Lottery Jackpot Odds Calculator

Lottery jackpot odds depend upon how many numbers you have to match, and the set of size of the set from which these numbers are drawn. The more numbers you have to match or the larger the set, the lower the odds of winning. In addition, some lotteries draw an extra number or numbers from a different set than the original numbers. This is a feature of the US Powerball and Mega Millions lotteries, which draw a single extra number. The European lottery EuroMillions draws two extra numbers from a separate set.

You can use the lottery calculator below to compute the odds of winning the jackpot by entering the lottery game's parameters.

Jackpot Probability Calculator

* Note: For the Canadian lotteries 6/49 and Lotto Max, check "no" for the extra pick. In 6/49 and Lotto Max, the bonus ball is selected from the same set as the original numbers, and moreover does not affect the odds of winning the jackpot prize.

Example 1

In a simple lottery, players must match 6 distinct numbers drawn from 1 to 50. The total number of possible ticket combinations is calculated as follows:

50*49*48*47*46*45
----------------- = 15890700
   6*5*4*3*2*1

Thus, the probability of winning the jackpot is 1 out of 15,890,700.

Example 2

In another lottery, players must match 4 distinct numbers drawn from 1 to 80, plus a fifth number drawn from 1 to 10. This fifth number may match one of the previous 4 since it is drawn from a separate set. The total number of ticket combinations is

80*79*78*77
----------- x 10 = 15815800
  4*3*2*1

So the probability of winning this lottery is 1 out of 15,815,800.

Example 3

A new lottery requires players must match 5 distinct numbers between 1 and 41, plus an extra number selected from 1 to 21. As before, this extra number might match one of the previously drawn 5. The total number of ticket combinations is

41*40*39*38*37
-------------- x 21 = 15737358
  5*4*3*2*1

The probability of winning the jackpot is 1 out of 15,737,358.

Example 4

In yet another lotto game, players must match 6 different numbers drawn from 1 to 20, plus two extra numbers selected from 1 to 29. These extra numbers may possibly match the other 6. The number of possible ticket combinations is

20*19*18*17*16*15   29*28
----------------- x ----- = 15736560
   6*5*4*3*2*1        2

The probability of winning the jackpot is 1 out of 15,736,560.

Notice that in the four examples above the lotteries have very different structures and yet similar probabilities of winning the jackpot.

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