This may seem overly precise, but will make it easier to the subsequent derivations. the player’s 5 selections match the 5 winning numbers but no match with the Mega winning number), we need to choose 5 numbers from the 5 winning numbers, choose 0 numbers from the 42 non-winning numbers, choose 0 numbers from the 1 Mega winning number and choose 1 number from the 26 non-Mega winning numbers. To find the odds of matching “All 5 of 5” (i.e. Thus the odds of matching “All 5 of 5 and Mega” are 1 in 41,416,353. To find the odds of the match of “All 5 of 5 and Mega”, the total number of possibilities is obtained by choosing 5 numbers from 47 numbers and choose 1 number from 27 numbers. To win the top prize, there must be a match between the player’s 5 selections and the 5 winning numbers as well as a match between the player’s Mega number and the winning Mega number (All 5 of 5 and Mega in Figure 6 below). The player also chooses an additional number called a Mega number from 1 to 27. Here are the pictures of a playslip and a sample ticket of the game of SuperLOTTO Plus.īased on the playslip (Figure 4), the player chooses 5 numbers from 1 to 47. Similarly, the following shows how to calculate the odds of matching 2 out of 5 winning numbers: To find the odds for matching 3 out of 5 winning numbers, we need to find the probability that 3 of the player’s chosen numbers are from the 5 winning numbers and 2 of the selected numbers are from the 34 non-winning numbers. Thus the probability of matching 4 out of 5 winning numbers is: To match 4 out of 5 winning numbers, 4 of the player’s chosen numbers are winning numbers and 1 of the player’s chosen numbers is from the non-winning numbers (34 of them). Thus we have:īased on, the odds of matching all 5 winning numbers is 1 in 575,757 (the odds of winning the top prize). Thus in the calculation of odds, we use combination rather than permutation. In matching the player’s chosen numbers with the winning numbers, the order of the numbers do not matter. The following figure shows the prize categories and the winning odds of Fantasy 5. There are lower tier prizes that are easier to win but with much lower winning amounts. The odds of winning the top prize are 1 in 575,757. If all 5 chosen numbers match the 5 winning numbers, the player wins the top prize which starts at $50,000 and can go up to $500,000 or more. In the game of Fantasy 5, the player chooses 5 numbers from 1 to 39. The following figures show a playslip and a sample ticket for the game of Fantasy 5. It is a self contained step by step explanation at the basic level on how to calculate winning odds in the Powerball game. For any reader who would like to further understand how lottery odds are calculated, see this blog post on Powerball. The calculation in this post assumes certain background knowledge on combination and the multiplication principle (not explained here). The calculation is an excellent combinatorial exercise as well as in calculating hypergeometric probability.Īll figures and data are obtained from the California Lottery. In this post, we show how to calculate the odds for these games in the California Lottery. The winnings odds of the top prize of Mega Millions are 1 in 175,711,534. The winnings odds of the top prize of SuperLOTTO plus are 1 in 41,416,353. Ever wonder how to calculate winning odds of lottery games? The winning odds of the top prize of Fantasy 5 in California Lottery are 1 in 575,757.
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