Lotto System Development Simplified
A lot of energy is expended here trying to design a system that might help a player win a Lotto Jackpot. The problem is that the dimensions of the state games are such that designers must deal with very LARGE numbers of combinations and very SMALL probabilities. Very often, the designer's ideas become obscured by complicated and tedious calculations. This thread is an attempt to provide a Lotto game model of scaled down dimensions to allow people to focus on system theories, rather than boring calculations. So, let's take a look at an arbitrary scaled down version of a Lotto game. Although I know of no Lotto game, state sanctioned or otherwise, that has these dimensions,it should be clear that any system designed for it can be extrapolated to a game with a larger matrix. For this purpose, I've designed a (5,2) Lotto game. It will be much easier to understand a betting system when it's applied to a (5,2) game as opposed to say, a (56,5) game!
(1) (2) (3) (4) (5)
Remember now, we're playing Lotto, not Pick-2. Initially, there are 5 Balls in the drawing machine, numbered 1 through 5. The first selection is made from these 5, and the second is drawn from the 4 remaining. The order they are drawn is not significant so we will list the results for each draw in ascending order, left to right.
(1,2) (2,4)
(1,3) (2,5) OK, in a (5,2) Lotto game,
(1,4) (3,4) here are the possible outcomes.
(1,5) (3,5)
(2,3) (4,5)
That's a total of Ten (10) possibilities. In a (56,5) game, this number would be 3,819,816. I think our scaled down game will be a little easier to work with! In this simplified model, ODDS and PAYOFFS will be easy to determine by inspection. Look at the list of 10 winning ticket possibilites and convince yourself that the theoretical chance of matching both numbers you select is one in ten, or 1:10, or 1/10, or 0.1, or 10%, however you like to express it. This is our Jackpot. Our 2nd tier prize will be awarded for correctly selecting 1 number on your ticket. By inspection, you should see above that the chance of matching one of the two numbers you select is four in ten, or 4:10, or 2/5, or 0.4, or 40%. Consequently, to ensure the Expected Value of this game is 0.50, the typical state lottery case, our $1 tickets will pay $4.00 for matching both numbers (the Jackpot,) and 25 Cents for a one number match. So, ON AVERAGE, for each set of 10 tickets we purchase, we can expect to match one number four times, and both numbers one time, for a return of $5.00 on our $10 investment, our desired ROI.
Since some people in another Forum have been studying subsets of the total number field, I thought I would do some of the setup that will help them use this (5,2) game in their research. They have been looking at a subset of 28 of the Megamillions total of 56. They observe that IF they could select a subset of the 56 number field that contains the 5 numbers that are ultimately drawn, Then they would have better odds of winning a Jackpot. So, let's see how we can partition our (5,2) game in an analogous way. If we eliminate one of the five numbers from play, we would only have to deal with four, so...
(1,2,3,4)
(1,2,3,5) ...here are the partitions of our
(1,2,4,5) 5 numbers taken 4 at a time.
(1,3,4,5) Note that each set is missing
(2,3,4,5) one of the five numbers.
Hint to the subset researchers:
Each of the 10 winning (Jackpot) pairs of numbers in our first list above appears in 3 of the 5 possible subsets of 5 numbers taken 4 at a time. I'll leave speculation on the probabilities and other implications of this model for a later post.
Perhaps someone has a system they would like to present using this simple model.
--Jimmy4164