# Probabilities of 20-Number Lotto System in 6 of 45 Lotto Game

## By Ion Saliu, Founder of Lottery Mathematics

First, calculate all possible combinations of 20 lotto numbers taken 6 at a time. Then divide that amount by total possible combinations of 45 lotto numbers taken 6 per combination. Better still, run OddsCalc or the free online odds calculator (in the footer of most Web pages here).

Posted on August 02, 2000.

In Reply to: Calculate lotto probability of 20 numbers in a 6 of 45 lotto game posted by Dazza on August 02, 2000.

: In a 6 from 45 lotto, how do you work out the probability of getting all 6 lotto numbers if you purchase a system 20 (pick 20 numbers) entry?

• Total combinations for the 6/45 lotto game:
C(45 taken 6 at a time) = 8,145,060

Total combinations of 20 numbers taken 6 at a time:
Combination C(20, 6) = 38,760

The probability to get the 6 lotto winners in the 20-number bloc:
38,760 / 8,145,060 = 0.48% (less than half a percentage point).
You can expect 6 winners once every 210 drawings.

As I showed several times, it's best to use WHEEL-6 with filters. You can also use the WHEEL45.36 system you can find on the download site. You still need to use it in conjunction with PURGE-6. If you are totally new to this site and my lottery software, you could feel out of luck in the first moment. But after some searching, many pieces will fall in place.

``` The odds calculated as EXACTLY in a lotto game 6 winners from 45, 20-number pool:

0 of 6 in 20 from 45: 1 in 45.99
1 of 6 in 20 from 45: 1 in 7.67
2 of 6 in 20 from 45: 1 in 3.39
3 of 6 in 20 from 45: 1 in 3.11
4 of 6 in 20 from 45: 1 in 5.6
5 of 6 in 20 from 45: 1 in 21.01
6 of 6 in 20 from 45: 1 in 210.14

The odds calculated as AT LEAST in a lotto game 6 winners from 45 numbers, 20-number pool:

0 of 6 in 20 from 45: 1 in 1
1 of 6 in 20 from 45: 1 in 1.02
2 of 6 in 20 from 45: 1 in 1.18
3 of 6 in 20 from 45: 1 in 1.81
4 of 6 in 20 from 45: 1 in 4.33
5 of 6 in 20 from 45: 1 in 19.1
6 of 6 in 20 from 45: 1 in 210.14
```

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