Tri-State Heads or Tails Probability Calculations - Vermont Lottery

Over All Probability of Winning:
The over-all probability of winning in either game or both is:
Prob [Over All Win Both Games] = + Prob [Over All Win Base Game]
+ Prob [Over All Win Multi-Hand Game]
- Prob [Over All Win Base Game and Over All Win Base Game]
The probability of winning in both games, the and condition, is determined from the Multi-Hand Break-out table
above. The value is derived by adding all the break-outs probabilities that correspond to the “Y” (Winner on both).
There are 186 break-outs of the 216 possible break-outs.
The calculation is:
And
Prob [Over All Win Base Game]
= + 1.9518E-02 (From Above)
Prob [Over All Win Multi-Hand Game]
= + 2.2255E-01 (From Above)
Prob [Over All Win Base Game and Multi-Hand Game] = - 1.3962E-02 (From Break-out Table)
Prob [Over All Win on Both Games]
= 2.2811E-01
1/Prob [Over All Win on Both Games]
= 4.3839E+00
Richard Mishelof
Games Design Consultants
Scientific Games International Corporation
Alpharetta, GA
June 18, 2005
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