This Java Script calculator computes optimized sets of plays for lotto games.
To operate the calculator, enter the count of possible choices for the game after "Numbers", the count of numbers to chose after "Select", and the count of the number of entries after "Plays" -- then press the Listing button to generate a list of plays for a lotto drawing.
On invalid entries, a message dialog box will be displayed.
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The Java Script source code for this program can be viewed by using the View|Source command of your web browser.
You may use or modify this source code in any way you find useful, provided that you agree that the author has no warranty, obligations or liability. You must determine the suitability of this source code for your use.
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In games of lotto, a player must match a selection of a sub-set numbers chosen from a larger set by the dealer. Each number in the set is unique. The odds are determined by the number of combinations possible. For example, there are 1,947,792 combination of 6 items selected from a set of 36. The odds of winning for one play are one in 1,947,792.
To play or not to play
The odds of winning are usually very small. The small price per play and the large payouts make these games appealing. State lotteries payout about 50% of what is taken in. So, on average, players should expect to lose money. Investing large sums of money in these games is unwise. For alternatives, try this.
Can you to improve your odds?
You can buy a few tickets for a single drawing. If the numbers are selected carefully, you can double your odds when you buy two tickets and triple your odds when you buy three tickets. How? Make sure that no duplicate numbers are selected. In the game of pick 6 numbers in the range 1...36, you can buy up to six tickets at one time without duplicating any numbers; each of the dealer's numbers will be on one of your tickets. In this case, your odds are six in 1,947,792 or one in 324,632.
In a lottery pool several individuals each contribute a small amount so that a large number of tickets can be purchased. The partners share in the winnings, if any. For the example above, duplication of numbers is unavoidable when more than six tickets are purchased. The objective for a pool of tickets is to cover the maximum number of combinations with as few tickets as possible; the initial first few plays should not repeat any number. For the example, a group of 24 sets of numbers can be chosen so that at most one duplicate number occurs on any pair of tickets. One way to do this is to first select numbers from rows, columns, forward diagonals, and backward diagonals of the entire set of numbers arranged in an array as shown below:
Then, for each group of 24 plays, create a random one-to-one map of these numbers into the numbers to be played. For the first block of 24 you could use the map:
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
For the next, you might use:01 --> 17 02 --> 33 03 --> 05 etc.
01 --> 07 02 --> 35 03 --> 11 etc.
The calculator will generate groups of random plays. In each group, there will be at most one matching number between any pair of plays. Between plays selected from different groups there can be more matching numbers. This is because the random map is updated between the generation of random groups.
Note: For this technique to work, the number of rows in the array must be equal to or greater than the number of columns. The number of columns is equal to the count of the numbers selected for a play. For the game, pick 10 of 80, the number of columns is 10 and the number of rows is 8 -- so, the calculator will not work.
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