’re playing under
• Expected value by rank — understand where the efficiency actually improves
• Mix fixed + excluded numbers — narrow the pool first, then lock what you trust
• Works with the Simulator — import conditions and test ticket distributions across many draws

From fixed numbers to data-validated play

Locking fixed numbers focuses budget—but the real edge appears when you generate and test. The Lotto 6/49 Number Generator leverages a Wheeling System to respect your fixeds, balance coverage, and optimise probability across the remaining pool. Combine fixed + excluded numbers to tune efficiency further.

In the Lotto 6/49 Simulator, play out realistic cases—both fixeds hit, only one hits, or neither hits—and visualise rank distributions. Confirm how your odds shift under each scenario, adjust the build, and repeat until it behaves as intended.

Working cycle: Fix → Generate → Simulate → Verify odds. That’s the bridge from casual picks to strategy.

👉 Try it now: Lotto 6/49 Number Generator
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