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Prize Tables for Covers or Wheels in 6/49 Lotto Game  
LottoPoster Forums : ANALYSIS OF VARIOUS LOTTO NUMBER SETS : Prize Tables for Covers or Wheels in 6/49 Lotto Game 
Topic: Calculating Likely Wins 1 Line or more  
Author  Message  
Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Topic: Calculating Likely Wins 1 Line or more Posted: March 17 2014 at 11:59pm 

CALCULATING LIKELY WINS IN LOTTO FOR 1 LINE OR OPTIMUM STRUCTURED SETS OR DISTORTED SETS by Colin Fairbrother Lotto players can refer to information printed or online from Lotto Operators which give the Odds for winning a prize for one line or ticket and in some cases for the minimum lines playable, which is simply the respective multiple of that applicable to one line. In this article I will use the Classic Lotto game where 6 numbers or distinct balls are randomly picked from 49 and where a prize is obtained if in any line played there is a match of at least 3, 4, 5 or 6 integers. To simplify matters the bonus ball is ignored and the principles outlined here are applicable to any Pick 5 or Pick 6 Lotto game. For any given Lotto game matrix the odds or probability, as I shall refer to it from hereon, can be calculated for any given match. Consider first one line in our 6/49 game, say, 01 02 03 04 05 06, realizing the numbers used are just identifiers with no magnitude. This combination of 6 numbers or integers (CombSix) is just 1 combination to pit against the 1 combination first prize of which there are 13,983,816 distinct possibilities for the draw. Each line or draw also has 6 combinations of 5 integers, 15 combinations of 4 integers and 20 combinations of 3 integers for a possible match. One line is flawless and is no better than any other line. Any combination of 3 integers will for an enumerated 13,983,816 CombSixes appear 15,180 times. Any combination of 4 integers will appear 990 times and any combination of 5 integers will appear 44 times. Due to overlaps the combinations when considered distinctly are 1,906,884 CombFives, 211,876 CombFours and 18,424 CombThrees. Theoretical calculation of odds for one line. match3 1 / (49c6 / (6c3 * 43c3)) = 1 / (13983816 / (20 * 12341)) = 1 / (13983816 / 246820) = 1 / 56.6559273 = 0.0176504 Multiplying this probability for 1 draw gives 0.0176504 of a match3. Multiplying this probability for 29 draws gives 0.5118616 of a match3. Multiplying this probability for 57 draws gives 1.0060728 match3's. Multiplying this probability for 114 draws gives 2.0121456 match3's ________________________________________________________ match4 1 / (49c6 / (6c4 * 43c2)) = 1 / (13983816 / (15 * 903)) = 1 / (13983816 / 13545) = 1 / 1032.3968 = 0.0009686 Multiplying this probability for 1 draw gives 0.0009686 of a match4. Multiplying this probability for 518 draws gives 0.5017348 of a match4. Multiplying this probability for 1033 draws gives 1.0005638 match4's. Multiplying this probability for 2065 draws gives 2.000159 match4's. ________________________________________________________________ match5 1 / (49c6 / (6c5 * 43c1)) = 1 / (13983816 / (6 * 43)) = 1 / (13983816 / 258) = 1 / 54200.837 = 0.0000184 Multiplying this probability for 1 draw gives 0.0000184 of a match5. Multiplying this probability for 27180 draws gives 0.500112 of a match5. Multiplying this probability for 54380 draws gives 1.000592 match5's. Multiplying this probability for 109000 draws gives 2.0056 match5's. ________________________________________________________________ match6 1 / (49c6 / (6c6 * 43c0)) = 1 / (13983816 / (1 * 1)) = 1 / (13983816 / 1) = 1 / 13983816 = 0.0000001 While highly likely there is no guarantee you will get a 1st prize in 14,000,000 draws. _________________________________________________________________ match0 1  (0.0176504 + 0.0009686 + 0.0000184 + 0.0000001) = 0.9813625 As the number of draws increases the likelihood of no prizes decreases. _________________________________________________________________ Building a Prize Table for just one line. By testing against all 13,983,816 possibilities a Prize Table can be produced for one line that gives exactly the same probability as the theoretical caculation. Multiplying the probabilty by the number of plays, which in this case is the same as the draws, is exactly the same as one would do to work out potential winnings using the theoretical calculation.. Combs Probability Likely Likely Likely Likely 6 5 4 3 1 29 518 27180 Draw Draws Draws Draws  0 0 0 0 13723192 0.9813625 1 28 508 26673 0 0 0 1 246820 0.0176540 0 1 9 480 0 0 1 0 13,545 0.0009686 0 0 1 26 0 1 0 0 258 0.0000184 0 0 0 1 1 0 0 0 1 0.0000001 0 0 0 0 _______________________________________________________ Note that for two or more CombSixes it is possible to build distortion into the set when compared to Random Selections where for say, a 6/49 Lotto game, it is extremely rare to get high repeat subsets. The System 8 or Full Wheel 8 will be used as an example of an abnormal set as enumerated below  1 2 3 4 5 6 1 2 3 4 5 7 1 2 3 4 5 8 1 2 3 4 6 7 1 2 3 4 6 8 1 2 3 4 7 8 1 2 3 5 6 7 1 2 3 5 6 8 1 2 3 5 7 8 1 2 3 6 7 8 1 2 4 5 6 7 1 2 4 5 6 8 1 2 4 5 7 8 1 2 4 6 7 8 1 2 5 6 7 8 1 3 4 5 6 7 1 3 4 5 6 8 1 3 4 5 7 8 1 3 4 6 7 8 1 3 5 6 7 8 1 4 5 6 7 8 2 3 4 5 6 7 2 3 4 5 6 8 2 3 4 5 7 8 2 3 4 6 7 8 2 3 5 6 7 8 2 4 5 6 7 8 3 4 5 6 7 8 Building a Prize Table for the 28 Line System 8 or Full Wheel By testing against all 13,983,816 possibilities a Prize Table can be produced which gives the groupings and by dividing by 13983816 the probability for each group based on the structure of the set. If the same set is used for more simulated draws then simply multiplying the probabilty for each group by the number of simulated draws required will give proportionally the likely wins makeup.
These figures are a guide. For the more exotic like the 3 Fives with 15 Fours and 10 Threes ie each line of 28 line set has a hit then flexibility is required; 0.5 is only 2985 draws whereas closer to 1 is more like 6090 draws. Initially one can use the Ceiling function but if the total does not equal the draws a manual check may be required. The allocation between no prizes and prizes is the first priority and within prizes some can be consolidated to a lower prize but always guided by probability. Building a Prize Table for the Twenty Eight Normal Line Partial Cover By testing against all 13,983,816 possibilities a Prize Table can be produced which gives the groupings and by dividing by 13983816 the probability for each group based on the structure of the set. If the same set is used for more simulated draws then simply multiplying the probabilty for each group by the number of simulated draws required will give proportionally the likely wins makeup.


Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.


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