Abbreviated Wheel

An Abbreviated Wheel is an economical alternative for a Full Wheel (Full Wheel includes all combinations that can be generated from a set of numbers a player picks, and therefore guarantees a first tier prize if all of the drawn numbers are within the player's set of numbers; it also guarantees a number of lower tier prizes. The only drawback with full wheels is they become fairly expensive with increasing the size of the set of the player's chosen numbers. A player who wishes to play a full wheel with 10 numbers in a pick 6 lottery game will have to play 210 combinations.). Although an Abbreviated Wheel does not include all possible combinations of the chosen numbers, it still guarantees at least one winning ticket if some of the numbers drawn are within the player's selection of numbers.

The following is an example of an abbreviated lottery wheeling system for pick-6 with 10 numbers, 4 if 4 guarantee and the minimum possible number of combinations for that guarantee, 20. The original system is given as 20 combinations on the numbers from 1 to 10. The next table gives a possible selection of the player’s numbers and his/her set of tickets, which are obtained after substituting the numbers 1-10 with the player’s numbers.

 Numbers in the original system 01 02 03 04 05 06 07 08 09 10 The player’s numbers (example) 04 07 11 12 16 22 25 29 33 37

 Comb. Original system Player’s tickets 1 01 02 03 04 05 10 04 07 11 12 16 37 2 01 02 03 04 07 09 04 07 11 12 25 33 3 01 02 03 06 07 08 04 07 11 22 25 29 4 01 02 05 06 08 09 04 07 16 22 29 33 5 01 02 06 08 09 10 04 07 22 29 33 37 6 01 03 04 06 07 10 04 11 12 22 25 37 7 01 03 05 07 08 10 04 11 16 25 29 37 8 01 04 05 06 07 09 04 12 16 22 29 33 9 01 05 06 07 09 10 04 16 22 25 33 37 10 02 03 05 06 09 10 07 11 16 22 33 37 11 02 04 05 06 07 08 07 12 16 22 25 29 12 02 04 07 08 09 10 07 12 25 29 33 37 13 03 04 05 06 07 09 11 12 16 25 29 33 14 03 04 06 08 09 10 11 12 22 29 33 37

This example can be used to illustrate the main guarantee of the chosen system (a 5-win if 6 of the 10 player’s numbers are drawn): Suppose the numbers 7,12,22,29,33 and 37 are drawn (these are bolded and green in the player's tickets), then the system guarantees at least one 5-win, by design. Indeed, it is easy to check that this is so. In fact, in this particular case, the system gives tthree 5-wins (in tickets 5, 12 and 14), and it also gives four 4-wins (these can be found in tickets 4,8,10, and 11). The number of combinations in an Abbreviated Wheel is significantly smaller than the number of combinations in a Full Wheel on the same set of numbers. In the example above, the Abbreviated Wheel for pick-6 lottery with 10 numbers and 5 if 6 guarantee has 14 tickets. A full wheel with 10 numbers requires 210 combinations and has 6 if 6 guarantee.

All the reduced systems offered on this site were generated with our software Aleator.

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