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OH Lot O'Play - Do the Math

Published:

Took a few minutes off work to look at the Ohio Lot O'Play, since there's been so much rumbling and grumbling about it. There are some truly massive numbers involved here. I haven't had the time to do a complete workup and won't for quite a while, so all the numbers here are approximate.

Each ticket has five rows of five numbers from 00 to 99. There are no duplicate numbers on a ticket.

Each player can pick the five numbers in the first row only. The other 20 numbers in the other four rows are quick-pick only.

Game:

Number of possibilities for 25 numbers drawn from 100: 3,761,767,332,270,610,000,000,000,000,000,000,000,000,000,000,000, in specific order. This is the number of different tickets possible in the game.

Number of ways to arrange any 25 given numbers on a ticket: 15,511,210,043,331,000,000,000,000.

Ticket:

On a specific ticket there are 12 different jackpot possibilities - each row, each column and each diagonal, and each number in that row, column or diagonal must be the same as five of the 25 numbers drawn to win. When I do the complete workup I'll have the odds, but it looks like the Ohio Lottery's quoted 1::6,200,000 odds would be close.

More as time allows.

gl

j

Entry #106

1.
Comment by RJOh - January 11, 2006, 11:52 pm
When I did the math, I got 75,287,520 possible(sorted) combinations of 5 numbers in a field of 100. When I divided that number by twelve chances per play(75,287,520/12) it came out 1:6,273,960 however since I actually get 12 chances to win one time instead of one chance to win 12 times, the real figure will be less which I haven't figured how to calculate.
2.
Comment by johnph77 - January 12, 2006, 6:49 am
Your calculations coincide with the quoted figures from the Ohio Lottery website on the game. I'll do a number of workouts before I publish, though, as there is a thought in the back of my head telling me something isn't right. For one thing, there are 120 permutations of those five numbers possible on the ticket in any given row, column and/or diagonal. Unfortunately, time is rather short for me right now and that isn't very high on my priority list.

And then there are the workouts for the lower-tier prizes - 4/5, 3/5 and 2/5.....