Tri-State Heads or Tails Probability Calculations - Vermont Lottery
Tri-State Heads or Tails Probability Calculations - Vermont Lottery
Tri-State Heads or Tails Probability Calculations - Vermont Lottery
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
1. Matching a single set of player numbers to <strong>Lottery</strong>’s Winning numbers.<br />
2. Combining the three set of numbers.<br />
3. Multi-Hand match-up.<br />
4. Over-All winning with Base and Multi-Hand games.<br />
Matching 5 of 45 on Single Set of Numbers<br />
Given a set of five numbers of 45, then<br />
Total Ways Single Set = COMBIN (45, 5) = 1,221,759 ways<br />
Using the Microsoft EXCEL notation, the function COMBIN (n, k) is the number of combinations of n items taken k<br />
at a time. This f<strong>or</strong>mula is sometimes called: Combination f<strong>or</strong>mula <strong>or</strong> the Binomial f<strong>or</strong>mula. The COMBIN<br />
function is defined as:<br />
COMBIN (n, k) = n! /k! (N-k)!<br />
Where the notation m! is called m fact<strong>or</strong>ial and is equal to m*(m-1)*(m-2)*(m-3)*...*2*1 and by definition 0! = 1.<br />
<strong>Probability</strong> is defined as the number of ways a match can be made divided by the Total Ways they can be<br />
distributed. F<strong>or</strong> example, there is only 1 way to match 5 of 5 of 45 numbers. Theref<strong>or</strong>e, the probability of a<br />
match is 1 in 1,221,759 ways.<br />
The general f<strong>or</strong>mula of Ways to match w numbers is:<br />
Ways to Match {w of 5 of 45} = COMBIN (5, w)*COMBIN (45-5, 5-w)<br />
The w variable can have only six values (5, 4, 3, 2, 1, and 0) which determines the number of possible tiers. F<strong>or</strong><br />
the Base Game, three tiers are winning tiers and 3 are not.<br />
The Reciprocal <strong>Probability</strong> <strong>or</strong> 1/<strong>Probability</strong> f<strong>or</strong> each tier is:<br />
1/<strong>Probability</strong> {w} = (Total Ways Single Set) divided by (Ways to Match {w of 5 of 45})<br />
The following table describes the f<strong>or</strong>mulas and count of all the ways to win and lose on the Base game and their<br />
c<strong>or</strong>responding reciprocal probability.<br />
Base Game<br />
Winning Tiers<br />
Tier<br />
Matches<br />
(w)<br />
F<strong>or</strong>mula f<strong>or</strong> Ways Ways <strong>Probability</strong> 1/<strong>Probability</strong><br />
1 5 (COMBIN(5,5) * COMBIN(45-5,5-5) 1 8.1849E-07 1,221,759.000<br />
2 4 (COMBIN(5,4) * COMBIN(45-5,5-4) 200 1.6370E-04 6,108.795<br />
3 3 (COMBIN(5,3) * COMBIN(45-5,5-3) 7,800 6.3842E-03 156.636<br />
Total Ways and Overall Ways to Win: 8,001 6.5488E-03 152.701<br />
The notation 6.5488E-03 is the floating point notation representing of the value “ .0065488 “ and the “E-xx”<br />
represents the decimal point moving to the left xx positions. An exponential value of “E+xx” means the decimal<br />
point moves to the right xx positions.<br />
2 - 10
Change language