# How to Play Lotto 6/49

In Canada, Lotto 6/49 is a national lottery played in all 13 provinces and territories. Each ticket costs \$2.00 and the object is to correctly guess 6 distinct numbers drawn from 1 to 49, hence the name. A seventh bonus number is also selected for each drawing; this number only comes into play when you match exactly 5 out of 6 or 2 out of 6 regular numbers. (It is not possible to match 6 out of 6 + bonus because you can only select 6 numbers, and there are no special prizes for selecting 4 out of 6 + bonus, or 3 out of 6 + bonus.)

The Jackpot is worth 80.5% of the pool and is awarded to the ticket holder(s) with 6 out of 6 correct numbers. Lesser prizes are awarded from the remainder of the pool.

### 6/49 Lottery Odds

For a \$2.00 ticket, the odds of correctly picking x out of 6 numbers are as follows:

6 out of 6:
1/(49 c 6) = (6*5*4*3*2*1)/(49*48*47*46*45*44) = 1/13983816
PRIZE: 80.5% of pool

5 out of 6 + bonus:
[(6 c 5)(42 c 0)]/[49 c 6] = 6/13983816 = 1/2330636
PRIZE: 5.75% of pool

5 out of 6, no bonus:
[(6 c 5)(42 c 1)]/[49 c 6] = 252/13983816 ≈ 1/55492
PRIZE: 4.75% of pool

4 out of 6:
[(6 c 4)(43 c 2)]/[49 c 6] = 13545/13983816 ≈ 1/1033
PRIZE: 9% of pool

3 out of 6:
[(6 c 3)(43 c 3)]/[49 c 6] = 246820/13983816 ≈ 1/57
PRIZE: \$10

2 out of 6 + bonus:
[(6 c 2)(42 c 3)]/[49 c 6] = 172200/13983816 ≈ 1/82
PRIZE: \$5

There are no prizes for 2 out of 6 without the bonus, nor for correctly guessing 1 out of 6 with or without the bonus. The total odds of winning any prize are

(1 + 6 + 252 + 13545 + 246820 + 172200)/13983816
≈ 1/33

Notice that it is easier to correctly pick 3 out of 6 than it is to pick 2 out of 6 + bonus, yet 3 out of 6 has a higher payout! All prizes are split evenly among the number of winning tickets. For example, matching 4 out of 6 earns 9% of the pool funds. If 18 people correctly match 4 out of 6 numbers then each person gets (9/18)% = 0.5% of the pool funds.