ABSTRACT

                 LEVERAGING A LOTTERY  (REV:R-1)    
                                       (c) John T. Thorngren 1999

    A gambling casino introduces a simple lottery based upon
    the roll of a single die -- every player on each game has
    one out of six chances to win.  In several 6,000 game series
    as well as one for 59,000 games, seven players try their
    various "systems" and demonstrate the concept of short and
    long term random. Each player's "system" is subsequently
    converted into a mathematical relationship called a "filter".
    Simple probability and statistical techniques describe the 
    concept of filters: when they are successful, when they fail,
    and why they have a unique, reflexive property.  Every system,
    even same-ticket-bets, machine quick picks, and Wheeling, can
    be converted into a filter.  A financial analysis (Leveraging
    a Lottery) uses eleven filters with their associated probabil-
    ities for success.  Each filter has a bank account, and any
    two filters may be combined into a joint account using the
    probability Law of Multiplication thus giving the player a
    total of 66 separate bank accounts.  These accounts become
    leveraged when used to generate a bet ticket.  Rather than a
    simple "win/no-win" at each lottery drawing, a player now has a
    statistical tool -- a dollar balance in his accounts -- to gauge
    whether he is on a winning streak (Winning Wave) or in a loosing
    slump (Terriblium Trough).  Leveraging a Lottery is a game within
    a game that, with a little skill and a little luck, might give one
    a real advantage and a better chance to win the lottery. It is not
    a gimmick. A fiction novel format presents supporting mathematical
    proofs ranging from very simple to extremely complex; simply 
    glossing over that which he does not understand, a reader with 
    only high school math skills will still benefit and will understand
    filters as they apply to Leveraging a Lottery.  For the more 
    mathematically inclined, the last chapter presents several tests
    for significance on lottery bias with emphasis on frequency, subtle
    patterns, and ball pair affinity using the Texas Lottery as an
    example. Radically new statistical concepts include the 9824 Rule;
    a variable correction factor for approximating a binomial with a
    normal distribution; identification of those few places where the
    Student's t and Z distributions are applicable in  lottery analysis;
    a normally distributed transformation for Hit Intervals; and the
    Significant Other Test for significance.  The Appendix contains all
    statistical equations used in the eleven filters (Even/Prime Integer,
    Sum Total, Short/Tall SixPacks, Distribution, Immediate Prior Hit,
    MPF, PFR, and Forward Difference) as well as short source codes
    written in Quick Basic for the Normal, Student's t, Z, Binomial,
    and Chi Squared distributions. The Appendix also gives instructions
    for obtaining a diskette with these source codes, the Leveraging
    a Lottery computer program, and a utility program with statistical
    procedures for lottery bias. Earlier development efforts include:
    Most Likely Draw Lotto (c) 1994, Lottery Leverage REV:P-1 (c) 1996,
    Lottery Leverage REV:P-2 (c) 1996. Word count: ~ 28,000 (exclusive
    of figures & tables). Reading grade level: Flesch-Kincaide = 8.1,
    Coleman-Liau = 11.4, Bormuth = 10.3. Flesch Reading Ease 65.3.